Quasi-Cyclic LDPC Codes With Parity-Check Matrices of Column Weight Two or More for Correcting Phased Bursts of Erasures
Quasi-Cyclic LDPC Codes With Parity-Check Matrices of Column Weight Two or More for Correcting Phased Bursts of Erasures
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DOI：
10.1109/tcomm.2021.3059001
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发表时间：
2021-05
影响因子：
8.3
通讯作者：
Xin Xiao;B. Vasic;Shu Lin;Juane Li;K. Abdel-Ghaffar
中科院分区：
文献类型：
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作者：
Xin Xiao;B. Vasic;Shu Lin;Juane Li;K. Abdel-Ghaffar
在他对LDPC码的开创性工作中，Gallager在证明了具有重量为2的奇偶校验矩阵的码的最小汉明距离至多与其码长对数增长后，对其进行了摒弃。尽管具有较差的最小汉明距离，但具有列重为2的奇偶校验矩阵的准循环LDPC码具有良好的纠错能力，这是使用具有列重为3或更多的奇偶校验矩阵的准循环LDPC码所无法超越的。通过修改列权重2的奇偶校验矩阵并将其全局耦合，可以进一步增强纠删能力。此外，还考虑了具有列重为3或更多的奇偶校验矩阵的准循环LDPC码，这种码能够纠正相控突发擦除，并且在AWGN信道上具有良好的性能。给出了基于里德-所罗门码和Gabidlin码的这种码的例子。
In his pioneering work on LDPC codes, Gallager dismissed codes with parity-check matrices of weight two after proving that their minimum Hamming distances grow at most logarithmically with their code lengths. In spite of their poor minimum Hamming distances, it is shown that quasi-cyclic LDPC codes with parity-check matrices of column weight two have good capability to correct phased bursts of erasures which may not be surpassed by using quasi-cyclic LDPC codes with parity-check matrices of column weight three or more. By modifying the parity-check matrices of column weight two and globally coupling them, the erasure correcting capability can be further enhanced. Quasi-cyclic LDPC codes with parity-check matrices of column weight three or more that can correct phased bursts of erasures and perform well over the AWGN channel are also considered. Examples of such codes based on Reed-Solomon and Gabidulin codes are presented.