多进制LDPC码的线性规划译码方法研究

项目名称： 多进制LDPC码的线性规划译码方法研究

项目编号： No.61201265

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 电子学与信息系统

项目作者： 刘海洋

作者单位： 中国科学院微电子研究所

项目金额： 20万元

中文摘要： 线性码的线性规划译码(LP decoding)方法是目前差错控制编码领域的研究热点，并且将成为传统的迭代译码算法的有力竞争者。本项目将瞄准这一热点，创新性地研究基于有限域GF(2^m)构造的多进制低密度奇偶校验(LDPC)码的线性规划译码。 针对多进制LDPC码线性规划译码复杂度高和存储量大的问题，拟利用线性规划理论，在不损失译码性能的前提下，创造性地提出一种低复杂度和存储量的线性规划译码方法。 相对于传统的迭代译码，LP译码的性能能够用伪码字刻画，使得LP译码易于理论分析。本项目拟对多进制LDPC码的伪码字性质进行研究，从而得到LP译码性能的理论分析结果。特别地，对于几类具有代数结构的LDPC码，拟确定其低重量的(最小)伪码字的重量分布。此外，本项目拟提出改进的LP译码算法，当标准LP译码收敛到非码字的伪码字时，增加少量复杂度，获得性能改善。

中文关键词： 多进制LDPC码；线性规划；线性规划译码；伪码字；

英文摘要： Linear programming (LP) decoding is a hot research topic in the area of error-control coding and may become a competitive alternative of the traditional iterative decoding algorithms for linear codes. This project focuses on this hot topic and investigates the LP decoding of non-binary low-density parity-check (LDPC) codes constructed from the finite field GF(2^m). In order to address the complexity and storage requirement issue of LP decoding of non-binary LDPC codes, a low-complexity and low-storage-requirement LP decoding algorithm without performance losses is to be proposed based on the theories of linear programming. Compared with traditional iterative decoding, the performance of LP decoding is described by pseudocodewords, which makes it easier to theoretically analyze LP decoding. In this project, the properties of pseudocodewords of non-binary LDPC codes will be studied and the theoretical results of LP decoding performance will be obtained. In particular, the distributions of low-weight (minimal) pseudocodewords of some classes of algebraically-structured LDPC codes will be completely determined. Besides, the improved LP decoding algorithm will be developed in the project. The proposed algorithm will improve the decoding performance with a slight increase in computational complexity when the origin

英文关键词： non-binary LDPC codes；linear programming (LP)；LP decoding；pseudocodeword；