This paper introduces a class of structured low-density parity-check (LDPC) codes whose parity check matrices are arrays of permutation matrices. The permutation matrices are obtained from Latin squares and form a finite field under some matrix operations. They are chosen so that the Tanner graphs do not contain subgraphs harmful to iterative decoding algorithms. The construction of column-weight-three codes is presented. Although the codes are optimized for the Gallager A/B algorithm over the binary symmetric channel (BSC), their error performance 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。介绍了列权三码的构造。尽管这些代码已针对二进制对称信道（BSC）上的Gallager A / B算法进行了优化，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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