Column weights optimization for semi-regular nonbinary LDPC codes

The paper concerns Low Density Parity Check (LDPC) codes over nonbinary Galois Fields GF(q), that are a generalization of the industrial standard binary LDPC codes for forward error correction in communication and information systems. The semi-regular nonbinary LDPC codes can outperform their binary counterparts in the case of short to moderate code word lengths. The methods for the good code construction based on a computer search techniques are already well investigated. However, there is a lack of systematic results for optimal weight distribution of columns of parity check matrices for codes over different field order and different rate. In this article we present a Monte Carlo like algorithm for column weight optimization devoted to nonbinary semi-regular codes along with optimization results that facilitate the codes construction computer-based methods.