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Generalized and Doubly Generalized LDPC Codes With Random Component Codes for the Binary Erasure Channel

机译:二进制擦除信道的带有随机分量码的广义和双广义LDPC码

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摘要

In this paper, a method for the asymptotic analysis of generalized low-density parity-check (GLDPC) codes and doubly generalized low-density parity-check (D-GLDPC) codes over the binary erasure channel (BEC), based on extrinsic information transfer (EXIT) chart, is described. This method overcomes the problem consisting of the impossibility to evaluate the EXIT function for the check or variable component codes, in situations where the information functions or split information functions for component codes are unknown. According to the proposed technique, GLDPC codes and D-GLDPC codes where the generalized check and variable component codes are random codes with minimum distance at least 2, are considered. A technique is then developed which finds the EXIT chart for the overall GLDPC or D-GLDPC code, by evaluating the expected EXIT function for each check and variable component code. This technique is finally combined with the differential evolution algorithm in order to generate some good GLDPC and D-GLDPC edge distributions. Numerical results of long, random codes, are presented which confirm the effectiveness of the proposed approach. They also reveal that D-GLDPC codes can outperform standard LDPC codes and GLDPC codes in terms of both waterfall performance and error floor.
机译:本文基于外在信息,在二进制擦除信道(BEC)上渐进分析广义低密度奇偶校验(GLDPC)码和双重广义低密度奇偶校验(D-GLDPC)码说明转移(出口)图。该方法克服了以下问题,即在未知用于组分代码的信息功能或拆分信息功能的情况下,无法评估校验或可变组分代码的EXIT函数。根据提出的技术,考虑了广义校验和可变分量码是最小距离至少为2的随机码的GLDPC码和D-GLDPC码。然后开发一种技术,通过评估每个检查和可变组件代码的预期EXIT函数,为整个GLDPC或D-GLDPC代码找到EXIT图表。最后,将该技术与差分进化算法相结合,以生成一些良好的GLDPC和D-GLDPC边缘分布。给出了长随机码的数值结果,证实了所提方法的有效性。他们还揭示了D-GLDPC码在瀑布性能和错误率方面都可以胜过标准LDPC码和GLDPC码。

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