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Информационно-управляющие системы

Оценка минимальной длины циклов квазициклических регулярных кодов с малой плотностью проверок на четность

Fedor I. Ivanov, Victor Zyablov, В. Г. Потапов

Published Jan 1, 2012• 0 citations
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Abstract

The condition of absence of the length 4 cycles in parity-check matrices of regular quasi-cyclic LDPC codes which are based on permutation matrices is proven, the assemble of a binary LDPC code is built with minimum cycle length of 6. The results of the received code construction modeling are presented for the iterative algorithm Sum-Product when the codeword is transmitted through a binary channel with additive Gaussian white noise (AGWN).

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The condition of absence of the length 4 cycles in parity-check matrices of regular quasi-cyclic LDPC codes which are based on permutation matrices is proven, the assemble of a binary LDPC code is built with minimum cycle length of 6. The results of the received code construction modeling are presented for the iterative algorithm Sum-Product when the codeword is transmitted through a binary channel with additive Gaussian white noise (AGWN).
An algorithm for generating parity-check matrices of regular low-density paritycheck codes based on permutation matrices and Steiner triple systems S(v, 3, 2), v = 2 m − 1, is proposed. Estimations of the rate, minimum distance, and girth for obtained code constructions are presented. Results of simulation of the obtained code constructions for an iterative “belief propagation” (Sum-Product) decoding algorithm applied in the case of transmission over a binary channel with additive Gaussian white noise and BPSK modulation are presented.