LDPC码快速及低错误平层译码算法研究
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摘要
LDPC码具有逼近香农限的良好译码性能，故而得到了广泛的研究。为了获取更好的译码性能，LDPC码的各种译码算法得到深入的研究。置信传播具有良好的译码性能，但是在其译码过程中易出现较高的错误平层，因此无法满足一些对数据传输质量要求极高的通信系统数据高可靠传输的需求；改进型比特翻转算法计算复杂度较低可以用于构造大吞吐量LDPC译码器，能够更好地满足高速数据传输系统纠错译码的需求。本文主要研究置信传播算法的低错误平层译码以及改进型比特翻转算法的快速译码等问题，主要研究内容如下。
首先，为了提高LDPC译码器的译码速度，本文提出了并行比特选择机制来降低加权比特翻转算法硬件实现时挑选翻转比特造成的时延。具体来讲，依据接收向量中错误比特均匀分布的特点，将所有比特划分成若干子块，从每个子块挑选出一个比特作为候选翻转比特，最后根据一定的准则从这些候选比特中选择部分比特进行翻转完成译码迭代。此外，本文还通过引入树形搜索技术降低候选比特查找的计算复杂度，进一步增加算法硬件实现时的译码速度。
其次，为了提高可靠性权重比特翻转(reliability ratio-based weighted bit-flipping,RRWBF)算法的译码速度，本文提出多比特翻转机制来加快RRWBF算法的收敛速度。具体来讲，在每次译码迭代中，根据伴随向量的重量选择合理数量的比特，然后同时翻转这些比特的硬判结果来完成迭代译码，进而有效的解决RRWBF算法中由单比特翻转造成的收敛速度慢的问题。另外，本文还提出了一种新颖的迭代提前停止机制用于消除算法译码过程中出现的无效迭代，从而进一步提高算法的收敛速度。但是，使用多比特翻转机制的RRWBF算法，译码过程中出现与单比特翻转类似的循环翻转现象，影响其译码性能。为此，本文提出一种循环翻转消除机制来破坏多比特翻转译码过程中产生的循环翻转，进而提高其译码性能。
本文还提出稳定陷阱集的概念来描述LDPC码译码过程中出现的错误平层现象，并且相应提出一种基于稳定陷阱集破坏的改进置信传播算法用以降低LDPC码的错误平层。具体来讲，稳定陷阱集中比特节点信息值的排名会随着译码迭代进行不断下降。利用这一特性可以更加高效准确地将这些节点挑选出来，之后将其初始对数似然值翻转达到集破坏的目的。最后将修正后的初始似然值序列送入译码器进行翻转译码尝试以降低LDPC码的错误平层。另外，在置信传播算法的译码过程中会出现大量的震荡错误，即一些比特节点的硬判决结果在译码过程中呈现震荡状态从而导致译码失败。本文提出不稳定陷阱集的概念来描述这种错误类型，并且相应提出一种改进型置信传播算法以消除译码过程中出现的震荡错误进而达到提高LDPC码译码性能的目的。
最后，本文针对欧氏几何LDPC码码字的循环特性以及fast weighted bitflipping (FWBF)算法的结构特点设计高速LDPC译码器。欧氏几何LDPC码具有良好的低错误平层特性，结合FWBF算法的快速译码特性，可以很好满足光通信等高速、高质量传输通信系统的要求。
Because of its near Shannon-limit performance, low-density parity-check (LDPC)codes has obtained considerable study. In order to obtain a good decoding performance,all the decoding algorithms of LDPC codes have been extensively studied. Beliefpropagation (BP) algorithm has good decoding performance but appears a high errorfloor in its decoding process. Hence, BP cannot work well in the communicationssystem requiring an extremely low error rate. The modified weighted bit flipping (WBF)algorithms can be used to design a high-speed decoder because of their lowcomputational complexity, which makes the WBF-based algorithms work well in thehigh-speed data transmission system. In this paper, we study the modified BP algorithmto lower the error floor and the enhanced WBF algorithm to implement the fastdecoding of the LDPC codes.
Firstly, In order to improve the decoding speed of LDPC codes, a fast weighted bitflipping algorithm with parallel bit-chosen is proposed to lower the delay of choosingthe flipped bit. In this scheme, all the bits are first divided into several blocks accordingto the uniform error distribution in the received vector. And then, one bit is chosen fromeach block to form the candidate set of the flipped bits. Finally, a proper number of bitsare chosen from the candidate set and flipped to implement the flipping decoding.Furthermore, the tree sorting method is adopted to decrease the computationalcomplexity of the key module of the proposed algorithm. The proposed scheme and themethod of hardware implement can achieve significant improvement in the decodingspeed.
Secondly, in order to improve the decoding speed of the reliability ratio-basedweighted bit-flipping (RRWBF) algorithm, we propose a multiple-bits selectionmechanism to accelerate the decoding convergence of the RRWBF algorithm.Specifically, based on the weight of syndrome vector, reasonable quantities of bits areselected to flip in each iteration. This mechanism can effectively solve the problem oflow convergence speed of single-bit flipping algorithm. In addition, a novel earlystopping criterion is also introduced which can further raise up the convergence speedof the LDPC decoding. However, the RRWBF algorithm with the multiple-bits selection mechanism will appear the bit-repeated flipping, which can impair thedecoding performance of the RRWBF algorithm. Hence, a bit-repeated flippingelimination mechanism is proposed to reduce the bit-repeated flipping in the process ofthe multiple-bits flipping decoding.
Thirdly, in order to more exactly describe the error-floor phenomenon in the iterativedecoding of LDPC codes, a modified concept of the stable trapping set is introduced.Based on this new concept, an improved belief propagation algorithm with set-breakingmechanism is proposed to lower the error-floors of LDPC codes. Specifically, messageranking of the bit nodes in the stable trapping sets will be greatly lowered than that ofother bit nodes in the iterative decoding process. By using this characteristic to label thebit nodes in the set, their initial log likelihood ratios will be flipped to break the stabletrapping set and then restart to decode. In the decoding process of the BP algorithm, itwill appear much oscillation error, namely, the hard-decision digits of some bit nodesare always changed, which can result in decoding failure. In order to describe this typeof decoding failure, a modified concept of the unstable trapping set is introduced. Basedon this new concept, an improved belief propagation algorithm is proposed to eliminatethe oscillation error to improve the decoding performance of the LDPC codes.
Finally, a FWBF decoder is designed to implement the high-speed decoding ofEG-LDPC codes according to their cyclic characteristic. EG-LDPC codes have a lowerror floor and FWBF has a fast decoding speed. Hence, the FWBF decoder based onEG-LDPC codes can well applied in the communications systems which require thedata is transmitted with high speed and reliablity.
首先，为了提高LDPC译码器的译码速度，本文提出了并行比特选择机制来降低加权比特翻转算法硬件实现时挑选翻转比特造成的时延。具体来讲，依据接收向量中错误比特均匀分布的特点，将所有比特划分成若干子块，从每个子块挑选出一个比特作为候选翻转比特，最后根据一定的准则从这些候选比特中选择部分比特进行翻转完成译码迭代。此外，本文还通过引入树形搜索技术降低候选比特查找的计算复杂度，进一步增加算法硬件实现时的译码速度。
其次，为了提高可靠性权重比特翻转(reliability ratio-based weighted bit-flipping,RRWBF)算法的译码速度，本文提出多比特翻转机制来加快RRWBF算法的收敛速度。具体来讲，在每次译码迭代中，根据伴随向量的重量选择合理数量的比特，然后同时翻转这些比特的硬判结果来完成迭代译码，进而有效的解决RRWBF算法中由单比特翻转造成的收敛速度慢的问题。另外，本文还提出了一种新颖的迭代提前停止机制用于消除算法译码过程中出现的无效迭代，从而进一步提高算法的收敛速度。但是，使用多比特翻转机制的RRWBF算法，译码过程中出现与单比特翻转类似的循环翻转现象，影响其译码性能。为此，本文提出一种循环翻转消除机制来破坏多比特翻转译码过程中产生的循环翻转，进而提高其译码性能。
本文还提出稳定陷阱集的概念来描述LDPC码译码过程中出现的错误平层现象，并且相应提出一种基于稳定陷阱集破坏的改进置信传播算法用以降低LDPC码的错误平层。具体来讲，稳定陷阱集中比特节点信息值的排名会随着译码迭代进行不断下降。利用这一特性可以更加高效准确地将这些节点挑选出来，之后将其初始对数似然值翻转达到集破坏的目的。最后将修正后的初始似然值序列送入译码器进行翻转译码尝试以降低LDPC码的错误平层。另外，在置信传播算法的译码过程中会出现大量的震荡错误，即一些比特节点的硬判决结果在译码过程中呈现震荡状态从而导致译码失败。本文提出不稳定陷阱集的概念来描述这种错误类型，并且相应提出一种改进型置信传播算法以消除译码过程中出现的震荡错误进而达到提高LDPC码译码性能的目的。
最后，本文针对欧氏几何LDPC码码字的循环特性以及fast weighted bitflipping (FWBF)算法的结构特点设计高速LDPC译码器。欧氏几何LDPC码具有良好的低错误平层特性，结合FWBF算法的快速译码特性，可以很好满足光通信等高速、高质量传输通信系统的要求。
Because of its near Shannon-limit performance, low-density parity-check (LDPC)codes has obtained considerable study. In order to obtain a good decoding performance,all the decoding algorithms of LDPC codes have been extensively studied. Beliefpropagation (BP) algorithm has good decoding performance but appears a high errorfloor in its decoding process. Hence, BP cannot work well in the communicationssystem requiring an extremely low error rate. The modified weighted bit flipping (WBF)algorithms can be used to design a high-speed decoder because of their lowcomputational complexity, which makes the WBF-based algorithms work well in thehigh-speed data transmission system. In this paper, we study the modified BP algorithmto lower the error floor and the enhanced WBF algorithm to implement the fastdecoding of the LDPC codes.
Firstly, In order to improve the decoding speed of LDPC codes, a fast weighted bitflipping algorithm with parallel bit-chosen is proposed to lower the delay of choosingthe flipped bit. In this scheme, all the bits are first divided into several blocks accordingto the uniform error distribution in the received vector. And then, one bit is chosen fromeach block to form the candidate set of the flipped bits. Finally, a proper number of bitsare chosen from the candidate set and flipped to implement the flipping decoding.Furthermore, the tree sorting method is adopted to decrease the computationalcomplexity of the key module of the proposed algorithm. The proposed scheme and themethod of hardware implement can achieve significant improvement in the decodingspeed.
Secondly, in order to improve the decoding speed of the reliability ratio-basedweighted bit-flipping (RRWBF) algorithm, we propose a multiple-bits selectionmechanism to accelerate the decoding convergence of the RRWBF algorithm.Specifically, based on the weight of syndrome vector, reasonable quantities of bits areselected to flip in each iteration. This mechanism can effectively solve the problem oflow convergence speed of single-bit flipping algorithm. In addition, a novel earlystopping criterion is also introduced which can further raise up the convergence speedof the LDPC decoding. However, the RRWBF algorithm with the multiple-bits selection mechanism will appear the bit-repeated flipping, which can impair thedecoding performance of the RRWBF algorithm. Hence, a bit-repeated flippingelimination mechanism is proposed to reduce the bit-repeated flipping in the process ofthe multiple-bits flipping decoding.
Thirdly, in order to more exactly describe the error-floor phenomenon in the iterativedecoding of LDPC codes, a modified concept of the stable trapping set is introduced.Based on this new concept, an improved belief propagation algorithm with set-breakingmechanism is proposed to lower the error-floors of LDPC codes. Specifically, messageranking of the bit nodes in the stable trapping sets will be greatly lowered than that ofother bit nodes in the iterative decoding process. By using this characteristic to label thebit nodes in the set, their initial log likelihood ratios will be flipped to break the stabletrapping set and then restart to decode. In the decoding process of the BP algorithm, itwill appear much oscillation error, namely, the hard-decision digits of some bit nodesare always changed, which can result in decoding failure. In order to describe this typeof decoding failure, a modified concept of the unstable trapping set is introduced. Basedon this new concept, an improved belief propagation algorithm is proposed to eliminatethe oscillation error to improve the decoding performance of the LDPC codes.
Finally, a FWBF decoder is designed to implement the high-speed decoding ofEG-LDPC codes according to their cyclic characteristic. EG-LDPC codes have a lowerror floor and FWBF has a fast decoding speed. Hence, the FWBF decoder based onEG-LDPC codes can well applied in the communications systems which require thedata is transmitted with high speed and reliablity.
引文
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