Quasi-Cyclic Representation and Vector Representation of RS-LDPC Codes
Quasi-Cyclic Representation and Vector Representation of RS-LDPC Codes
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DOI：
10.1109/tcomm.2015.2399395
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发表时间：
2015-02
影响因子：
8.3
通讯作者：
Haiyang Liu;Qin Huang;Gang Deng;Jie Chen
中科院分区：
文献类型：
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作者：
Haiyang Liu;Qin Huang;Gang Deng;Jie Chen
RS-LDPC码是LDPC码中的一类重要码，它是基于具有两个信息符号的RS码的码字构造的。本文提出了RS-LDPC码的两种表示方法，即准循环表示法和矢量表示法。在第一种表示下，全长RS-LDPC码的校验矩阵的大部分由循环置换矩阵和零矩阵组成。因此，这类码可以享受的优势，在硬件实现的QC-LDPC码。此外，可以显式地给出RS-LDPC码的QC表示下的基矩阵，使得可以组合地分析其奇偶校验矩阵的秩。在第二种表示下，RS-LDPC码的奇偶校验矩阵中的每个置换矩阵由非二进制向量定义，其条目是构造RS码的字段中的条目的置换。然后，证明了全长RS-LDPC码的仿射不变性，这有利于码的结构分析。
RS-LDPC codes, constructed based on the codewords of Reed-Solomon (RS) codes with two information symbols, are an important class of LDPC codes. In this paper, we present two representations, namely, quasi-cyclic (QC) representation and vector representation, for RS-LDPC codes. Under the first representation, most part of the parity-check matrix of a full-length RS-LDPC code consists of circulant permutation matrices and zero matrices. As a result, the class of codes can enjoy the advantages in hardware implementation as QC-LDPC codes. In addition, the base matrix under the QC representation of an RS-LDPC code can be explicitly given such that the rank of its parity-check matrix can be analyzed combinatorially. Under the second representation, each permutation matrix in the parity-check matrix of an RS-LDPC code is defined by a nonbinary vector, whose entries are a permutation of entries in the field from which the RS code is constructed. Then, the “affine invariance” property is proved for full-length RS-LDPC codes, which can facilitate the structural analysis of the codes.