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On the analysis of spatially-coupled GLDPC codes and the weighted min-sum algorithm.

机译：分析了空间耦合的GLDPC码和加权最小和算法。

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摘要

This dissertation studies methods to achieve reliable communication over unreliable channels. Iterative decoding algorithms for low-density parity-check (LDPC) codes and generalized LDPC (GLDPC) codes are analyzed.;A new class of error-correcting codes to enhance the reliability of the communication for high-speed systems, such as optical communication systems, is proposed. The class of spatially-coupled GLDPC codes is studied, and a new iterative hard- decision decoding (HDD) algorithm for GLDPC codes is introduced. The main result is that the minimal redundancy allowed by Shannon's Channel Coding Theorem can be achieved by using the new iterative HDD algorithm with spatially-coupled GLDPC codes. A variety of low-density parity-check (LDPC) ensembles have now been observed to approach capacity with iterative decoding. However, all of them use soft (i.e., non-binary) messages and a posteriori probability (APP) decoding of their component codes. To the best of our knowledge, this is the first system that can approach the channel capacity using iterative HDD.;The optimality of a codeword returned by the weighted min-sum (WMS) algorithm, an iterative decoding algorithm which is widely used in practice, is studied as well. The attenuated max-product (AttMP) decoding and weighted min-sum (WMS) decoding for LDPC codes are analyzed. Applying the max-product (and belief-propagation) algorithms to loopy graphs are now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there is no general understanding of the conditions required for convergence and/or the optimality of converged solutions. This work presents an analysis of both AttMP decoding and WMS decoding for LDPC codes which guarantees convergence to a fixed point when a weight factor, beta, is sufficiently small. It also shows that, if the fixed point satisfies some consistency conditions, then it must be both a linear-programming (LP) and maximum-likelihood (ML) decoding solution.
机译：本文研究了在不可靠通道上实现可靠通信的方法。分析了低密度奇偶校验（LDPC）码和广义LDPC（GLDPC）码的迭代解码算法。;一类新型纠错码，用于提高光通信等高速系统的通信可靠性系统，建议。研究了空间耦合GLDPC码的类别，并介绍了一种新的GLDPC码迭代硬判决解码（HDD）算法。主要结果是，可以通过使用具有空间耦合GLDPC码的新型迭代HDD算法来实现香农信道编码定理所允许的最小冗余。现在已经观察到各种低密度奇偶校验（LDPC）集合通过迭代解码接近容量。然而，它们全部使用软（即，非二进制）消息和其组成代码的后验概率（APP）解码。据我们所知，这是第一个可以使用迭代HDD达到信道容量的系统。加权最小和（WMS）算法返回的码字的最优性，WMS算法是一种在实践中广泛使用的迭代解码算法，也被研究。分析了LDPC码的衰减最大乘积（AttMP）解码和加权最小和（WMS）解码。现在，将最大乘积（和置信传播）算法应用于循环图对于最佳分配问题非常流行。这主要是由于它们的低计算复杂度和实践中令人印象深刻的性能。但是，对于收敛和/或收敛解的最优性所需的条件还没有普遍的了解。这项工作提出了对LDPC码的AttMP解码和WMS解码的分析，当权重因子beta足够小时，可以保证收敛到固定点。它还表明，如果不动点满足某些一致性条件，则它必须同时是线性编程（LP）和最大似然（ML）解码解决方案。

著录项

  • 作者

    Jian, Yung-Yih.;

  • 作者单位

    Texas A&M University.;

  • 授予单位 Texas A&M University.;
  • 学科 Engineering Electronics and Electrical.
  • 学位 Ph.D.
  • 年度 2013
  • 页码 156 p.
  • 总页数 156
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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