LDPC block and convolutional codes based on circulant matrices
LDPC block and convolutional codes based on circulant matrices
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DOI：
10.1109/tit.2004.838370
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发表时间：
2004-12-01
影响因子：
2.5
通讯作者：
Costello, DJ
中科院分区：
文献类型：
--
作者：
Tanner, RM;Sridhara, D;Costello, DJ
提出了一类代数结构的准循环(QC)低密度奇偶校验(LDPC)码及其卷积码。QC码由由循环矩阵块组成的稀疏奇偶校验矩阵来描述。稀疏的奇偶校验表示允许实用的基于图的迭代消息传递解码。基于这种代数结构，求出了码的围长和最小距离的界，并描述了几种可能的编码技术。对于短到中等的块长度，QC LDPC分组码的性能与随机构造的LDPC码相比是有利的。LDPC卷积码的性能优于它们所基于的QC码；这种性能是通过增加基本QC码的循环大小而获得的极限性能。最后，描述了LDPC卷积码的连续译码过程。
A class of algebraically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes and their convolutional counterparts is presented. The QC codes are described by sparse parity-check matrices comprised of blocks of circulant matrices. The sparse parity-check representation allows for practical graph-based iterative message-passing decoding. Based on the algebraic structure, bounds on the girth and minimum distance of the codes are found, and several possible encoding techniques are described. The performance of the QC LDPC block codes compares favorably with that of randomly constructed LDPC codes for short to moderate block lengths. The performance of the LDPC convolutional codes is superior to that of the QC codes on which they are based; this performance is the limiting performance obtained by increasing the circulant size of the base QC code. Finally, a continuous decoding procedure for the LDPC convolutional codes is described.