关于 LDPC 码的校验矩阵密度与可达码率
信息论
2007-07-13 v2 math.IT
摘要
本文给出了在记忆无二进制输入输出对称信道上传输的二进制线性分组码在校验矩阵渐近密度及 ML 译码下可达码率的新界。关于校验矩阵密度的下界用可靠通信可达的码率与信道容量之间的差距表示，并对每一序列二进制线性分组码均成立。这些界解决了 Sason 与 Urbanke 曾考虑的问题，即二进制线性分组码的校验矩阵相对于容量间隙可以有多稀疏。关于二进制线性分组码可达码率的新上界收紧了 Burshtein 等人此前报告的界，从而能够得到 ML 译码下二进制线性分组码序列阈值的更紧上界。将这些界应用于低密度奇偶校验（LDPC）码，并以数值示例说明了其紧度的改进。
引用
@article{arxiv.cs/0505078,
title = {On the Parity-Check Density and Achievable Rates of LDPC Codes},
author = {Gil Wiechman and Igal Sason},
journal= {arXiv preprint arXiv:cs/0505078},
year = {2007}
}
备注
12 pages. Submitted to the Forty-Third Annual Allerton Conference on Communication, Control, and Computing, September 28--30, 2005. It is a shortened version of the paper: G. Wiechman and I. Sason, "Improved bounds on the parity-check density and achievable rates of binary linear block codes with applications to LDPC codes," submitted to IEEE Trans. on Information Theory, May 2005. See http://arxiv.org/abs/cs.IT/0505057