This paper introduces a class of structured lowdensity parity-check (LDPC)codes whose parity check matrices are arrays of permutation matrices. Thepermutation matrices are obtained from Latin squares and form a finite fieldunder some matrix operations. They are chosen so that the Tanner graphs do notcontain subgraphs harmful to iterative decoding algorithms. The construction ofcolumn-weight-three codes is presented. Although the codes are optimized forthe Gallager A/B algorithm over the binary symmetric channel (BSC), their errorperformance is very good on the additive white Gaussian noise channel (AWGNC)as well.
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机译：本文介绍了一类结构化的低密度奇偶校验（LDPC）码，其奇偶校验矩阵是置换矩阵的数组。置换矩阵是从拉丁方获得的，并在某些矩阵运算下形成有限域。选择它们是为了使Tanner图不包含对迭代解码算法有害的子图。介绍了列重三码的构造。尽管已针对二进制对称信道（BSC）上的Gallager A / B算法对代码进行了优化，但它们的错误性能在加性高斯白噪声信道（AWGNC）上也非常出色。
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