# A method for constructing parity-check matrices of non-binary quasi-cyclic LDPC codes

## TL;DR

This paper introduces an algorithm for constructing parity-check matrices of non-binary quasi-cyclic LDPC codes that effectively reduces short cycles, leading to codes with performance close to the best existing non-binary LDPC codes.

## Contribution

The paper presents a novel algorithm for constructing NB QC-LDPC codes that minimizes short cycles, improving code performance with less than 0.1 dB loss compared to optimal codes.

## Key findings

- Algorithm effectively reduces short cycles in base matrices.
- Constructed codes lose less than 0.1 dB compared to best NB LDPC codes.
- Simulation results demonstrate improved code performance.

## Abstract

An algorithm for constructing parity-check matrices of non-binary quasi-cyclic low-density parity-check (NB QC-LDPC) codes is proposed. The algorithm finds short cycles in the base matrix and tries to eliminate them by selecting the circulants and the elements of GF(q). Firstly the algorithm tries to eliminate the cycles with the smallest number edges going outside the cycle. The efficiency of the algorithm is demonstrated by means of simulations. In particular, it was shown that NB QC-LDPC codes constructed with use of our algorithm loose less that 0.1 dB in comparison to the best NB LDPC codes.