Structural Analysis of Nonbinary Cyclic and Quasi-Cyclic LDPC Codes with α-Multiplied Parity-Check Matrices

Haiyang LIU  Hao ZHANG  Lianrong MA  Lingjun KONG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.11   pp.1299-1303
Publication Date: 2020/11/01
Publicized: 2020/05/12
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2020EAL2031
Type of Manuscript: LETTER
Category: Coding Theory
low-density parity-check (LDPC) codes,  nonbinary,  cyclic,  quasi-cyclic (QC),  α-multiplied parity-check matrix (PCM),  

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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.