软判决译码综述

本文首先介绍了纠错码中软判决译码算法提出的背景,概述了线性分组码的主要几类软判决译码算法的基本概念和发展过程,它们的优缺点和发展趋势。最后介绍了卷积码软判决译码算法发展概况。     

RS码短码的软判决方法

RS码是差错控制领域中一种重要的线性分组码,而相对于普通的硬判决来说,软判决译码具有纠错能力强的优势。针对RS码(15,11),提出了使用Chase算法实现非二进制码的软判决译码方法,并通过计算机模拟,给出在AWGN信道中的译码结果。     

神经网络在分组码软判决译码中的应用

本文对线性分组码构造了一个神经网络软判决译码器，并提出了循环码的一个神经网络软判决译码算法。对Ｇｏｌａｙ码的计算机仿真表明，新算法不仅译码速度快，而且，具有优越的性能。     

并行级联分组码的一种新的迭代译码算法

并行级联分组码比串行级联分组码具有更高的码率,基于LLR计算的Turbo迭代译码算法使其内外分量码均做到了软判决译码。通过引入校正因子a（m）,将接收信息与子译码器的输出软信息进行线性叠加反馈能在省去繁琐的LLR计算的情况下实现并行级联分组码的Turbo迭代译码。仿真研究表明,若将译码器的输出进行简单的相关运算,可进一步改善译码器性能。     

Rayleigh衰落信道中分组码最大似然译码的性能

摆脱了传统代数译码方法,对分组码进行基于广义阵列码（ＧＡＣ）结构的网格译码（Ｔｒｅｌｌｉｓ ｄｅｃｏｄｉｎｇ）,研究了Ｒａｙｌｅｉｇｈ衰落信道中分组码与这种软判决最大似然译码方法相结合的性能。模拟结果显示。分组码采用网格译码,可为移动衰落信道带来显著的性能改善。     

一类三元线性分组码的译码

Ｐｌｅｓｓ［１］证明了三元（１２，６，６）Ｇｏｌａｙ码具有一种双层结构，并据此给出了该码的快速硬判决译码算法。本文推广了Ｇｏｌａｙ码的Ｐｌｅｓｓ结构，给出了由三元（ｎ，ｋ，ｄ）线性分组码构造的三元（３，ｎ＋ｋ，≥ｍｉｎ（ｎ，２ｄ，６））线性分组码，其中包括（１２，６，６）Ｇｏｌａｙ码和（１８，９，６）码，并以三元（１８，９，６）码为例给出了这类码的最大似然软判决译码算法。     

LDPC编译码算法分析

低密度奇偶校验(LDPC)码是一种线性分组码,其纠错能力可以接近香农极限。针对LDPC码的编译码问题,分析了校验矩阵的构造方法。给出了LDPC码的编码算法以及算法的实现结构。分析了基于软判决的置信传播(BP)译码算法,并给出了可以进一步降低计算复杂度的简化译码方法。通过仿真对比了不同的译码算法在高斯信道下的译码性能。     

TETRA中Reed-Muller码的大数逻辑译码方法

TETRA数字集群移动通信系统的物理层协议中采用了缩短Reed-Muller(RM)码,它与经典RM码的差异极大,无法采用Reed大数逻辑译码算法.根据正交校验矩阵的特点,提出了一种一般线性分组码的正交校验矩阵的穷举搜索算法.使用该算法搜索了缩短RM码的正交校验矩阵,对搜索速度进行了分析.证明了该码是两步完全可正交码,给出了它的Massey大数逻辑译码方法.仿真结果表明,无论是硬判决还是软判决,该译码方法的纠错性能都优于伴随式译码方法.     

线性分组码的神经网络译码

介绍了神经网络与线性分组码之间的关系，并在文献[1]的基础上证明了软判决译码与求解能量函数最大值之间的等价性，然后以(7，4，3)汉明码为例介绍了神经网络在循环码硬判决、软判决译码中的应用。     

软判决多步法相关攻击在PN码快速捕获中的应用

针对非协作接收的扩频通信系统,低信噪比情况下长周期且生成多项式抽头数较多的扩频码的快速捕获问题一直是研究的重点和难点。本文借鉴密码学中密钥攻击基本思想,提出一种基于软判决多步法快速相关攻击的长周期扩频码快速捕获新算法。通过将PN序列看成线性分组码,将序列相位捕获看成线性分组码的解码,采用软判决方法进行分步串行译码,充分利用序列本身的软信息,实现低信噪比情况下长周期扩频序列的快速捕获。理论分析和仿真结果表明本文算法与多项式抽头个数无关,具有较好的捕获性能,能够在低信噪比下稳定工作;与硬判决相关攻击方法相比,本文算法大约有3．5 dB以上的性能提升。     

一类循环码的神经网络软判决译码算法

本文分析了一类循环码的结构特性，提出了这类循环码的神经网络软判决译码算法。新算法的复杂度比现有一般的神经网络译码算法要低得多，而其译码性能接近大似然译码。     

Two Bit-Flipping Decoding Algorithms for Low-Density Parity-Check Codes

In this letter, a low complexity decoding algorithm for binary linear block codes is applied to low-density paritycheck (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performances at smaller complexity.     

Soft decoding of linear block codes with differential phasedetection

Soft decoding of linear block codes is considered over a Gaussian channel. A noncoherent soft decision differential phase detector that operates on many preselected regions is considered for detection. Numerical results demonstrate the improvement of soft decoding over hard decoding and the effect of the number of regions in the phase detector     

Iterative reliability-based decoding of linear block codes with adaptive belief propagation

In this letter, an iterative decoding algorithm for linear block codes combining reliability-based decoding with adaptive belief propagation decoding is proposed. At each iteration, the soft output values delivered by the adaptive belief propagation algorithm are used as reliability values to perform reduced order reliability-based decoding of the code considered. This approach allows to bridge the gap between the error performance achieved by the lower order reliability-based decoding algorithms which remain sub-optimum, and the maximum likelihood decoding, which is too complex to be implemented for most codes employed in practice. Simulations results for various linear block codes are given and elaborated.     

Iterative maximum-likelihood trellis decoding for block codes

An iterative trellis search technique is described for the maximum-likelihood (ML) soft decision decoding of block codes. The proposed technique derives its motivation from the fact that a given block code may be a subcode for a parent code whose associated trellis has substantially fewer edges. Through the use of list-Viterbi (1967) decoding and an iterative algorithm, the proposed technique allows for the use of a trellis for the parent code in the ML decoding of the desired subcode. Complexity and performance analyses, as well as details of potential implementations, indicate a substantial reduction in decoding complexity for linear block codes of practical length while achieving ML or near-ML soft decision performance     

Complexity Reduction in SISO Decoding of Block Codes

SISO decoding for block codes can be carried out based on a trellis representation of the code. However, the complexity entailed by such decoding is most often prohibitive and thus prevents practical implementation. This paper examines a new decoding scheme based on the soft-output Viterbi algorithm (SOVA) applied to a sectionalized trellis for linear block codes. The computational complexities of the new SOVA decoder and of the conventional SOVA decoder, based on a bit-level trellis, are theoretically analyzed and derived for different linear block codes. These results are used to obtain optimum sectionalizations of a trellis for SOVA. For comparisons, the optimum sectionalizations for Maximum A Posteriori (MAP) and Maximum Logarithm MAP (Max-Log-MAP) algorithms, and their corresponding computational complexities are included. The results confirm that the new SOVA decoder is the most computationally efficient SISO decoder, in comparisons to MAP and Max-Log-MAP algorithms. The simulation results of the bit error rate (BER) performance, assuming binary phase -- shift keying (BPSK) and additive white Gaussian noise (AWGN) channel, demonstrate that the performance of the new decoding scheme is not degraded. The BER performance of iterative SOVA decoding of serially concatenated block codes shows no difference in the quality of the soft outputs of the new decoding scheme and of the conventional SOVA.     

线性分组码与时空分组码级联的迭代译码

提出了线性分组码与时空分组码的级联编码方案,推导了时空分组码在比特级上的软输入软输出译码算法,进而给出了在线性分组码和时空分组码之间进行迭代译码的算法。仿真结果表明这种方案与现有方案相比在能够获得最大分集增益的同时还能获得更大的编码增益。     

Asymptotically optimal soft decision decoding algorithms for Hamming codes

Asymptotically optimal soft decision decoding algorithms for d = 3 and d = 4 Hamming codes are given and analysed. Only error sequences with probability exponent larger than that of maximum-likelihood decoding are corrected. Upper bounds on the block error probability for the Gaussian channel are given.     

Comparison of decoding algorithms of binary linear block codes inRayleigh fading channels with diversity reception

The word error probability of binary linear block codes is evaluated in Rayleigh fading channels with diversity reception for three decoding algorithms: error correction (EC), error/erasure correction (EEC), and maximum likelihood (ML) soft decoding algorithms. The performance advantage of EEC over EC in the required average SNR decreases as the number of diversity channels increases. The performance advantage of EEC over EC does not depend on the specific value of word error probability although the advantage of ML soft decoding over EC increases for lower word error probability