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Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

Construction of Quasi-Cyclic LDPC Codes with Diagonal Structure of Parity-Check Matrices

Hengzhou Xu, Huaan Li, Min Zhu, Bo Zhang, Baoming Bai

Published Jan 1, 2018• 2 citations
Publisher
DOI
10.1007/978-3-319-78130-3_48

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In this letter, the structural analysis of nonbinary cyclic and quasi-cyclic (QC) low-density parity-check (LDPC) codes with α-multiplied parity-check matrices (PCMs) is concerned. Using analytical methods, several structural parameters of nonbinary cyclic and QC LDPC codes with α-multiplied PCMs are determined. In particular, some classes of nonbinary LDPC codes constructed from finite fields and finite geometries are shown to have good minimum and stopping distances properties, which may explain to some extent their wonderful decoding performances.
Quasi-cyclic low density parity check (LDPC) codes and rotation LDPC codes are investigated in this paper, based on which, a new class of well-structured LDPC codes are proposed. Additionally, for ease of coding, a dual-diagonal structure is applied to the parity-check matrices of those codes, which ensure that parity-check bits can be recursively calculated with linear computational complexity. With the rotating and cyclic shift structure, decoders can be effectively implemented with partially parallel architecture appeared in some literatures on QC-LDPC codes and other structured LDPC codes. Simulation results show that the proposed structured LDPC codes are feasible.