喷泉码与极化码的改进及应用
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摘要
在现代社会中伴随着互联网技术和无线通信技术的快速发展，各式各样的数据均能够通过数字通信系统方便、快捷、完整地传输至世界各地。为了保证数字通信系统在传输过程中的可靠性，纠错码技术的改进研究受到人们的高度重视。
线性分组码就是纠错码的一种主要类型，近十年间出现的新型线性分组码正逐渐引领着纠错码技术的改革和突破，它们的不断发展和完善势必会在未来数字通信中发挥至关重要的作用。新型线性分组码主要包括：喷泉码、极化码，他们的出现是纠错码领域在新世纪的一项重要成果。对于喷泉码，通过度分布函数进行有选择限制的编码，然后进行广播式的转发，当译码器接收到固定数量的编码码字后，就能够成功恢复信源信号，此过程由于其灵活的码率形式和较高的性能而得到青睐。基于信道极化理论的极化码，构造编码过程主要采用巴氏参数或是传输信道量化。极化码构造编码的关键点是：通过巴氏参数迭代或是传输信道量化公式简化计算，得到衡量信道可靠性的估计值，再进行虚拟信道的筛选。其根本在于如何迅速而精确地计算虚拟信道的可靠程度，构造所使用的算法偏离实际信道越少，其计算信道可靠性准确度就会越高，所构造极化码的性能也就越好。首先，本文改善喷泉码的译码算法，同时分析构造极化码时巴氏参数的性能，提出更适应于其他二进制对称信道极化码的构造方式，最后，提出极化码在中继信道和无线光通信系统中的应用。
本文的主要贡献包括：
1.介绍当前新型线性分组码：喷泉码、极化码，并对他们的技术背景和发展现状进行了详细的分析、归纳与总结。基于不同喷泉码度分布函数的特殊构造，得到喷泉码的编译码特征和性质。另外，通过分析极化信道的聚合和分离的数字特性，定义连续删除译码算法的判断标准，得到极化码的编译码特征和性质。从而给出现有新型线性分组码之间的相互关系，并指出他们目前存在亟须解决的关键问题和解决建议。
2.提出喷泉码的优化部分译码方式。针对短码长的LT码，介绍了传统的置信度传播译码算法和高斯消元译码算法的应用，分析传统译码法存在的优缺点，将他们的优势选择合并，提出可应用于喷泉码的快速置信度传播译码算法。同时，还证明了快速置信度传播译码算法是LT码的最优化译码算法之一。此算法不仅提高了置信度传播算法的译码成功概率，而且其独特的排列译码方式，能够减少了译码的时延和对数据存储的需求。通过仿真结果可知，在二进制对称信道中，快速置信度传播译码算法比置信度传播译码算法的成功率至多提高了48.09%。在仿真时间方面，LT码的快速置信度传播译码算法所用的时间少于高斯消元译码算法但略高于置信度传播译码算法，同时存在一个时间平台的阈值。所以在短码长和低码率LT码传输过程中，快速置信度传播译码算法优于传统算法。
3.证明错误指数函数和极化码巴氏参数存在特定的上下界。首先，从错误指数函数的定义入手，分析在二进制无记忆对称信道中，以信道容量为变量域，错误指数函数及其辅助函数在二进制差错信道和二进制对称信道下具有极值的性质，进而提出二进制无记忆对称信道的极值定理。通过辅助函数，将此极值关系扩展至极化码编译码的巴氏参数当中，并证明当信道容量为变量域时，极化码编码后虚拟信道的巴氏参数也存在类似上下界关系。我们推断出在构造极化码过程中，估计虚拟信道的可靠性时应该关注二进制差错信道和二进制对称信道巴氏参数的数值。理论上，通过分析这两个信道的传输可靠性，我们能够重新构造可应用于其它信道的最优极化码方案。
4.提出基于极化码下界的一系列编码构造算法。以巴氏参数的极值定理为基础，通过分析巴氏参数和极化码构造时的性质，给出极化码迭代算法中，欠可靠信道的巴氏参数更为精确和更为收敛的下界。将此下界公式应用于极化码对虚拟信道可靠性的估计，对极化码欠可靠信道的构造方法进行改进和优化，提出适合于二进制对称信道的极化码构造算法，较传统巴氏参数迭代的估计更为准确，使得极化码的性能有小幅提升。而针对高斯白噪声信道，提出线性构造算法，并通过仿真得出参数选择的方案。
5.将极化码应用于半双工中继信道。由于极化码存在信道聚合与分离的特性能够在中继节点中转发，所以极化码能够在中继信道中得以应用。针对在半双工中继系统中，我们分析其模型及各节点的特性，基于译码转发协议与系统中传输向量的正交性，提出一个适合于极化码的构造及传输策略。同时，证明极化码在半双工中继信道中能够达到香农限信道容量的定理。我们提出对半双工系统中时分和码分参数的优化方案，以及说明随机编码信息选择策略是最优中继策略。最后给出仿真结果与总结。
6.分析了极化码在带光学湍流的自由空间光通信系统中的错误概率及性能，其系统采用辐照强度调制和直接检测的光学调制方式构造，调制方式选用副载波二进制相移键控数字调制方式，系统的纠错码选用极化码。针对不同气候所产生的大气湍流，我们主要考虑强湍流条件下的Gamma-Gamma湍流信道模型。在位逐位交织信道中，配对错误概率将能够有效而准确地表示虚拟信道中序列的传输，同时还能够求出有渐近性的配对错误概率。在准静态衰落信道条件下，不同帧内的信号所受衰落是相互独立的，在其基础上，研究极化码误帧率性能存在的上界与下界，我们采用两种方法：巴氏参数估计法和密度演化估计法，其中，密度深化的估计方法得到的结果更加精确。仿真的数据结果说明在自由空间光通信系统中，极化码的应用能够改进系统的性能。
总体来说，针对上述提出的算法，论文都通过软件仿真、测试及与传统算法的比较来验证其有效性和先进性。针对所有提出的定理，论文通过严格的数学推导证明，说明定理存在的严谨性及适用范围。
In modern society, with the rapid growth of Internet technology and wirelesscommunication technology, it becomes quite convenient, real-time and complete to transmitvarious data to all over the world through digital communication systems. In order toguarantee the reliability of digital communication systems during transmitting process, highattention has been paid to the improvement and research of error correcting codes.
In recent ten years, as a main type of error correcting codes, the novel linear block codesare proposed to lead the revolution of error correcting codes. Their continuous developmentand improvement certainly will play an crucial role in the future digital communication.Novel linear block codes mainly include fountain codes and polar codes. Their appearance isan important achievement of error correcting codes field in the21st century. For fountaincodes, source singals are encoded by the degree distribution function for selecting restrictionand then are broadcasted forwardly. When the decoder receives a specified number of thecoded words, the source singals can be recovered successfully. This process is favoredbecause of the flexible codes rate and good performance. Based on channel polarizationtheory, polar codes mainly adopt the iteration of Bhattachayya parameters or the quantizationof transmitting channels to construct the codewords. The key points of construction are shownas: the reliability of virtual channels is simplified by Bhattachayya parameter iterations orquantization of transmitting channels. The values of reliability are obtained while theinformation bits can be screened. The key issue of optimal construction is how to calculate thereliability of virtual channels rapidly and accurately. The deviation between proposedencoding algorithm and the actual value is less, the accuracy of channel reliability is higher.Then, polar codes can be constructed with better performance. This paper first focuses on howto improve decoding efficiency for fountain codes. Moreover, the properties of Bhattachayyaparameters are analyzed in polar codes while the new construction of polar codes is proposedin other binary-input momoryless symmetric channels. Finally, the schemes based on polarcodes are considered in relay channels and wireless optical communication systems.
Main contributions include:
1. Some new linear block codes are introduced, in terms of fountain codes and polarcodes. Their technology backgrounds and development situations are presented with detailedanalysis, summary and conclusion. Some features and properties of encoder/decoder are obtained because of special construction and different degree distribution functions infountain codes. In addition, some properties and characteristics of polar codes are procured byanalyzing the numberical characteristics of combining, splitting and the judging standards ofsuccessive cancellation decoding algorithm for polarization channels. Thereby, some existingrelations between the new types of linear block codes are summarized. Some of the currenttechnical issues and suggestions which are waiting to be solved urgently are pointed out.
2. The optimal partial decoding algorithm are proposed for fountain codes. For shortlength LT codes, the traditional belief propagation (BP) and Gaussian elimination (GE)decoding algorithms are given also with their advantages and disadvantages. Fast beliefpropagation (FBP) algorithm which combines some advantages of traditional algorithms isapplied to the decoder of fountain codes. Besides, it has been proved that FBP algorithm isone of the optimal decoding algorithm for the short length LT codes. The FBP algorithm notonly improves successful decoding probability of LT codes, but also reduces the decodingdelay and demand of data storage due to its unique arrangement. Simulation results indicatethat the successful probability of FBP algorithm is48.09%higher than BP algorithm in binarysymmetric channel (BSC). For delay of transmission system, FBP algorithm is less than GEalgorithm but a little higher than BP algorithm. Moreover, there is a time platform threshold inFBP algorithm. Then FBP algorithm is superior to the traditional algorithms in the shortlength and low rate LT codes.
3. The upper/lower bounds of error exponent function and Bhattachayya parameter areproved in polar codes. First, the error exponent function should be defined. The relationbetween the channel capacity, which is the variable domain, and error exponent function isconsidered in binary memoryless symmetric channel (BMSC). The error exponent functionand its auxiliary function have extreme properties in binary error channel (BEC) and BSC. So,the binary memoryless extremal theorem is proposed for any BMSC. For the auxiliaryfunction, the extremal theorem can be extended to Bhattachayya parameter in polar codes. Ifthe channel capacity is to be the viriable, it will be proved that the Bhattachayya parameters ofvirtual channels exist a similar relationship of the upper and lower bounds in polar codes.When polar codes are constructed with estimating exact reliability of virtual channels, theBhattachayya parameter values of BEC and BSC should be concerned. Theoretically, byanalyzing both the transmitting reliability of two channels, the optimal scheme should bereconstructed for polar codes in the other BMSC.
4. A series of encoding constructing schemes are proposed by the lower bound in polarcodes. Based on the Bhattachayya parameter extremal theorem, the properties about Bhattachayya parameters are analyzed before and after polar codes. The more accurate andconvergent Bhattachayya parameters for unreliable channel are obtained in polar codes. Thelower bound formula is used to estimate the reliability of virtual channels, which improvesand optimizes the polarization structure of unreliable channels. Then, the lower boundconstruction scheme is proposed for BSC which has more accurate estimation and lessimprovement of performance compared with the traditional iterations. For additive whiteGaussian noise channels, the linear construting scheme is proposed and the selecting methodof parameter is obtained by the simulation.
5. Polar codes are applied to the time-division half-duplex relay channel. Due to thecharacteristics of channels combining and splitting, polar codes are considered to transmit inthe relay channels. For the half-duplex relay systems, the characteristics of the model andeach node are analyzed. Based on the forwarding protocols and the orthogonal vectors oftransmission, a suitable polarized transmission structure and a transmitting strategy arepresented. Moreover, polar codes are proved to achieve the Shannon limit in the half-duplexrelay systems. The optimizations of time-division and information-division parameters areproposed, while the random selection strategy is optimal in the half-duplex relay systems,.Finally, the simulation results and conclusions are presented.
6. In optical turbulence channels, error probability performances of free-space optical(FSO) communication are analyzed for irradiance modulation and direct detection (IM/DD)systems with subcarrier intensity modulation using binary phase-shift keying (SIM-BPSK)and polar codes. The analysis is carried out by different climates in the Gamma-Gammaturbulence channels. For bit-by-bit interleaved channels, the pairwise error probability (PEP)makes a high accurate series presentation about the virtual channels which deduces anasymptotic PEP. Each block has the independent fading in quasi-static fading channels. Thenwe study the upper and lower bound of the frame error ratio performance with Bhattachayyaparameter and density evolution estimations in polar coding FSO systems. Density evolutionestimation is better than Bhattachayya parameter. The numerical results are given to presentthe improvement and performance in polar coding FSO systems.
In conclusion, software simulations, tests and comparisons with traditional algorithmsare considered to verify their effectiveness and progressiveness of the proposed algorithms.For all the proposed theorems, their preciseness and scope is proved by the analysis ofmathematical derivation in this paper.
线性分组码就是纠错码的一种主要类型，近十年间出现的新型线性分组码正逐渐引领着纠错码技术的改革和突破，它们的不断发展和完善势必会在未来数字通信中发挥至关重要的作用。新型线性分组码主要包括：喷泉码、极化码，他们的出现是纠错码领域在新世纪的一项重要成果。对于喷泉码，通过度分布函数进行有选择限制的编码，然后进行广播式的转发，当译码器接收到固定数量的编码码字后，就能够成功恢复信源信号，此过程由于其灵活的码率形式和较高的性能而得到青睐。基于信道极化理论的极化码，构造编码过程主要采用巴氏参数或是传输信道量化。极化码构造编码的关键点是：通过巴氏参数迭代或是传输信道量化公式简化计算，得到衡量信道可靠性的估计值，再进行虚拟信道的筛选。其根本在于如何迅速而精确地计算虚拟信道的可靠程度，构造所使用的算法偏离实际信道越少，其计算信道可靠性准确度就会越高，所构造极化码的性能也就越好。首先，本文改善喷泉码的译码算法，同时分析构造极化码时巴氏参数的性能，提出更适应于其他二进制对称信道极化码的构造方式，最后，提出极化码在中继信道和无线光通信系统中的应用。
本文的主要贡献包括：
1.介绍当前新型线性分组码：喷泉码、极化码，并对他们的技术背景和发展现状进行了详细的分析、归纳与总结。基于不同喷泉码度分布函数的特殊构造，得到喷泉码的编译码特征和性质。另外，通过分析极化信道的聚合和分离的数字特性，定义连续删除译码算法的判断标准，得到极化码的编译码特征和性质。从而给出现有新型线性分组码之间的相互关系，并指出他们目前存在亟须解决的关键问题和解决建议。
2.提出喷泉码的优化部分译码方式。针对短码长的LT码，介绍了传统的置信度传播译码算法和高斯消元译码算法的应用，分析传统译码法存在的优缺点，将他们的优势选择合并，提出可应用于喷泉码的快速置信度传播译码算法。同时，还证明了快速置信度传播译码算法是LT码的最优化译码算法之一。此算法不仅提高了置信度传播算法的译码成功概率，而且其独特的排列译码方式，能够减少了译码的时延和对数据存储的需求。通过仿真结果可知，在二进制对称信道中，快速置信度传播译码算法比置信度传播译码算法的成功率至多提高了48.09%。在仿真时间方面，LT码的快速置信度传播译码算法所用的时间少于高斯消元译码算法但略高于置信度传播译码算法，同时存在一个时间平台的阈值。所以在短码长和低码率LT码传输过程中，快速置信度传播译码算法优于传统算法。
3.证明错误指数函数和极化码巴氏参数存在特定的上下界。首先，从错误指数函数的定义入手，分析在二进制无记忆对称信道中，以信道容量为变量域，错误指数函数及其辅助函数在二进制差错信道和二进制对称信道下具有极值的性质，进而提出二进制无记忆对称信道的极值定理。通过辅助函数，将此极值关系扩展至极化码编译码的巴氏参数当中，并证明当信道容量为变量域时，极化码编码后虚拟信道的巴氏参数也存在类似上下界关系。我们推断出在构造极化码过程中，估计虚拟信道的可靠性时应该关注二进制差错信道和二进制对称信道巴氏参数的数值。理论上，通过分析这两个信道的传输可靠性，我们能够重新构造可应用于其它信道的最优极化码方案。
4.提出基于极化码下界的一系列编码构造算法。以巴氏参数的极值定理为基础，通过分析巴氏参数和极化码构造时的性质，给出极化码迭代算法中，欠可靠信道的巴氏参数更为精确和更为收敛的下界。将此下界公式应用于极化码对虚拟信道可靠性的估计，对极化码欠可靠信道的构造方法进行改进和优化，提出适合于二进制对称信道的极化码构造算法，较传统巴氏参数迭代的估计更为准确，使得极化码的性能有小幅提升。而针对高斯白噪声信道，提出线性构造算法，并通过仿真得出参数选择的方案。
5.将极化码应用于半双工中继信道。由于极化码存在信道聚合与分离的特性能够在中继节点中转发，所以极化码能够在中继信道中得以应用。针对在半双工中继系统中，我们分析其模型及各节点的特性，基于译码转发协议与系统中传输向量的正交性，提出一个适合于极化码的构造及传输策略。同时，证明极化码在半双工中继信道中能够达到香农限信道容量的定理。我们提出对半双工系统中时分和码分参数的优化方案，以及说明随机编码信息选择策略是最优中继策略。最后给出仿真结果与总结。
6.分析了极化码在带光学湍流的自由空间光通信系统中的错误概率及性能，其系统采用辐照强度调制和直接检测的光学调制方式构造，调制方式选用副载波二进制相移键控数字调制方式，系统的纠错码选用极化码。针对不同气候所产生的大气湍流，我们主要考虑强湍流条件下的Gamma-Gamma湍流信道模型。在位逐位交织信道中，配对错误概率将能够有效而准确地表示虚拟信道中序列的传输，同时还能够求出有渐近性的配对错误概率。在准静态衰落信道条件下，不同帧内的信号所受衰落是相互独立的，在其基础上，研究极化码误帧率性能存在的上界与下界，我们采用两种方法：巴氏参数估计法和密度演化估计法，其中，密度深化的估计方法得到的结果更加精确。仿真的数据结果说明在自由空间光通信系统中，极化码的应用能够改进系统的性能。
总体来说，针对上述提出的算法，论文都通过软件仿真、测试及与传统算法的比较来验证其有效性和先进性。针对所有提出的定理，论文通过严格的数学推导证明，说明定理存在的严谨性及适用范围。
In modern society, with the rapid growth of Internet technology and wirelesscommunication technology, it becomes quite convenient, real-time and complete to transmitvarious data to all over the world through digital communication systems. In order toguarantee the reliability of digital communication systems during transmitting process, highattention has been paid to the improvement and research of error correcting codes.
In recent ten years, as a main type of error correcting codes, the novel linear block codesare proposed to lead the revolution of error correcting codes. Their continuous developmentand improvement certainly will play an crucial role in the future digital communication.Novel linear block codes mainly include fountain codes and polar codes. Their appearance isan important achievement of error correcting codes field in the21st century. For fountaincodes, source singals are encoded by the degree distribution function for selecting restrictionand then are broadcasted forwardly. When the decoder receives a specified number of thecoded words, the source singals can be recovered successfully. This process is favoredbecause of the flexible codes rate and good performance. Based on channel polarizationtheory, polar codes mainly adopt the iteration of Bhattachayya parameters or the quantizationof transmitting channels to construct the codewords. The key points of construction are shownas: the reliability of virtual channels is simplified by Bhattachayya parameter iterations orquantization of transmitting channels. The values of reliability are obtained while theinformation bits can be screened. The key issue of optimal construction is how to calculate thereliability of virtual channels rapidly and accurately. The deviation between proposedencoding algorithm and the actual value is less, the accuracy of channel reliability is higher.Then, polar codes can be constructed with better performance. This paper first focuses on howto improve decoding efficiency for fountain codes. Moreover, the properties of Bhattachayyaparameters are analyzed in polar codes while the new construction of polar codes is proposedin other binary-input momoryless symmetric channels. Finally, the schemes based on polarcodes are considered in relay channels and wireless optical communication systems.
Main contributions include:
1. Some new linear block codes are introduced, in terms of fountain codes and polarcodes. Their technology backgrounds and development situations are presented with detailedanalysis, summary and conclusion. Some features and properties of encoder/decoder are obtained because of special construction and different degree distribution functions infountain codes. In addition, some properties and characteristics of polar codes are procured byanalyzing the numberical characteristics of combining, splitting and the judging standards ofsuccessive cancellation decoding algorithm for polarization channels. Thereby, some existingrelations between the new types of linear block codes are summarized. Some of the currenttechnical issues and suggestions which are waiting to be solved urgently are pointed out.
2. The optimal partial decoding algorithm are proposed for fountain codes. For shortlength LT codes, the traditional belief propagation (BP) and Gaussian elimination (GE)decoding algorithms are given also with their advantages and disadvantages. Fast beliefpropagation (FBP) algorithm which combines some advantages of traditional algorithms isapplied to the decoder of fountain codes. Besides, it has been proved that FBP algorithm isone of the optimal decoding algorithm for the short length LT codes. The FBP algorithm notonly improves successful decoding probability of LT codes, but also reduces the decodingdelay and demand of data storage due to its unique arrangement. Simulation results indicatethat the successful probability of FBP algorithm is48.09%higher than BP algorithm in binarysymmetric channel (BSC). For delay of transmission system, FBP algorithm is less than GEalgorithm but a little higher than BP algorithm. Moreover, there is a time platform threshold inFBP algorithm. Then FBP algorithm is superior to the traditional algorithms in the shortlength and low rate LT codes.
3. The upper/lower bounds of error exponent function and Bhattachayya parameter areproved in polar codes. First, the error exponent function should be defined. The relationbetween the channel capacity, which is the variable domain, and error exponent function isconsidered in binary memoryless symmetric channel (BMSC). The error exponent functionand its auxiliary function have extreme properties in binary error channel (BEC) and BSC. So,the binary memoryless extremal theorem is proposed for any BMSC. For the auxiliaryfunction, the extremal theorem can be extended to Bhattachayya parameter in polar codes. Ifthe channel capacity is to be the viriable, it will be proved that the Bhattachayya parameters ofvirtual channels exist a similar relationship of the upper and lower bounds in polar codes.When polar codes are constructed with estimating exact reliability of virtual channels, theBhattachayya parameter values of BEC and BSC should be concerned. Theoretically, byanalyzing both the transmitting reliability of two channels, the optimal scheme should bereconstructed for polar codes in the other BMSC.
4. A series of encoding constructing schemes are proposed by the lower bound in polarcodes. Based on the Bhattachayya parameter extremal theorem, the properties about Bhattachayya parameters are analyzed before and after polar codes. The more accurate andconvergent Bhattachayya parameters for unreliable channel are obtained in polar codes. Thelower bound formula is used to estimate the reliability of virtual channels, which improvesand optimizes the polarization structure of unreliable channels. Then, the lower boundconstruction scheme is proposed for BSC which has more accurate estimation and lessimprovement of performance compared with the traditional iterations. For additive whiteGaussian noise channels, the linear construting scheme is proposed and the selecting methodof parameter is obtained by the simulation.
5. Polar codes are applied to the time-division half-duplex relay channel. Due to thecharacteristics of channels combining and splitting, polar codes are considered to transmit inthe relay channels. For the half-duplex relay systems, the characteristics of the model andeach node are analyzed. Based on the forwarding protocols and the orthogonal vectors oftransmission, a suitable polarized transmission structure and a transmitting strategy arepresented. Moreover, polar codes are proved to achieve the Shannon limit in the half-duplexrelay systems. The optimizations of time-division and information-division parameters areproposed, while the random selection strategy is optimal in the half-duplex relay systems,.Finally, the simulation results and conclusions are presented.
6. In optical turbulence channels, error probability performances of free-space optical(FSO) communication are analyzed for irradiance modulation and direct detection (IM/DD)systems with subcarrier intensity modulation using binary phase-shift keying (SIM-BPSK)and polar codes. The analysis is carried out by different climates in the Gamma-Gammaturbulence channels. For bit-by-bit interleaved channels, the pairwise error probability (PEP)makes a high accurate series presentation about the virtual channels which deduces anasymptotic PEP. Each block has the independent fading in quasi-static fading channels. Thenwe study the upper and lower bound of the frame error ratio performance with Bhattachayyaparameter and density evolution estimations in polar coding FSO systems. Density evolutionestimation is better than Bhattachayya parameter. The numerical results are given to presentthe improvement and performance in polar coding FSO systems.
In conclusion, software simulations, tests and comparisons with traditional algorithmsare considered to verify their effectiveness and progressiveness of the proposed algorithms.For all the proposed theorems, their preciseness and scope is proved by the analysis ofmathematical derivation in this paper.
引文
[1] Raychaudhuri D, Mandayam N B. Frontiers of Wireless and MobileCommunications[J]. Proceedings of the IEEE,2012,100(4):824–840.
[2]岳殿武,徐澄圻.关于纠错码的若干新方向[J].重庆邮电学院学报(自然科学版),2000(04):1–6.
[3]王新梅,肖国镇.纠错码——原理与方法(修订版)[M].西安市:西安电子科技大学出版社,1991.
[4] Shannon C E. A mathematical theory of communication[J]. Bell System TechnicalJournal,1948,27:379–423,623–656.
[5] Muller D E. Application of Boolean algebra to switching circuit design and to errordetection[J]. Professional Group on Electronic Computers, Transactions of the I.R.E,1954, EC-3(3):6–12.
[6] Bose R C, Ray-Chaudhuri D K. On a Class of Error Correcting Binary Group Codes[J].Information and Control,1960,3:68–79.
[7] Reed I S, Solomon G. Polynomial Codes over Certain Finite Fields[J]. Journal of theSociety for Industrial and Applied Mathematics,1960, Vol.8(no.2):300–304.
[8] Gallager R G. Low-density parity-check codes[J]. IRE Transactions on InformationTheory,1962,8(1):21–28.
[9] Viterbi A J. Error bounds for convolutional codes and an asymptotically optimumdecoding algorithm[J]. IEEE Transactions on Information Theory,1967,13(2):260–269.
[10] Chien R T. Cyclic decoding procedures for Bose-Chaudhuri-Hocquenghem codes[J].IEEE Transactions on Information Theory,1964,10(4):357–363.
[11] Forney G D. On decoding BCH codes[J]. IEEE Transactions on Information Theory,1965,11(4):549–557.
[12] Forney G D. Concatenated Codes[M]. Cambridge: M. I. T. Press,1966.
[13] Ungerboeck G. Channel coding with multilevel/phase signals[J]. IEEE Transactions onInformation Theory,1982,28(1):55–67.
[14] Divsalar D, Simon M K. Multiple trellis coded modulation (MTCM)[J]. IEEETransactions on Communications,1988,36(4):410–419.
[15] Berrou C, Glavieux A. Near optimum error correcting coding and decoding:turbo-codes[J]. IEEE Transactions on Communications,1996,44(10):1261–1271.
[16] MacKay D J C, Neal R M. Near Shannon limit performance of low density parity checkcodes[J]. Electronics Letters,1996,32(18):1645–.
[17] Stefania S, Issam T, Matthew B. LTE-the UMTS Long Term Evolution: from Theory toPractice (the2nd Edition)[M]. New York: John Wiley&Sons Ltd.,2011.
[18] Byers J W, Luby M, Mitzenmacher M. A digital fountain approach to asynchronousreliable multicast[J]. IEEE Journal on Selected Areas in Communications,2002,20(8):1528–1540.
[19] Luby M. LT codes[A]. The43rd Annual IEEE Symposium on Foundations ofComputer Science,2002[C]. Vancouver:2002:271–280.
[20] Shokrollahi A. Raptor codes[J]. IEEE Transactions on Information Theory,2006,52(6):2551–2567.
[21] Shamai S, Telatar I E, Verdu S. Fountain Capacity[J]. IEEE Transactions onInformation Theory,2007,53(11):4372–4376.
[22] Studholme C, Blake I. Windowed Erasure Codes[A].2006IEEE InternationalSymposium on Information Theory[C].2006:509–513.
[23] Thomos N, Pulikkoonattu R, Frossard P. Growth Codes: Intermediate PerformanceAnalysis and Application to Video[J]. IEEE Transactions on Communications,2013,61(11):4710–4721.
[24] Wang Z, Luo J. Fountain Communication using Concatenated Codes[J]. IEEETransactions on Communications,2013,61(2):443–454.
[25]黄诚，易本顺.基于抛物线映射的混沌LT编码算法[J].电子与信息学报,2009,31(10):2527–2531.
[26] Chen S, Zhang Z, Zhu L et al. Accumulate rateless codes and their performances overadditive white gaussian noise channel[J]. IET Communications,2013,7(4):372–381.
[27] Draper S C, Kschischang F R, Frey B. Rateless Coding for Arbitrary Channel MixturesWith Decoder Channel State Information[J]. IEEE Transactions on Information Theory,2009,55(9):4119–4133.
[28] Mao Y, Huang J, Wang B et al. A new iterative LT decoding algorithm for binary andnonbinary Galois fields[J]. Journal of Communications and Networks,2013,15(4):411–421.
[29] Mirrezaei S M, Faez K, Yousefi S. Analysis and design of a new fountain codec underbelief propagation[J]. IET Communications,2014,8(1):27–40.
[30] Sejdinovic D, Vukobratovic D, Doufexi A et al. Expanding window fountain codes forunequal error protection[J]. IEEE Transactions on Communications,2009,57(9):2510–2516.
[31] Sorensen J H, Popovski P, Ostergaard J. UEP LT Codes with Intermediate Feedback[J].IEEE Communications Letters,2013,17(8):1636–1639.
[32] Arslan S S, Cosman P C, Milstein L B. Generalized Unequal Error Protection LT Codesfor Progressive Data Transmission[J]. IEEE Transactions on Image Processing,2012,21(8):3586–3597.
[33] Forward Error Correction FEC Algorithm Technologies[EB/OL]. Qualcomm./2013-10-29. http://www.qualcomm.com/solutions/multimedia/media-delivery.
[34] Lu Y, Lai I, Lee C et al. Low-Complexity Decoding for RaptorQ Codes Using aRecursive Matrix Inversion Formula[J]. IEEE Wireless Communications Letters,2014,Early Access Online.
[35] Liau A, Kim I, Yousefi S. Improved Low-Complexity Soliton-Like Network Coding fora Resource-Limited Relay[J]. IEEE Transactions on Communications,2013,61(8):3327–3335.
[36] Duy T T, Anpalagan A, Kong H-Y. Multi-hop cooperative transmission using fountaincodes over Rayleigh fading channels[J]. Journal of Communications and Networks,2012,14(3):267–272.
[37] Cao R, Yang L. Decomposed LT Codes for Cooperative Relay Communications[J].IEEE Journal on Selected Areas in Communications,2012,30(2):407–414.
[38] Jiang C, Li D, Xu M. LTTP: An LT-Code Based Transport Protocol for Many-to-OneCommunication in Data Centers[J]. IEEE Journal on Selected Areas inCommunications,2014,32(1):52–64.
[39] Hu L, Nooshabadi S, Mladenov T. Forward error correction with Raptor GF(2) andGF(256) codes on GPU[J]. IEEE Transactions on Consumer Electronics,2013,59(1):273–280.
[40] Cao R, Yang L. Reliable relay-aided underwater acoustic communications with hybridDLT codes[A]. MILITARY COMMUNICATIONS CONFERENCE,2011-MILCOM2011[C]. Baltimore:2011:412–417.
[41] Chieochan S, Hossain E. Wireless Fountain Coding with IEEE802.11e Block ACK forMedia Streaming in Wireline-cum-WiFi Networks: A Performance Study[J]. IEEETransactions on Mobile Computing,2011,10(10):1416–1433.
[42] Yang K-C, Wang J-S. Unequal Error Protection for Streaming Media Based on RatelessCodes[J]. IEEE Transactions on Computers,2012,61(5):666–675.
[43] Sugiura S. Decentralized-Precoding Aided Rateless Codes for Wireless SensorNetworks[J]. IEEE Communications Letters,2012,16(4):506–509.
[44] Pang K, Lin Z, Uchoa-Filho B F et al. Distributed Network Coding for Wireless SensorNetworks Based on Rateless LT Codes[J]. IEEE Wireless Communications Letters,2012,1(6):561–564.
[45] Arikan E. Channel combining and splitting for cutoff rate improvement[J]. IEEETransactions on Information Theory,2006,52(2):628–639.
[46] Arikan E. Channel polarization: a method for constructing capacity-achieving codes forsymmetric binary-input memoryless channels[J]. IEEE Transactions on InformationTheory,2009,55(7):3051–3073.
[47] Korada S B, a og lu E, Urbanke R. Polar Codes: Characterization of Exponent,Bounds, and Constructions[J]. IEEE Transactions on Information Theory,2010,56(12):6253–6264.
[48] Hassani S H, Mori R, Tanaka T et al. Rate-Dependent Analysis of the AsymptoticBehavior of Channel Polarization[J]. IEEE Transactions on Information Theory,2013,59(4):2267–2276.
[49] Valipour M, Yousefi S. On Probabilistic Weight Distribution of Polar Codes[J]. IEEECommunications Letters,2013,17(11):2120–2123.
[50] Alsan M. Extremality properties for Gallager’s random coding exponent[A].2012IEEE International Symposium on Information Theory Proceedings (ISIT)[C].Cambridge:2012:2944–2948.
[51] Guillen i Fabregas A, Land I, Martinez A. Extremes of Error Exponents[J]. IEEETransactions on Information Theory,2013,59(4):2201–2207.
[52] Zhao S, Shi P, Wang B. Designs of Bhattacharyya parameter in the construction ofpolar codes[A].20117th International Conference on Wireless Communications,Networking and Mobile Computing (WiCOM)[C]. Wuhan:2011:1–4.
[53] Mori R, Tanaka T. Performance of polar codes with the construction using densityevolution[J]. IEEE Communications Letters,2009,13(7):519–521.
[54] Pedarsani R, Hassani S H, Tal I et al. On the construction of polar codes[A].2011IEEEInternational Symposium on Information Theory Proceedings (ISIT)[C]. St. Petersburg:2011:11–15.
[55] Tal I, Vardy A. How to Construct Polar Codes[J]. IEEE Transactions on InformationTheory,2013,59(10):6562–6582.
[56] Honda J, Yamamoto H. Polar Coding without Alphabet Extension for AsymmetricModels[J]. IEEE Transactions on Information Theory,2013,59(12):7829–7838.
[57] Sahebi A G, Pradhan S S. Multilevel Channel Polarization for Arbitrary DiscreteMemoryless Channels[J]. IEEE Transactions on Information Theory,2013,59(12):7839–7857.
[58] Valipour M, Yousefi S. On Probabilistic Weight Distribution of Polar Codes[J]. IEEECommunications Letters,2013,17(11):2120–2123.
[59] Mori R, Tanaka T. Non-binary polar codes using Reed-Solomon codes and algebraicgeometry codes[A].2010IEEE Information Theory Workshop (ITW)[C]. Dublin:2010:1–5.
[60] Alamdar-Yazdi A, Kschischang F R. A Simplified Successive-Cancellation Decoder forPolar Codes[J]. IEEE Communications Letters,2011,15(12):1378–1380.
[61] Hassani S H, Urbanke R. Polar codes: Robustness of the successive cancellationdecoder with respect to quantization[A].2012IEEE International Symposium onInformation Theory Proceedings (ISIT)[C]. Cambridge:2012:1962–1966.
[62] Trifonov P. Efficient Design and Decoding of Polar Codes[J]. IEEE Transactions onCommunications,2012,60(11):3221–3227.
[63] Niu K, Chen K. CRC-Aided Decoding of Polar Codes[J]. IEEE CommunicationsLetters,2012,16(10):1668–1671.
[64] Li B, Shen H, Tse D. An Adaptive Successive Cancellation List Decoder for PolarCodes with Cyclic Redundancy Check[J]. IEEE Communications Letters,2012,16(12):2044–2047.
[65] Eslami A, Pishro-Nik H. On Finite-Length Performance of Polar Codes: Stopping Sets,Error Floor, and Concatenated Design[J]. IEEE Transactions on Communications,2013,61(3):919–929.
[66] Shin D-M, Lim S-C, Yang K. Design of Length-Compatible Polar Codes Based on theReduction of Polarizing Matrices[J]. IEEE Transactions on Communications,2013,61(7):2593–2599.
[67] Yuan B, Parhi K K. Low-Latency Successive-Cancellation Polar Decoder ArchitecturesUsing2-Bit Decoding[J]. IEEE Transactions on Circuits and Systems I: Regular Papers,2013, PP(99):1–14.
[68] Huang Z L, Diao C J, Chen M. Latency reduced method for modified successivecancellation decoding of polar codes[J]. Electronics Letters,2012,48(23):1505–15061506.
[69] Sarkis G, Gross W J. Increasing the Throughput of Polar Decoders[J]. IEEECommunications Letters,2013,17(4):725–728.
[70] Chen K, Niu K, Lin J R. List successive cancellation decoding of polar codes[J].Electronics Letters,2012,48(9):500–501.
[71] Tal I, Vardy A. List decoding of polar codes[A].2011IEEE International Symposiumon Information Theory Proceedings (ISIT)[C]. St. Petersburg:2011:1–5.
[72] Niu K, Chen K. Stack decoding of polar codes[J]. Electronics Letters,2012,48(12):695–697.
[73] Chen K, Niu K, Lin J. Improved Successive Cancellation Decoding of Polar Codes[J].IEEE Transactions on Communications,2013,61(8):3100–3107.
[74] Arkan E. A performance comparison of polar codes and Reed-Muller codes[J]. IEEECommunications Letters,2008,12(6):447–449.
[75] Goela N, Korada S B, Gastpar M. On LP decoding of polar codes[A].2010IEEEInformation Theory Workshop (ITW)[C]. Dublin:2010:1–5.
[76] Kahraman S, Celebi M E. Code based efficient maximum-likelihood decoding of shortpolar codes[A].2012IEEE International Symposium on Information TheoryProceedings (ISIT)[C]. Cambridge:2012:1967–1971.
[77] Arikan E. Source polarization[A].2010IEEE International Symposium on InformationTheory Proceedings (ISIT)[C]. Austin:2010:899–903.
[78] Korada S B, Urbanke R L. Polar Codes are Optimal for Lossy Source Coding[J].Information Theory, IEEE Transactions on,2010,56(4):1751–1768.
[79] Cronie H S, Korada S B. Lossless source coding with polar codes[A].2010IEEEInternational Symposium on Information Theory Proceedings (ISIT)[C]. Austin:2010:904–908.
[80] Karzand M, Telatar I E. Polar codes for q-ary source coding[A].2010IEEEInternational Symposium on Information Theory Proceedings (ISIT)[C]. Austin:2010:909–912.
[81] Sahebi A G, Pradhan S S. Polar codes for sources with finite reconstructionalphabets[A].201250th Annual Allerton Conference on Communication, Control, andComputing (Allerton)[C]. Monticello:2012:580–586.
[82] Trang V T T, Kang J W, Jang M et al. The performance of polar codes in distributedsource coding[A].2012Fourth International Conference on Communications andElectronics (ICCE)[C]. Hue:2012:196–199.
[83] Onay S. Polar codes for distributed source coding[J]. Electronics Letters,2013,49(5):346–348.
[84] Lv X, Liu R, Wang R. A Novel Rate-Adaptive Distributed Source Coding SchemeUsing Polar Codes[J]. IEEE Communications Letters,2013,17(1):143–146.
[85] Burshtein D, Strugatski A. Polar Write Once Memory Codes[J]. IEEE Transactions onInformation Theory,2013,59(8):5088–5101.
[86] Wilde M M, Renes J M. Quantum polar codes for arbitrary channels[A].2012IEEEInternational Symposium on Information Theory Proceedings (ISIT)[C]. Cambridge:2012:334–338.
[87] Guha S, Wilde M M. Polar coding to achieve the Holevo capacity of a pure-loss opticalchannel[A].2012IEEE International Symposium on Information Theory Proceedings(ISIT)[C]. Cambridge:2012:546–550.
[88] Wilde M M, Guha S. Polar Codes for Classical-Quantum Channels[J]. IEEETransactions on Information Theory,2013,59(2):1175–1187.
[89] Wilde M M, Guha S. Polar Codes for Degradable Quantum Channels[J]. IEEETransactions on Information Theory,2013,59(7):4718–4729.
[90] Leroux C, Raymond A J, Sarkis G et al. Hardware implementation ofsuccessive-cancellation decoders for polar codes[J]. Journal of Signal ProcessingSystems for Signal Image and Video Technology,2012,69(3):305–315.
[91] Leroux C, Raymond A J, Sarkis G et al. A Semi-Parallel Successive-CancellationDecoder for Polar Codes[J]. IEEE Transactions on Signal Processing,2013,61(2):289–299.
[92] Liu Y-H, Huang X, Vidojkovic M et al. An energy-efficient polar transmitter for IEEE802.15.6body area networks: system requirements and circuit designs[J]. IEEECommunications Magazine,2012,50(10):118–127127.
[93] Chen K, Niu K, Lin J-R. Practical polar code construction over parallel channels[J].IET Communications,2013,7(7):620–627.
[94] Zhang C, Parhi K K. Low-Latency Sequential and Overlapped Architectures forSuccessive Cancellation Polar Decoder[J]. IEEE Transactions on Signal Processing,2013,61(10):2429–2441.
[95] Korada S B. Polar codes for Channel and Source Coding[D]. Lausanne, Switzerland:EPFL,2009.
[96] Andersson M, Schaefer R F, Oechtering T J et al. Polar Coding for BidirectionalBroadcast Channels with Common and Confidential Messages[J]. IEEE Journal onSelected Areas in Communications,2013,31(9):1901–1908.
[97] Abbe E, Telatar I E. Polar Codes for the m-User Multiple Access Channel[J]. IEEETransactions on Information Theory,2012,58(8):5437–5448.
[98] Sasoglu E, Telatar E, Yeh E M. Polar Codes for the Two-User Multiple-AccessChannel[J]. IEEE Transactions on Information Theory,2013,59(10):6583–6592.
[99] Hof E, Sason I, Shamai S et al. Capacity-Achieving Polar Codes for ArbitrarilyPermuted Parallel Channels[J]. IEEE Transactions on Information Theory,2013,59(3):1505–1516.
[100] Bravo-Santos A. Polar Codes for the Rayleigh Fading Channel[J]. IEEECommunications Letters,2013,17(12):2352–2355.
[101] Koyluoglu O O, El Gamal H. Polar coding for secure transmission and keyagreement[J]. IEEE Transactions on Information Forensics and Security,2012,7(5):1472–1483.
[102] Seidl M, Schenk A, Stierstorfer C et al. Polar-Coded Modulation[J]. IEEE Transactionson Communications,2013,61(10):4108–4119.
[103] Bhattacharyya A. On a measure of divergence between two statistical populationsdefined by their probability distributions[J]. Bulletin of the Calcutta MathematicalSociety,1943(35):99–109.
[104] Maatouk G, Shokrollahi A. Analysis of the Second Moment of the LT Decoder[J]. IEEETransactions on Information Theory,2012,58(5):2558–2569.
[105] Ozyurt S, Torlak M. Exact Joint Distribution Analysis of Zero-Forcing V-BLAST Gainswith Greedy Ordering[J]. IEEE Transactions on Wireless Communications,2013,12(11):5377–5385.
[106] Arikan E. Systematic polar coding[J]. Communications Letters, IEEE,2011,15(8):860–862.
[107] Hu K, Castura J, Mao Y. Performance-Complexity Tradeoffs of Raptor Codes overGaussian Channels[J]. IEEE Communications Letters,2007,11(4):343–345.
[108] Zeng M, Calderbank R, Cui S. On Design of Rateless Codes over Dying BinaryErasure Channel[J]. IEEE Transactions on Communications,2012,60(4):889–894.
[109] Sanghavi S. Intermediate Performance of Rateless Codes[A]. IEEE Information TheoryWorkshop,2007. ITW’07[C]. Tahoe City:2007:478–482.
[110] Thomos N, Pulikkoonattu R, Frossard P. Growth Codes: Intermediate PerformanceAnalysis and Application to Video[J]. IEEE Transactions on Communications,2013,61(11):4710–4721.
[111] Zhang D, Li B, Li H. Intermedia-based video adaptation system: Design andimplementation[J]. Tsinghua Science and Technology,2012,17(2):113–127.
[112] Ong L, Johnson S J, Kellett C M. The Half-Duplex AWGN Single-Relay Channel: FullDecoding or Partial Decoding?[J]. IEEE Transactions on Communications,2012,60(11):3156–3160.
[113] Ghabeli L, Aref M-R. Comprehensive partial decoding approach for two-level relaynetworks[J]. IET Communications,2009,3(4):585–596.
[114] Meng J, Yang E. Interactive Encoding and Decoding Based on Binary LDPC CodesWith Syndrome Accumulation[J]. IEEE Transactions on Information Theory,2013,59(5):3068–3103.
[115] Chen L. Iterative Soft-Decision Decoding of Hermitian Codes[J]. IEEE Transactions onCommunications,2013,61(1):33–42.
[116] Zhou Y, Lai X, Li Y et al. Ant Colony Optimization With Combining GaussianEliminations for Matrix Multiplication[J]. IEEE Transactions on Cybernetics,2013,43(1):347–357.
[117] Salamanca L, Olmos P M, Murillo-Fuentes J J et al. Tree Expectation Propagation forML Decoding of LDPC Codes over the BEC[J]. IEEE Transactions onCommunications,2013,61(2):465–473.
[118] Saejoon Kim, Karam Ko, Sae-Young Chung. Incremental Gaussian eliminationdecoding of raptor codes over BEC[J]. IEEE Communications Letters,2008,12(4):307–309.
[119] MacKay D J C. Fountain codes[J]. IEE Proceedings of Communications,2005,152(6):1062–1068.
[120] Lin S, Costello D.差错控制编码[M].北京:人民文学出版社,1992.
[121] Lay D.线性代数及其应用[M].刘深泉,译.北京:机械工业出版社,2005.
[122] Bioglio V, Grangetto M, Gaeta R et al. On the fly gaussian elimination for LT codes[J].IEEE Communications Letters,2009,13(12):953–955.
[123] Bai B, Chen W, Letaief K B et al. Outage Exponent: A Unified Performance Metric forParallel Fading Channels[J]. IEEE Transactions on Information Theory,2013,59(3):1657–1677.
[124] Hachem W, Moulines E, Roueff F. Error Exponents for Neyman-Pearson Detection of aContinuous-Time Gaussian Markov Process From Regular or Irregular Samples[J].IEEE Transactions on Information Theory,2011,57(6):3899–3914.
[125] Cohen K, Leshem A. Performance Analysis of Likelihood-Based Multiple Access forDetection Over Fading Channels[J]. IEEE Transactions on Information Theory,2013,59(4):2471–2481.
[126] Gallager R G. Information Theory and Reliable Communication[M]. New York, UnitedStates of America: John Wiley&Sons,1976.
[127] Land I, Huber J. Information combining[J]. Foundation Trends CommunicationInformation Theory,2006,3(3):227–330.
[128] Bhattacharyya A. On a measure of divergence between two statistical populationsdefined by their probability distributions[J]. Bulletin of the Calcutta MathematicalSociety,1943,35:99–109.
[129] Yuan J. Active contour driven by region-scalable fitting and local Bhattacharyyadistance energies for ultrasound image segmentation[J]. IET Image Processing,2012,6(8):1075–1083.
[130] Lou Y, Irimia A, Vela P A et al. Multimodal Deformable Registration of TraumaticBrain Injury MR Volumes via the Bhattacharyya Distance[J]. IEEE Transactions onBiomedical Engineering,2013,60(9):2511–2520.
[131] Nielsen F, Boltz S. The Burbea-Rao and Bhattacharyya Centroids[J]. IEEETransactions on Information Theory,2011,57(8):5455–5466.
[132] Chu J P K, Adve R S, Eckford A W. Using the Bhattacharyya parameter for design andanalysis of cooperative wireless systems[J]. IEEE Transactions on WirelessCommunications,2009,8(3):1384–1395.
[133] Varshney L R. Performance of LDPC codes under faulty iterative decoding[J].Information Theory, IEEE Transactions on,2011,57(7):4427–4444.
[134] J. Pearl. Probabilistic reasoning in intelligent systems: networks of plausibleinference[M].1988.
[135] Cooper M. Antennas get smart[J]. Scientific American,2003,289(1):48–55.
[136] Van der Meulen E C. Three-terminal communication channels[J]. Advances in AppliedProbability,1971,3(01):120–154.
[137] Sato H. Information transmission through a channel with relay[M]. University ofHawaii, Honolulu: Technology Republic,1976.
[138] Cover T, Gamal A E. Capacity theorems for the relay channel[J]. IEEE Transactions onInformation theory,1979,25(05):572–584.
[139] Gamal A E, Aref M. The capacity of the semideterministic relay channel (Corresp.)[J].IEEE Transactions on Information Theory,1982,28(3):536–536.
[140] El Gamal A, Zahedi S. Capacity of a class of relay channels with orthogonalcomponents[J]. IEEE Transactions on Information Theory,2005,51(5):1815–1817.
[141] Cover T. Elements of Information Theory[M]. New York: Wiley,1991.
[142] Zeng C-M, Kuhlmann F, Buzo A. Achievability proof of some multiuser channelcoding theorems using backward decoding[J]. IEEE Transactions on InformationTheory,1989,35(6):1160–1165.
[143]3GPP Technical Specification25.106, UTRA repeater radio transmission andreception[S].
[144]3GPP Technical Specification36.106, Evolved Universal Terrestrial Radio Access(E_UTRA): FDD Repeater radio transmission and reception[S].
[145] Host-Madsen A, Zhang J. Capacity bounds and power allocation for wireless relaychannels[J]. IEEE Transactions on Information Theory,2005,51(6):2020–2040.
[146] Host-Madsen A. Capacity bounds for Cooperative diversity[J]. IEEE Transactions onInformation Theory,2006,52(4):1522–1544.
[147] El Gamal A, Mohseni M, Zahedi S. Bounds on capacity and minimum energy-per-bitfor AWGN relay channels[J]. IEEE Transactions on Information Theory,2006,52(4):1545–1561.
[148] Wang B, Zhang J, Host-Madsen A. On the capacity of MIMO relay channels[J]. IEEETransactions on Information Theory,2005,51(1):29–43.
[149] Chun Y J, Kim D I, Kim S W. Optimization of Network Coded MIMO Transmission inMultiple-Access Relay Network[J]. IEEE Transactions on Wireless Communications,2013,12(5):2436–2444.
[150] Brante G, Souza R D, Garcia-Frias J. Spatial Diversity Using Analog Joint SourceChannel Coding in Wireless Channels[J]. IEEE Transactions on Communications,2013,61(1):301–311.
[151] Muralidharan V T, Rajan B S. Physical Layer Network Coding for the K-User MultipleAccess Relay Channel[J]. IEEE Transactions on Wireless Communications,2013,12(6):3107–3119.
[152] Joda R, Lahouti F. Network Code Design for Orthogonal Two-Hop Network withBroadcasting Relay: A Joint Source-Channel-Network Coding Approach[J]. IEEETransactions on Communications,2012,60(1):132–142.
[153]3GPP Technical Specification36.216, Evolved Universal Terrestrial Radio Access(E_UTRA): Physical Layer for Relaying Operation (Release10)[S].
[154] Ding Z, Cumanan K, Ma Z et al. Linear Detection for Cooperative Multiple-AccessTransmission Protocols[J]. IEEE Transactions on Vehicular Technology,2013,62(6):2807–2812.
[155] Dabora R, Servetto S D. Broadcast Channels With Cooperating Decoders[J]. IEEETransactions on Information Theory,2006,52(12):5438–5454.
[156] Behboodi A, Piantanida P. Cooperative Strategies for Simultaneous and BroadcastRelay Channels[J]. IEEE Transactions on Information Theory,2013,59(3):1417–1443.
[157] Zhang Z, Lv T, Yang S. Round-Robin Relaying With Diversity inAmplify-and-Forward Multisource Cooperative Communications[J]. IEEETransactions on Vehicular Technology,2013,62(3):1251–1266.
[158] Chen Y. Chernoff information path loss in wireless relay sensor networks[J]. IETWireless Sensor Systems,2012,2(3):201–213.
[159] Razi A, Afghah F, Abedi A. Power Optimized DSTBC Assisted DMF Relaying inWireless Sensor Networks with Redundant Super Nodes[J]. IEEE Transactions onWireless Communications,2013,12(2):636–645.
[160] Chu S, Wang X, Yang Y. Exploiting Cooperative Relay for High PerformanceCommunications in MIMO Ad Hoc Networks[J]. IEEE Transactions on Computers,2013,62(4):716–729.
[161] Munari A, Levorato M, Zorzi M. On the Impact of Carrier Sense Based MediumAccess Control on Cooperative Schemes in Wireless Ad Hoc Networks[J]. IEEETransactions on Communications,2012,60(10):3032–3046.
[162] Lee D, Seo H, Clerckx B et al. Coordinated multipoint transmission and reception inLTE-advanced: deployment scenarios and operational challenges[J]. IEEECommunications Magazine,2012,50(2):148–155.
[163] Zhao J, Quek T Q S, Lei Z. Coordinated Multipoint Transmission with LimitedBackhaul Data Transfer[J]. IEEE Transactions on Wireless Communications,2013,12(6):2762–2775.
[164] Liu A, Lau V K N. Cache-Enabled Opportunistic Cooperative MIMO for VideoStreaming in Wireless Systems[J]. IEEE Transactions on Signal Processing,2014,62(2):390–402.
[165] Monteiro V, Mumtaz S, Rodriguez J et al. Energy efficient relay-aided shared LTEnetwork using CoMP and LB[A]. Future Network and Mobile Summit(FutureNetworkSummit),2013[C].2013:1–9.
[166] Liang H, Zhuang W. Cooperative data dissemination via roadside WLANs[J]. IEEECommunications Magazine,2012,50(4):68–74.
[167] Nishide K, Kubo H, Shinkuma R et al. Detecting Hidden and Exposed TerminalProblems in Densely Deployed Wireless Networks[J]. IEEE Transactions on WirelessCommunications,2012,11(11):3841–3849.
[168] Lin X, Li X. Achieving Efficient Cooperative Message Authentication in Vehicular AdHoc Networks[J]. IEEE Transactions on Vehicular Technology,2013,62(7):3339–3348.
[169] Zheng K, Liu F, Zheng Q et al. A Graph-Based Cooperative Scheduling Scheme forVehicular Networks[J]. IEEE Transactions on Vehicular Technology,2013,62(4):1450–1458.
[170] Li B, Li H, Wang W et al. Performance Analysis and Optimization for Energy-EfficientCooperative Transmission in Random Wireless Sensor Network[J]. IEEE Transactionson Wireless Communications,2013,12(9):4647–4657.
[171] Jung J W, Weitnauer M A. On Using Cooperative Routing for Lifetime Optimization ofMulti-Hop Wireless Sensor Networks: Analysis and Guidelines[J]. IEEE Transactionson Communications,2013,61(8):3413–3423.
[172] Moazzez-Estanjini R, Wang J, Paschalidis I C. Scheduling Mobile Nodes forCooperative Data Transport in Sensor Networks[J]. IEEE/ACM Transactions onNetworking,2013,21(3):974–989.
[173] Andersson M, Rathi V, Thobaben R et al. Nested polar codes for wiretap and relaychannels[J]. IEEE Communications Letters,2010,14(8):752–754.
[174] Wu F, Xing C, Zhao S et al. Encrypted polar codes for wiretap channel[A].20122ndInternational Conference on Computer Science and Network Technology (ICCSNT)[C].Changchun:2012:579–583.
[175] Blasco-Serrano R, Thobaben R, Rathi V et al. Polar codes for compress-and-forward inbinary relay channels[A].2010Conference Record of the Forty Fourth AsilomarConference on Signals, Systems and Computers (ASILOMAR)[C]. Pacific Grove:2010:1743–1747.
[176] Blasco-Serrano R, Thobaben R, Andersson M et al. Polar codes for cooperativerelaying[J]. IEEE Transactions on Communications,2012,60(11):3263–3273.
[177] Bravo-Santos A. Polar codes for Gaussian degraded relay channels[J]. IEEECommunications Letters,2013,17(2):365–368.
[178] Zhang Z, Duman T M. Capacity-approaching turbo coding and iterative decoding forrelay channels[J]. IEEE Transactions on Communications,2005,53(11):1895–1905.
[179] Dahlman E, Parkvall S, Skold J.4G LTE/LTE-Advanced for Mobile Broadband[M].Salt Lake City, UT, United States: Academic Press,2011.
[180] Alves H, da Costa D B, Souza R D et al. Performance of Block-Markov Full DuplexRelaying with Self Interference in Nakagami-m Fading[J]. IEEE WirelessCommunications Letters,2013,2(3):311–314.
[181] Ma S, Zhang J-K. Noncoherent Orthogonal Distributed Space-Time Block Codes forAmplify-and-Forward Half-Duplex Cooperative Relay Channels[J]. IEEE Transactionson Vehicular Technology,2012,61(6):2854–2858.
[182] Mesbah W, Davidson T N. Weighted-Sum-Rate Maximization in Certain Half-DuplexCooperative Systems[J]. IEEE Wireless Communications Letters,2012,1(3):213–216.
[183] Yang S, Lv T, Maunder R G et al. From Nominal to True A Posteriori Probabilities: AnExact Bayesian Theorem Based Probabilistic Data Association Approach for IterativeMIMO Detection and Decoding[J]. IEEE Transactions on Communications,2013,61(7):2782–2793.
[184] Kwon H, Lee J, Kang I. Successive Interference Cancellation via Rank-ReducedMaximum A Posteriori Detection[J]. IEEE Transactions on Communications,2013,61(2):628–637.
[185] Irawan A, Anwar K, Matsumoto T. Combining-after-Decoding Turbo Hybrid ARQ byUtilizing Doped-Accumulator[J]. IEEE Communications Letters,2013,17(6):1212–1215.
[186] Huo Y, El-Hajjar M, Hanzo L. Inter-Layer FEC Aided Unequal Error Protection forMultilayer Video Transmission in Mobile TV[J]. IEEE Transactions on Circuits andSystems for Video Technology,2013,23(9):1622–1634.
[187]樊平毅.网络信息论[M].北京:清华大学出版社,2009.
[188] Cover T M, Thomas J A. Elements of Information Theory[M]. New York: Wiley,1991.
[189] Parzysz F, Vu M, Gagnon F. Energy Minimization for the Half-Duplex Relay Channelwith Decode-Forward Relaying[J]. IEEE Transactions on Communications,2013,61(6):2232–2247.
[190] Zhang Z, Duman T M. Capacity approaching Turbo coding for half-duplex relaying[J].IEEE Transactions on Communications,2007,55(9):1822–1822.
[191] Zou Y, Wang X, Shen W. Optimal Relay Selection for Physical-Layer Security inCooperative Wireless Networks[J]. IEEE Journal on Selected Areas in Communications,2013,31(10):2099–2111.
[192] Chatzidiamantis N D, Michalopoulos D S, Kriezis E E et al. Relay selection protocolsfor relay-assisted free-space optical systems[J]. IEEE/OSA Journal of OpticalCommunications and Networking,2013,5(1):92–103.
[193] Brandao Harboe P, Souza J R. Passive Optical Network: Characteristics, Deployment,and Perspectives[J]. Latin America Transactions, IEEE (Revista IEEE America Latina),2013,11(4):995–1000.
[194] Cvijetic N, Tanaka A, Cvijetic M et al. Novel Optical Access and Digital ProcessingArchitectures for Future Mobile Backhaul[J]. Journal of Lightwave Technology,2013,31(4):621–627.
[195] Kazaura K, Wakamori K, Matsumoto M et al. RoFSO: A universal platform forconvergence of fiber and free-space optical communication networks[J]. IEEECommunications Magazine,2010,48(2):130–137.
[196] Kedar D, Arnon S. Urban optical wireless communication networks: the mainchallenges and possible solutions[J]. IEEE Communications Magazine,2004,42(5):S2–S7.
[197] Kartalopoulos S. Free Space Optical Networks for Ultra-Broad Band Services[M]. NewYork: Wiley,2011.
[198] Faruolo M, Coviello I, Lacava T et al. A Multi-Sensor Exportable Approach forAutomatic Flooded Areas Detection and Monitoring by a Composite SatelliteConstellation[J]. IEEE Transactions on Geoscience and Remote Sensing,2013,51(4):2136–2149.
[199]谌娟,柯熙政,程婷.自由空间光多输入多输出系统中的差分空时码[J].光学学报,2013(02):44–49.
[200]刘式达,梁福明.大气湍流[M].第1版.北京:北京大学出版社,2008.
[201]罗鹏飞.短距离无线光通信若干关键技术的研究[D].北京邮电大学,2013.
[202] Li J, Liu J Q, Taylor D P. Optical Communication Using Subcarrier PSK IntensityModulation Through Atmospheric Turbulence Channels[J]. IEEE Transactions onCommunications,2007,55(8):1598–1606.
[203] Djordjevic I B, Anguita J A, Vasic B. Error-Correction CodedOrbital-Angular-Momentum Modulation for FSO Channels Affected by Turbulence[J].Journal of Lightwave Technology,2012,30(17):2846–2852.
[204]黄根全.大气湍流下无线光通信信道性能研究[J].西安工业大学学报,2011(05):413–417.
[205] Parry G. Measurement of Atmospheric Turbulence Induced Intensity Fluctuations in aLaser Beam[J]. Optica Acta: International Journal of Optics,1981,28(5):715–728.
[206] Phillips R L, Andrews L C. Measured statistics of laser-light scattering in atmosphericturbulence[J]. Journal of the Optical Society of America,1981,71(12):1440–1445.
[207] Andrews L C, Phillips R L, Hopen C Y et al. Theory of optical scintillation[J]. Journalof the Optical Society of America A,1999,16(6):1417–1429.
[208] Al-Habash M A, Phillips R L, Andrews L C. Mathematical model for the irradianceprobability density function of a laser beam propagating through turbulent media[J].Optical Engineering,2001,40(8):1554–1562.
[209] Perlot N. Characterization of Signal Fluctuations in Optical Communications withIntensity Modulation and Direct Detection Through the Turbulent AtmosphericChannel[M]. Berichte aus der Kommunikationstechnik: Shaker Verlag GmbH,2005.
[210] Bhise A, Vyavahare P D. Improved low complexity hybrid turbo codes and unionbound analysis[J]. IET Communications,2011,5(4):512–518.
[211] Hadj Abderrahmane L. Design of a new interleaver using cross entropy method forturbo coding[J]. IET Communications,2013,7(9):828–835.
[212] Mansour M M. Fast Pruned Interleaving[J]. IEEE Transactions on Communications,2013,61(3):817–831.
[213] Uysal M, Li J, Yu M. Error rate performance analysis of coded free-space optical linksover gamma-gamma atmospheric turbulence channels[J]. IEEE Transactions onWireless Communications,2006,5(6):1229–1233.
[214] Gradshteyn I S, Ryzhik I M. Table of Integrals, Series and Products (the4thEdition)[M]. Amsterdam, Netherlands: Elsevier Science,2000.
[215] Greco J A. Design of the high-speed framing, FEC, and interleaving hardware used in a5.4km free-space optical communication experiment[J]. SPIE Proceedings,2009,7464:746409–1–746409–7.
[216] Mori R, Tanaka T. Performance and construction of polar codes on symmetricbinary-input memoryless channels[A]. IEEE International Symposium on InformationTheory,2009. ISIT2009[C].2009:1496–1500.
[217] Richardson T, Urbanke R. Modern Coding Theory[M]. Cambridge, U. K.: CambridgeUniversity Press,2008.
[218] Naila C B, Wakamori K, Matsumoto M et al. Transmission analysis of digital TVsignals over a Radio-on-FSO channel[J]. IEEE Communications Magazine,2012,50(8):137–144.
[219] Chow C W, Yeh C H, Liu Y F et al. Mitigation of Optical Background Noise inLight-Emitting Diode (LED) Optical Wireless Communication Systems[J]. IEEEPhotonics Journal,2013,5(1):7900307–7900307.
[220] Takai I, Ito S, Yasutomi K et al. LED and CMOS Image Sensor Based Optical WirelessCommunication System for Automotive Applications[J]. IEEE Photonics Journal,2013,5(5):6801418–6801418.
[2]岳殿武,徐澄圻.关于纠错码的若干新方向[J].重庆邮电学院学报(自然科学版),2000(04):1–6.
[3]王新梅,肖国镇.纠错码——原理与方法(修订版)[M].西安市:西安电子科技大学出版社,1991.
[4] Shannon C E. A mathematical theory of communication[J]. Bell System TechnicalJournal,1948,27:379–423,623–656.
[5] Muller D E. Application of Boolean algebra to switching circuit design and to errordetection[J]. Professional Group on Electronic Computers, Transactions of the I.R.E,1954, EC-3(3):6–12.
[6] Bose R C, Ray-Chaudhuri D K. On a Class of Error Correcting Binary Group Codes[J].Information and Control,1960,3:68–79.
[7] Reed I S, Solomon G. Polynomial Codes over Certain Finite Fields[J]. Journal of theSociety for Industrial and Applied Mathematics,1960, Vol.8(no.2):300–304.
[8] Gallager R G. Low-density parity-check codes[J]. IRE Transactions on InformationTheory,1962,8(1):21–28.
[9] Viterbi A J. Error bounds for convolutional codes and an asymptotically optimumdecoding algorithm[J]. IEEE Transactions on Information Theory,1967,13(2):260–269.
[10] Chien R T. Cyclic decoding procedures for Bose-Chaudhuri-Hocquenghem codes[J].IEEE Transactions on Information Theory,1964,10(4):357–363.
[11] Forney G D. On decoding BCH codes[J]. IEEE Transactions on Information Theory,1965,11(4):549–557.
[12] Forney G D. Concatenated Codes[M]. Cambridge: M. I. T. Press,1966.
[13] Ungerboeck G. Channel coding with multilevel/phase signals[J]. IEEE Transactions onInformation Theory,1982,28(1):55–67.
[14] Divsalar D, Simon M K. Multiple trellis coded modulation (MTCM)[J]. IEEETransactions on Communications,1988,36(4):410–419.
[15] Berrou C, Glavieux A. Near optimum error correcting coding and decoding:turbo-codes[J]. IEEE Transactions on Communications,1996,44(10):1261–1271.
[16] MacKay D J C, Neal R M. Near Shannon limit performance of low density parity checkcodes[J]. Electronics Letters,1996,32(18):1645–.
[17] Stefania S, Issam T, Matthew B. LTE-the UMTS Long Term Evolution: from Theory toPractice (the2nd Edition)[M]. New York: John Wiley&Sons Ltd.,2011.
[18] Byers J W, Luby M, Mitzenmacher M. A digital fountain approach to asynchronousreliable multicast[J]. IEEE Journal on Selected Areas in Communications,2002,20(8):1528–1540.
[19] Luby M. LT codes[A]. The43rd Annual IEEE Symposium on Foundations ofComputer Science,2002[C]. Vancouver:2002:271–280.
[20] Shokrollahi A. Raptor codes[J]. IEEE Transactions on Information Theory,2006,52(6):2551–2567.
[21] Shamai S, Telatar I E, Verdu S. Fountain Capacity[J]. IEEE Transactions onInformation Theory,2007,53(11):4372–4376.
[22] Studholme C, Blake I. Windowed Erasure Codes[A].2006IEEE InternationalSymposium on Information Theory[C].2006:509–513.
[23] Thomos N, Pulikkoonattu R, Frossard P. Growth Codes: Intermediate PerformanceAnalysis and Application to Video[J]. IEEE Transactions on Communications,2013,61(11):4710–4721.
[24] Wang Z, Luo J. Fountain Communication using Concatenated Codes[J]. IEEETransactions on Communications,2013,61(2):443–454.
[25]黄诚，易本顺.基于抛物线映射的混沌LT编码算法[J].电子与信息学报,2009,31(10):2527–2531.
[26] Chen S, Zhang Z, Zhu L et al. Accumulate rateless codes and their performances overadditive white gaussian noise channel[J]. IET Communications,2013,7(4):372–381.
[27] Draper S C, Kschischang F R, Frey B. Rateless Coding for Arbitrary Channel MixturesWith Decoder Channel State Information[J]. IEEE Transactions on Information Theory,2009,55(9):4119–4133.
[28] Mao Y, Huang J, Wang B et al. A new iterative LT decoding algorithm for binary andnonbinary Galois fields[J]. Journal of Communications and Networks,2013,15(4):411–421.
[29] Mirrezaei S M, Faez K, Yousefi S. Analysis and design of a new fountain codec underbelief propagation[J]. IET Communications,2014,8(1):27–40.
[30] Sejdinovic D, Vukobratovic D, Doufexi A et al. Expanding window fountain codes forunequal error protection[J]. IEEE Transactions on Communications,2009,57(9):2510–2516.
[31] Sorensen J H, Popovski P, Ostergaard J. UEP LT Codes with Intermediate Feedback[J].IEEE Communications Letters,2013,17(8):1636–1639.
[32] Arslan S S, Cosman P C, Milstein L B. Generalized Unequal Error Protection LT Codesfor Progressive Data Transmission[J]. IEEE Transactions on Image Processing,2012,21(8):3586–3597.
[33] Forward Error Correction FEC Algorithm Technologies[EB/OL]. Qualcomm./2013-10-29. http://www.qualcomm.com/solutions/multimedia/media-delivery.
[34] Lu Y, Lai I, Lee C et al. Low-Complexity Decoding for RaptorQ Codes Using aRecursive Matrix Inversion Formula[J]. IEEE Wireless Communications Letters,2014,Early Access Online.
[35] Liau A, Kim I, Yousefi S. Improved Low-Complexity Soliton-Like Network Coding fora Resource-Limited Relay[J]. IEEE Transactions on Communications,2013,61(8):3327–3335.
[36] Duy T T, Anpalagan A, Kong H-Y. Multi-hop cooperative transmission using fountaincodes over Rayleigh fading channels[J]. Journal of Communications and Networks,2012,14(3):267–272.
[37] Cao R, Yang L. Decomposed LT Codes for Cooperative Relay Communications[J].IEEE Journal on Selected Areas in Communications,2012,30(2):407–414.
[38] Jiang C, Li D, Xu M. LTTP: An LT-Code Based Transport Protocol for Many-to-OneCommunication in Data Centers[J]. IEEE Journal on Selected Areas inCommunications,2014,32(1):52–64.
[39] Hu L, Nooshabadi S, Mladenov T. Forward error correction with Raptor GF(2) andGF(256) codes on GPU[J]. IEEE Transactions on Consumer Electronics,2013,59(1):273–280.
[40] Cao R, Yang L. Reliable relay-aided underwater acoustic communications with hybridDLT codes[A]. MILITARY COMMUNICATIONS CONFERENCE,2011-MILCOM2011[C]. Baltimore:2011:412–417.
[41] Chieochan S, Hossain E. Wireless Fountain Coding with IEEE802.11e Block ACK forMedia Streaming in Wireline-cum-WiFi Networks: A Performance Study[J]. IEEETransactions on Mobile Computing,2011,10(10):1416–1433.
[42] Yang K-C, Wang J-S. Unequal Error Protection for Streaming Media Based on RatelessCodes[J]. IEEE Transactions on Computers,2012,61(5):666–675.
[43] Sugiura S. Decentralized-Precoding Aided Rateless Codes for Wireless SensorNetworks[J]. IEEE Communications Letters,2012,16(4):506–509.
[44] Pang K, Lin Z, Uchoa-Filho B F et al. Distributed Network Coding for Wireless SensorNetworks Based on Rateless LT Codes[J]. IEEE Wireless Communications Letters,2012,1(6):561–564.
[45] Arikan E. Channel combining and splitting for cutoff rate improvement[J]. IEEETransactions on Information Theory,2006,52(2):628–639.
[46] Arikan E. Channel polarization: a method for constructing capacity-achieving codes forsymmetric binary-input memoryless channels[J]. IEEE Transactions on InformationTheory,2009,55(7):3051–3073.
[47] Korada S B, a og lu E, Urbanke R. Polar Codes: Characterization of Exponent,Bounds, and Constructions[J]. IEEE Transactions on Information Theory,2010,56(12):6253–6264.
[48] Hassani S H, Mori R, Tanaka T et al. Rate-Dependent Analysis of the AsymptoticBehavior of Channel Polarization[J]. IEEE Transactions on Information Theory,2013,59(4):2267–2276.
[49] Valipour M, Yousefi S. On Probabilistic Weight Distribution of Polar Codes[J]. IEEECommunications Letters,2013,17(11):2120–2123.
[50] Alsan M. Extremality properties for Gallager’s random coding exponent[A].2012IEEE International Symposium on Information Theory Proceedings (ISIT)[C].Cambridge:2012:2944–2948.
[51] Guillen i Fabregas A, Land I, Martinez A. Extremes of Error Exponents[J]. IEEETransactions on Information Theory,2013,59(4):2201–2207.
[52] Zhao S, Shi P, Wang B. Designs of Bhattacharyya parameter in the construction ofpolar codes[A].20117th International Conference on Wireless Communications,Networking and Mobile Computing (WiCOM)[C]. Wuhan:2011:1–4.
[53] Mori R, Tanaka T. Performance of polar codes with the construction using densityevolution[J]. IEEE Communications Letters,2009,13(7):519–521.
[54] Pedarsani R, Hassani S H, Tal I et al. On the construction of polar codes[A].2011IEEEInternational Symposium on Information Theory Proceedings (ISIT)[C]. St. Petersburg:2011:11–15.
[55] Tal I, Vardy A. How to Construct Polar Codes[J]. IEEE Transactions on InformationTheory,2013,59(10):6562–6582.
[56] Honda J, Yamamoto H. Polar Coding without Alphabet Extension for AsymmetricModels[J]. IEEE Transactions on Information Theory,2013,59(12):7829–7838.
[57] Sahebi A G, Pradhan S S. Multilevel Channel Polarization for Arbitrary DiscreteMemoryless Channels[J]. IEEE Transactions on Information Theory,2013,59(12):7839–7857.
[58] Valipour M, Yousefi S. On Probabilistic Weight Distribution of Polar Codes[J]. IEEECommunications Letters,2013,17(11):2120–2123.
[59] Mori R, Tanaka T. Non-binary polar codes using Reed-Solomon codes and algebraicgeometry codes[A].2010IEEE Information Theory Workshop (ITW)[C]. Dublin:2010:1–5.
[60] Alamdar-Yazdi A, Kschischang F R. A Simplified Successive-Cancellation Decoder forPolar Codes[J]. IEEE Communications Letters,2011,15(12):1378–1380.
[61] Hassani S H, Urbanke R. Polar codes: Robustness of the successive cancellationdecoder with respect to quantization[A].2012IEEE International Symposium onInformation Theory Proceedings (ISIT)[C]. Cambridge:2012:1962–1966.
[62] Trifonov P. Efficient Design and Decoding of Polar Codes[J]. IEEE Transactions onCommunications,2012,60(11):3221–3227.
[63] Niu K, Chen K. CRC-Aided Decoding of Polar Codes[J]. IEEE CommunicationsLetters,2012,16(10):1668–1671.
[64] Li B, Shen H, Tse D. An Adaptive Successive Cancellation List Decoder for PolarCodes with Cyclic Redundancy Check[J]. IEEE Communications Letters,2012,16(12):2044–2047.
[65] Eslami A, Pishro-Nik H. On Finite-Length Performance of Polar Codes: Stopping Sets,Error Floor, and Concatenated Design[J]. IEEE Transactions on Communications,2013,61(3):919–929.
[66] Shin D-M, Lim S-C, Yang K. Design of Length-Compatible Polar Codes Based on theReduction of Polarizing Matrices[J]. IEEE Transactions on Communications,2013,61(7):2593–2599.
[67] Yuan B, Parhi K K. Low-Latency Successive-Cancellation Polar Decoder ArchitecturesUsing2-Bit Decoding[J]. IEEE Transactions on Circuits and Systems I: Regular Papers,2013, PP(99):1–14.
[68] Huang Z L, Diao C J, Chen M. Latency reduced method for modified successivecancellation decoding of polar codes[J]. Electronics Letters,2012,48(23):1505–15061506.
[69] Sarkis G, Gross W J. Increasing the Throughput of Polar Decoders[J]. IEEECommunications Letters,2013,17(4):725–728.
[70] Chen K, Niu K, Lin J R. List successive cancellation decoding of polar codes[J].Electronics Letters,2012,48(9):500–501.
[71] Tal I, Vardy A. List decoding of polar codes[A].2011IEEE International Symposiumon Information Theory Proceedings (ISIT)[C]. St. Petersburg:2011:1–5.
[72] Niu K, Chen K. Stack decoding of polar codes[J]. Electronics Letters,2012,48(12):695–697.
[73] Chen K, Niu K, Lin J. Improved Successive Cancellation Decoding of Polar Codes[J].IEEE Transactions on Communications,2013,61(8):3100–3107.
[74] Arkan E. A performance comparison of polar codes and Reed-Muller codes[J]. IEEECommunications Letters,2008,12(6):447–449.
[75] Goela N, Korada S B, Gastpar M. On LP decoding of polar codes[A].2010IEEEInformation Theory Workshop (ITW)[C]. Dublin:2010:1–5.
[76] Kahraman S, Celebi M E. Code based efficient maximum-likelihood decoding of shortpolar codes[A].2012IEEE International Symposium on Information TheoryProceedings (ISIT)[C]. Cambridge:2012:1967–1971.
[77] Arikan E. Source polarization[A].2010IEEE International Symposium on InformationTheory Proceedings (ISIT)[C]. Austin:2010:899–903.
[78] Korada S B, Urbanke R L. Polar Codes are Optimal for Lossy Source Coding[J].Information Theory, IEEE Transactions on,2010,56(4):1751–1768.
[79] Cronie H S, Korada S B. Lossless source coding with polar codes[A].2010IEEEInternational Symposium on Information Theory Proceedings (ISIT)[C]. Austin:2010:904–908.
[80] Karzand M, Telatar I E. Polar codes for q-ary source coding[A].2010IEEEInternational Symposium on Information Theory Proceedings (ISIT)[C]. Austin:2010:909–912.
[81] Sahebi A G, Pradhan S S. Polar codes for sources with finite reconstructionalphabets[A].201250th Annual Allerton Conference on Communication, Control, andComputing (Allerton)[C]. Monticello:2012:580–586.
[82] Trang V T T, Kang J W, Jang M et al. The performance of polar codes in distributedsource coding[A].2012Fourth International Conference on Communications andElectronics (ICCE)[C]. Hue:2012:196–199.
[83] Onay S. Polar codes for distributed source coding[J]. Electronics Letters,2013,49(5):346–348.
[84] Lv X, Liu R, Wang R. A Novel Rate-Adaptive Distributed Source Coding SchemeUsing Polar Codes[J]. IEEE Communications Letters,2013,17(1):143–146.
[85] Burshtein D, Strugatski A. Polar Write Once Memory Codes[J]. IEEE Transactions onInformation Theory,2013,59(8):5088–5101.
[86] Wilde M M, Renes J M. Quantum polar codes for arbitrary channels[A].2012IEEEInternational Symposium on Information Theory Proceedings (ISIT)[C]. Cambridge:2012:334–338.
[87] Guha S, Wilde M M. Polar coding to achieve the Holevo capacity of a pure-loss opticalchannel[A].2012IEEE International Symposium on Information Theory Proceedings(ISIT)[C]. Cambridge:2012:546–550.
[88] Wilde M M, Guha S. Polar Codes for Classical-Quantum Channels[J]. IEEETransactions on Information Theory,2013,59(2):1175–1187.
[89] Wilde M M, Guha S. Polar Codes for Degradable Quantum Channels[J]. IEEETransactions on Information Theory,2013,59(7):4718–4729.
[90] Leroux C, Raymond A J, Sarkis G et al. Hardware implementation ofsuccessive-cancellation decoders for polar codes[J]. Journal of Signal ProcessingSystems for Signal Image and Video Technology,2012,69(3):305–315.
[91] Leroux C, Raymond A J, Sarkis G et al. A Semi-Parallel Successive-CancellationDecoder for Polar Codes[J]. IEEE Transactions on Signal Processing,2013,61(2):289–299.
[92] Liu Y-H, Huang X, Vidojkovic M et al. An energy-efficient polar transmitter for IEEE802.15.6body area networks: system requirements and circuit designs[J]. IEEECommunications Magazine,2012,50(10):118–127127.
[93] Chen K, Niu K, Lin J-R. Practical polar code construction over parallel channels[J].IET Communications,2013,7(7):620–627.
[94] Zhang C, Parhi K K. Low-Latency Sequential and Overlapped Architectures forSuccessive Cancellation Polar Decoder[J]. IEEE Transactions on Signal Processing,2013,61(10):2429–2441.
[95] Korada S B. Polar codes for Channel and Source Coding[D]. Lausanne, Switzerland:EPFL,2009.
[96] Andersson M, Schaefer R F, Oechtering T J et al. Polar Coding for BidirectionalBroadcast Channels with Common and Confidential Messages[J]. IEEE Journal onSelected Areas in Communications,2013,31(9):1901–1908.
[97] Abbe E, Telatar I E. Polar Codes for the m-User Multiple Access Channel[J]. IEEETransactions on Information Theory,2012,58(8):5437–5448.
[98] Sasoglu E, Telatar E, Yeh E M. Polar Codes for the Two-User Multiple-AccessChannel[J]. IEEE Transactions on Information Theory,2013,59(10):6583–6592.
[99] Hof E, Sason I, Shamai S et al. Capacity-Achieving Polar Codes for ArbitrarilyPermuted Parallel Channels[J]. IEEE Transactions on Information Theory,2013,59(3):1505–1516.
[100] Bravo-Santos A. Polar Codes for the Rayleigh Fading Channel[J]. IEEECommunications Letters,2013,17(12):2352–2355.
[101] Koyluoglu O O, El Gamal H. Polar coding for secure transmission and keyagreement[J]. IEEE Transactions on Information Forensics and Security,2012,7(5):1472–1483.
[102] Seidl M, Schenk A, Stierstorfer C et al. Polar-Coded Modulation[J]. IEEE Transactionson Communications,2013,61(10):4108–4119.
[103] Bhattacharyya A. On a measure of divergence between two statistical populationsdefined by their probability distributions[J]. Bulletin of the Calcutta MathematicalSociety,1943(35):99–109.
[104] Maatouk G, Shokrollahi A. Analysis of the Second Moment of the LT Decoder[J]. IEEETransactions on Information Theory,2012,58(5):2558–2569.
[105] Ozyurt S, Torlak M. Exact Joint Distribution Analysis of Zero-Forcing V-BLAST Gainswith Greedy Ordering[J]. IEEE Transactions on Wireless Communications,2013,12(11):5377–5385.
[106] Arikan E. Systematic polar coding[J]. Communications Letters, IEEE,2011,15(8):860–862.
[107] Hu K, Castura J, Mao Y. Performance-Complexity Tradeoffs of Raptor Codes overGaussian Channels[J]. IEEE Communications Letters,2007,11(4):343–345.
[108] Zeng M, Calderbank R, Cui S. On Design of Rateless Codes over Dying BinaryErasure Channel[J]. IEEE Transactions on Communications,2012,60(4):889–894.
[109] Sanghavi S. Intermediate Performance of Rateless Codes[A]. IEEE Information TheoryWorkshop,2007. ITW’07[C]. Tahoe City:2007:478–482.
[110] Thomos N, Pulikkoonattu R, Frossard P. Growth Codes: Intermediate PerformanceAnalysis and Application to Video[J]. IEEE Transactions on Communications,2013,61(11):4710–4721.
[111] Zhang D, Li B, Li H. Intermedia-based video adaptation system: Design andimplementation[J]. Tsinghua Science and Technology,2012,17(2):113–127.
[112] Ong L, Johnson S J, Kellett C M. The Half-Duplex AWGN Single-Relay Channel: FullDecoding or Partial Decoding?[J]. IEEE Transactions on Communications,2012,60(11):3156–3160.
[113] Ghabeli L, Aref M-R. Comprehensive partial decoding approach for two-level relaynetworks[J]. IET Communications,2009,3(4):585–596.
[114] Meng J, Yang E. Interactive Encoding and Decoding Based on Binary LDPC CodesWith Syndrome Accumulation[J]. IEEE Transactions on Information Theory,2013,59(5):3068–3103.
[115] Chen L. Iterative Soft-Decision Decoding of Hermitian Codes[J]. IEEE Transactions onCommunications,2013,61(1):33–42.
[116] Zhou Y, Lai X, Li Y et al. Ant Colony Optimization With Combining GaussianEliminations for Matrix Multiplication[J]. IEEE Transactions on Cybernetics,2013,43(1):347–357.
[117] Salamanca L, Olmos P M, Murillo-Fuentes J J et al. Tree Expectation Propagation forML Decoding of LDPC Codes over the BEC[J]. IEEE Transactions onCommunications,2013,61(2):465–473.
[118] Saejoon Kim, Karam Ko, Sae-Young Chung. Incremental Gaussian eliminationdecoding of raptor codes over BEC[J]. IEEE Communications Letters,2008,12(4):307–309.
[119] MacKay D J C. Fountain codes[J]. IEE Proceedings of Communications,2005,152(6):1062–1068.
[120] Lin S, Costello D.差错控制编码[M].北京:人民文学出版社,1992.
[121] Lay D.线性代数及其应用[M].刘深泉,译.北京:机械工业出版社,2005.
[122] Bioglio V, Grangetto M, Gaeta R et al. On the fly gaussian elimination for LT codes[J].IEEE Communications Letters,2009,13(12):953–955.
[123] Bai B, Chen W, Letaief K B et al. Outage Exponent: A Unified Performance Metric forParallel Fading Channels[J]. IEEE Transactions on Information Theory,2013,59(3):1657–1677.
[124] Hachem W, Moulines E, Roueff F. Error Exponents for Neyman-Pearson Detection of aContinuous-Time Gaussian Markov Process From Regular or Irregular Samples[J].IEEE Transactions on Information Theory,2011,57(6):3899–3914.
[125] Cohen K, Leshem A. Performance Analysis of Likelihood-Based Multiple Access forDetection Over Fading Channels[J]. IEEE Transactions on Information Theory,2013,59(4):2471–2481.
[126] Gallager R G. Information Theory and Reliable Communication[M]. New York, UnitedStates of America: John Wiley&Sons,1976.
[127] Land I, Huber J. Information combining[J]. Foundation Trends CommunicationInformation Theory,2006,3(3):227–330.
[128] Bhattacharyya A. On a measure of divergence between two statistical populationsdefined by their probability distributions[J]. Bulletin of the Calcutta MathematicalSociety,1943,35:99–109.
[129] Yuan J. Active contour driven by region-scalable fitting and local Bhattacharyyadistance energies for ultrasound image segmentation[J]. IET Image Processing,2012,6(8):1075–1083.
[130] Lou Y, Irimia A, Vela P A et al. Multimodal Deformable Registration of TraumaticBrain Injury MR Volumes via the Bhattacharyya Distance[J]. IEEE Transactions onBiomedical Engineering,2013,60(9):2511–2520.
[131] Nielsen F, Boltz S. The Burbea-Rao and Bhattacharyya Centroids[J]. IEEETransactions on Information Theory,2011,57(8):5455–5466.
[132] Chu J P K, Adve R S, Eckford A W. Using the Bhattacharyya parameter for design andanalysis of cooperative wireless systems[J]. IEEE Transactions on WirelessCommunications,2009,8(3):1384–1395.
[133] Varshney L R. Performance of LDPC codes under faulty iterative decoding[J].Information Theory, IEEE Transactions on,2011,57(7):4427–4444.
[134] J. Pearl. Probabilistic reasoning in intelligent systems: networks of plausibleinference[M].1988.
[135] Cooper M. Antennas get smart[J]. Scientific American,2003,289(1):48–55.
[136] Van der Meulen E C. Three-terminal communication channels[J]. Advances in AppliedProbability,1971,3(01):120–154.
[137] Sato H. Information transmission through a channel with relay[M]. University ofHawaii, Honolulu: Technology Republic,1976.
[138] Cover T, Gamal A E. Capacity theorems for the relay channel[J]. IEEE Transactions onInformation theory,1979,25(05):572–584.
[139] Gamal A E, Aref M. The capacity of the semideterministic relay channel (Corresp.)[J].IEEE Transactions on Information Theory,1982,28(3):536–536.
[140] El Gamal A, Zahedi S. Capacity of a class of relay channels with orthogonalcomponents[J]. IEEE Transactions on Information Theory,2005,51(5):1815–1817.
[141] Cover T. Elements of Information Theory[M]. New York: Wiley,1991.
[142] Zeng C-M, Kuhlmann F, Buzo A. Achievability proof of some multiuser channelcoding theorems using backward decoding[J]. IEEE Transactions on InformationTheory,1989,35(6):1160–1165.
[143]3GPP Technical Specification25.106, UTRA repeater radio transmission andreception[S].
[144]3GPP Technical Specification36.106, Evolved Universal Terrestrial Radio Access(E_UTRA): FDD Repeater radio transmission and reception[S].
[145] Host-Madsen A, Zhang J. Capacity bounds and power allocation for wireless relaychannels[J]. IEEE Transactions on Information Theory,2005,51(6):2020–2040.
[146] Host-Madsen A. Capacity bounds for Cooperative diversity[J]. IEEE Transactions onInformation Theory,2006,52(4):1522–1544.
[147] El Gamal A, Mohseni M, Zahedi S. Bounds on capacity and minimum energy-per-bitfor AWGN relay channels[J]. IEEE Transactions on Information Theory,2006,52(4):1545–1561.
[148] Wang B, Zhang J, Host-Madsen A. On the capacity of MIMO relay channels[J]. IEEETransactions on Information Theory,2005,51(1):29–43.
[149] Chun Y J, Kim D I, Kim S W. Optimization of Network Coded MIMO Transmission inMultiple-Access Relay Network[J]. IEEE Transactions on Wireless Communications,2013,12(5):2436–2444.
[150] Brante G, Souza R D, Garcia-Frias J. Spatial Diversity Using Analog Joint SourceChannel Coding in Wireless Channels[J]. IEEE Transactions on Communications,2013,61(1):301–311.
[151] Muralidharan V T, Rajan B S. Physical Layer Network Coding for the K-User MultipleAccess Relay Channel[J]. IEEE Transactions on Wireless Communications,2013,12(6):3107–3119.
[152] Joda R, Lahouti F. Network Code Design for Orthogonal Two-Hop Network withBroadcasting Relay: A Joint Source-Channel-Network Coding Approach[J]. IEEETransactions on Communications,2012,60(1):132–142.
[153]3GPP Technical Specification36.216, Evolved Universal Terrestrial Radio Access(E_UTRA): Physical Layer for Relaying Operation (Release10)[S].
[154] Ding Z, Cumanan K, Ma Z et al. Linear Detection for Cooperative Multiple-AccessTransmission Protocols[J]. IEEE Transactions on Vehicular Technology,2013,62(6):2807–2812.
[155] Dabora R, Servetto S D. Broadcast Channels With Cooperating Decoders[J]. IEEETransactions on Information Theory,2006,52(12):5438–5454.
[156] Behboodi A, Piantanida P. Cooperative Strategies for Simultaneous and BroadcastRelay Channels[J]. IEEE Transactions on Information Theory,2013,59(3):1417–1443.
[157] Zhang Z, Lv T, Yang S. Round-Robin Relaying With Diversity inAmplify-and-Forward Multisource Cooperative Communications[J]. IEEETransactions on Vehicular Technology,2013,62(3):1251–1266.
[158] Chen Y. Chernoff information path loss in wireless relay sensor networks[J]. IETWireless Sensor Systems,2012,2(3):201–213.
[159] Razi A, Afghah F, Abedi A. Power Optimized DSTBC Assisted DMF Relaying inWireless Sensor Networks with Redundant Super Nodes[J]. IEEE Transactions onWireless Communications,2013,12(2):636–645.
[160] Chu S, Wang X, Yang Y. Exploiting Cooperative Relay for High PerformanceCommunications in MIMO Ad Hoc Networks[J]. IEEE Transactions on Computers,2013,62(4):716–729.
[161] Munari A, Levorato M, Zorzi M. On the Impact of Carrier Sense Based MediumAccess Control on Cooperative Schemes in Wireless Ad Hoc Networks[J]. IEEETransactions on Communications,2012,60(10):3032–3046.
[162] Lee D, Seo H, Clerckx B et al. Coordinated multipoint transmission and reception inLTE-advanced: deployment scenarios and operational challenges[J]. IEEECommunications Magazine,2012,50(2):148–155.
[163] Zhao J, Quek T Q S, Lei Z. Coordinated Multipoint Transmission with LimitedBackhaul Data Transfer[J]. IEEE Transactions on Wireless Communications,2013,12(6):2762–2775.
[164] Liu A, Lau V K N. Cache-Enabled Opportunistic Cooperative MIMO for VideoStreaming in Wireless Systems[J]. IEEE Transactions on Signal Processing,2014,62(2):390–402.
[165] Monteiro V, Mumtaz S, Rodriguez J et al. Energy efficient relay-aided shared LTEnetwork using CoMP and LB[A]. Future Network and Mobile Summit(FutureNetworkSummit),2013[C].2013:1–9.
[166] Liang H, Zhuang W. Cooperative data dissemination via roadside WLANs[J]. IEEECommunications Magazine,2012,50(4):68–74.
[167] Nishide K, Kubo H, Shinkuma R et al. Detecting Hidden and Exposed TerminalProblems in Densely Deployed Wireless Networks[J]. IEEE Transactions on WirelessCommunications,2012,11(11):3841–3849.
[168] Lin X, Li X. Achieving Efficient Cooperative Message Authentication in Vehicular AdHoc Networks[J]. IEEE Transactions on Vehicular Technology,2013,62(7):3339–3348.
[169] Zheng K, Liu F, Zheng Q et al. A Graph-Based Cooperative Scheduling Scheme forVehicular Networks[J]. IEEE Transactions on Vehicular Technology,2013,62(4):1450–1458.
[170] Li B, Li H, Wang W et al. Performance Analysis and Optimization for Energy-EfficientCooperative Transmission in Random Wireless Sensor Network[J]. IEEE Transactionson Wireless Communications,2013,12(9):4647–4657.
[171] Jung J W, Weitnauer M A. On Using Cooperative Routing for Lifetime Optimization ofMulti-Hop Wireless Sensor Networks: Analysis and Guidelines[J]. IEEE Transactionson Communications,2013,61(8):3413–3423.
[172] Moazzez-Estanjini R, Wang J, Paschalidis I C. Scheduling Mobile Nodes forCooperative Data Transport in Sensor Networks[J]. IEEE/ACM Transactions onNetworking,2013,21(3):974–989.
[173] Andersson M, Rathi V, Thobaben R et al. Nested polar codes for wiretap and relaychannels[J]. IEEE Communications Letters,2010,14(8):752–754.
[174] Wu F, Xing C, Zhao S et al. Encrypted polar codes for wiretap channel[A].20122ndInternational Conference on Computer Science and Network Technology (ICCSNT)[C].Changchun:2012:579–583.
[175] Blasco-Serrano R, Thobaben R, Rathi V et al. Polar codes for compress-and-forward inbinary relay channels[A].2010Conference Record of the Forty Fourth AsilomarConference on Signals, Systems and Computers (ASILOMAR)[C]. Pacific Grove:2010:1743–1747.
[176] Blasco-Serrano R, Thobaben R, Andersson M et al. Polar codes for cooperativerelaying[J]. IEEE Transactions on Communications,2012,60(11):3263–3273.
[177] Bravo-Santos A. Polar codes for Gaussian degraded relay channels[J]. IEEECommunications Letters,2013,17(2):365–368.
[178] Zhang Z, Duman T M. Capacity-approaching turbo coding and iterative decoding forrelay channels[J]. IEEE Transactions on Communications,2005,53(11):1895–1905.
[179] Dahlman E, Parkvall S, Skold J.4G LTE/LTE-Advanced for Mobile Broadband[M].Salt Lake City, UT, United States: Academic Press,2011.
[180] Alves H, da Costa D B, Souza R D et al. Performance of Block-Markov Full DuplexRelaying with Self Interference in Nakagami-m Fading[J]. IEEE WirelessCommunications Letters,2013,2(3):311–314.
[181] Ma S, Zhang J-K. Noncoherent Orthogonal Distributed Space-Time Block Codes forAmplify-and-Forward Half-Duplex Cooperative Relay Channels[J]. IEEE Transactionson Vehicular Technology,2012,61(6):2854–2858.
[182] Mesbah W, Davidson T N. Weighted-Sum-Rate Maximization in Certain Half-DuplexCooperative Systems[J]. IEEE Wireless Communications Letters,2012,1(3):213–216.
[183] Yang S, Lv T, Maunder R G et al. From Nominal to True A Posteriori Probabilities: AnExact Bayesian Theorem Based Probabilistic Data Association Approach for IterativeMIMO Detection and Decoding[J]. IEEE Transactions on Communications,2013,61(7):2782–2793.
[184] Kwon H, Lee J, Kang I. Successive Interference Cancellation via Rank-ReducedMaximum A Posteriori Detection[J]. IEEE Transactions on Communications,2013,61(2):628–637.
[185] Irawan A, Anwar K, Matsumoto T. Combining-after-Decoding Turbo Hybrid ARQ byUtilizing Doped-Accumulator[J]. IEEE Communications Letters,2013,17(6):1212–1215.
[186] Huo Y, El-Hajjar M, Hanzo L. Inter-Layer FEC Aided Unequal Error Protection forMultilayer Video Transmission in Mobile TV[J]. IEEE Transactions on Circuits andSystems for Video Technology,2013,23(9):1622–1634.
[187]樊平毅.网络信息论[M].北京:清华大学出版社,2009.
[188] Cover T M, Thomas J A. Elements of Information Theory[M]. New York: Wiley,1991.
[189] Parzysz F, Vu M, Gagnon F. Energy Minimization for the Half-Duplex Relay Channelwith Decode-Forward Relaying[J]. IEEE Transactions on Communications,2013,61(6):2232–2247.
[190] Zhang Z, Duman T M. Capacity approaching Turbo coding for half-duplex relaying[J].IEEE Transactions on Communications,2007,55(9):1822–1822.
[191] Zou Y, Wang X, Shen W. Optimal Relay Selection for Physical-Layer Security inCooperative Wireless Networks[J]. IEEE Journal on Selected Areas in Communications,2013,31(10):2099–2111.
[192] Chatzidiamantis N D, Michalopoulos D S, Kriezis E E et al. Relay selection protocolsfor relay-assisted free-space optical systems[J]. IEEE/OSA Journal of OpticalCommunications and Networking,2013,5(1):92–103.
[193] Brandao Harboe P, Souza J R. Passive Optical Network: Characteristics, Deployment,and Perspectives[J]. Latin America Transactions, IEEE (Revista IEEE America Latina),2013,11(4):995–1000.
[194] Cvijetic N, Tanaka A, Cvijetic M et al. Novel Optical Access and Digital ProcessingArchitectures for Future Mobile Backhaul[J]. Journal of Lightwave Technology,2013,31(4):621–627.
[195] Kazaura K, Wakamori K, Matsumoto M et al. RoFSO: A universal platform forconvergence of fiber and free-space optical communication networks[J]. IEEECommunications Magazine,2010,48(2):130–137.
[196] Kedar D, Arnon S. Urban optical wireless communication networks: the mainchallenges and possible solutions[J]. IEEE Communications Magazine,2004,42(5):S2–S7.
[197] Kartalopoulos S. Free Space Optical Networks for Ultra-Broad Band Services[M]. NewYork: Wiley,2011.
[198] Faruolo M, Coviello I, Lacava T et al. A Multi-Sensor Exportable Approach forAutomatic Flooded Areas Detection and Monitoring by a Composite SatelliteConstellation[J]. IEEE Transactions on Geoscience and Remote Sensing,2013,51(4):2136–2149.
[199]谌娟,柯熙政,程婷.自由空间光多输入多输出系统中的差分空时码[J].光学学报,2013(02):44–49.
[200]刘式达,梁福明.大气湍流[M].第1版.北京:北京大学出版社,2008.
[201]罗鹏飞.短距离无线光通信若干关键技术的研究[D].北京邮电大学,2013.
[202] Li J, Liu J Q, Taylor D P. Optical Communication Using Subcarrier PSK IntensityModulation Through Atmospheric Turbulence Channels[J]. IEEE Transactions onCommunications,2007,55(8):1598–1606.
[203] Djordjevic I B, Anguita J A, Vasic B. Error-Correction CodedOrbital-Angular-Momentum Modulation for FSO Channels Affected by Turbulence[J].Journal of Lightwave Technology,2012,30(17):2846–2852.
[204]黄根全.大气湍流下无线光通信信道性能研究[J].西安工业大学学报,2011(05):413–417.
[205] Parry G. Measurement of Atmospheric Turbulence Induced Intensity Fluctuations in aLaser Beam[J]. Optica Acta: International Journal of Optics,1981,28(5):715–728.
[206] Phillips R L, Andrews L C. Measured statistics of laser-light scattering in atmosphericturbulence[J]. Journal of the Optical Society of America,1981,71(12):1440–1445.
[207] Andrews L C, Phillips R L, Hopen C Y et al. Theory of optical scintillation[J]. Journalof the Optical Society of America A,1999,16(6):1417–1429.
[208] Al-Habash M A, Phillips R L, Andrews L C. Mathematical model for the irradianceprobability density function of a laser beam propagating through turbulent media[J].Optical Engineering,2001,40(8):1554–1562.
[209] Perlot N. Characterization of Signal Fluctuations in Optical Communications withIntensity Modulation and Direct Detection Through the Turbulent AtmosphericChannel[M]. Berichte aus der Kommunikationstechnik: Shaker Verlag GmbH,2005.
[210] Bhise A, Vyavahare P D. Improved low complexity hybrid turbo codes and unionbound analysis[J]. IET Communications,2011,5(4):512–518.
[211] Hadj Abderrahmane L. Design of a new interleaver using cross entropy method forturbo coding[J]. IET Communications,2013,7(9):828–835.
[212] Mansour M M. Fast Pruned Interleaving[J]. IEEE Transactions on Communications,2013,61(3):817–831.
[213] Uysal M, Li J, Yu M. Error rate performance analysis of coded free-space optical linksover gamma-gamma atmospheric turbulence channels[J]. IEEE Transactions onWireless Communications,2006,5(6):1229–1233.
[214] Gradshteyn I S, Ryzhik I M. Table of Integrals, Series and Products (the4thEdition)[M]. Amsterdam, Netherlands: Elsevier Science,2000.
[215] Greco J A. Design of the high-speed framing, FEC, and interleaving hardware used in a5.4km free-space optical communication experiment[J]. SPIE Proceedings,2009,7464:746409–1–746409–7.
[216] Mori R, Tanaka T. Performance and construction of polar codes on symmetricbinary-input memoryless channels[A]. IEEE International Symposium on InformationTheory,2009. ISIT2009[C].2009:1496–1500.
[217] Richardson T, Urbanke R. Modern Coding Theory[M]. Cambridge, U. K.: CambridgeUniversity Press,2008.
[218] Naila C B, Wakamori K, Matsumoto M et al. Transmission analysis of digital TVsignals over a Radio-on-FSO channel[J]. IEEE Communications Magazine,2012,50(8):137–144.
[219] Chow C W, Yeh C H, Liu Y F et al. Mitigation of Optical Background Noise inLight-Emitting Diode (LED) Optical Wireless Communication Systems[J]. IEEEPhotonics Journal,2013,5(1):7900307–7900307.
[220] Takai I, Ito S, Yasutomi K et al. LED and CMOS Image Sensor Based Optical WirelessCommunication System for Automotive Applications[J]. IEEE Photonics Journal,2013,5(5):6801418–6801418.