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Recursive Suboptimal Decoding Algorithm for Binary Linear Black Codes

二进制线性黑色码的递归次优译码算法

基本信息

批准号：
10650363
负责人：
KASAMI Tadao
金额：
$ 2.18万
依托单位：
Hiroshima City University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10650363/
关键词：
binary linear code suboptimum decoding complexity of decoding cosets weight distribution quantization level 2元線形符号

项目摘要

1. A soft-decision decoding algorithm is derived by approximating some computations in the recursive maximum likelihood decoding (RMLD) algorithm. In the RMLD algorithm, the most likely code vector is computed by constructing tables of most likely local vectors in a divide-and conquer manner. In the proposed suboptimum algorithm, vectors in the tables are pruned according to a certain criteria. The relation among the criteria of pruning, error performance and the decoding complexity is analyzed. A simulation result for the third order Reed-Muller code of length 64 shows that we can realize a suboptimum decoder which achieves almost the same error performance as an ML decoder and costs only one-fourth decoding complexity compared to the RMLD algorithm [1,2].2. The original RMLD is not adaptive to signal-to-noise (SN) ratios. In RMLD, every most likely local vectors are computed in bottom-up way. We propose a new version of RMLD which is very adaptive to SN-ratios by introducing "lazy evaluation" in a top-down way. That is, most likely local vectors are computed when it is required for the first time. These computation can be efficiently carried out by using parity check matrices of certain local subcodes of the entire code [3,4]. For several Reed-Muller codes and extended permuted BCH codes, simulation results show remarkable reduction of time and space complexity of decoding.3. The weight distribution of coset leaders of cosets with respect to a local subcode provides primary information on how to prune an insignificant subtables for most likely local vectors. A new relatively efficient algorithm for computing the weight distribution of coset leaders of binary linear block codes is proposed [5].4. The quantization levels for received sequences and the accuracy of the metric computation have effect on the probability of decoding error and the complexity of decoding circuits. A detailed case study of RMLD decoder for a (64, 35) Reed-Muller subcode has been done [6].

1. 通过逼近递归最大似然译码算法中的一些计算，推导出一种软判决译码算法。在RMLD算法中，通过分而治之的方式构造最可能的局部向量表来计算最可能的代码向量。在次优算法中，根据一定的准则对表中的向量进行剪枝。分析了剪枝标准、误码性能和译码复杂度之间的关系。对长度为64的三阶Reed-Muller码的仿真结果表明，我们可以实现一种次优解码器，其误差性能与ML解码器几乎相同，而解码复杂度仅为RMLD算法的四分之一[1,2].2。原始的RMLD不能适应信噪比。在RMLD中，每个最有可能的局部向量都是自下而上计算的。我们提出了一个新版本的RMLD，通过引入“懒惰评估”，以自上而下的方式非常适应sn比率。也就是说，最可能的局部向量是在第一次需要的时候计算的。这些计算可以通过使用整个码的某些局部子码的奇偶校验矩阵来有效地进行[3,4]。对于几种Reed-Muller码和扩展排列BCH码，仿真结果表明，该算法显著降低了解码的时间和空间复杂度。关于局部子码的协集前导的权值分布提供了如何为最有可能的局部向量修剪不重要的子表的基本信息。提出了一种计算二元线性分组码的协集前导权值分布的新算法。接收序列的量化水平和度量计算的精度影响译码错误的概率和译码电路的复杂度。对（64,35）Reed-Muller子码的RMLD解码器进行了详细的案例研究。