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China Communications

Genetic optimization of non-binary quasi-cyclic LDPC codes

Zhang Yidi, Jiang Ming, Zhao Chun-ming

Published Aug 1, 2025• 1 citation
Publisher

Abstract

This paper proposes a genetic optimization method for the construction of non-binary quasi-cyclic low-density parity-check (NB-QC-LDPC) codes with short block lengths. In our scheme, the initial template base matrices and the corresponding non-binary replacement matrices are constructed by the progressive edge growth algorithm and randomly generated, respectively. The genetic algorithm is then utilized to optimize the base matrices and the replacement ones. The simulation results show that the NB-QC-LDPC codes constructed by the proposed method achieve better decoding performance and lower implementation complexity compared to the existing NB-LDPC codes such as consultative committee for space data system and BeiDou satellite navigation system.

DOI
10.23919/jcc.ja.2023-0786

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This paper proposes a genetic optimization method for the construction of non-binary quasi-cyclic low-density parity-check (NB-QC-LDPC) codes with short block lengths. In our scheme, the initial template base matrices and the corresponding non-binary replacement matrices are constructed by the progressive edge growth algorithm and randomly generated, respectively. The genetic algorithm is then utilized to optimize the base matrices and the replacement ones. The simulation results show that the NB-QC-LDPC codes constructed by the proposed method achieve better decoding performance and lower implementation complexity compared to the existing NB-LDPC codes such as consultative committee for space data system and BeiDou satellite navigation system.
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.
In this paper, we propose an optimization scheme of quasi-cyclic low-density parity-check (QC-LDPC) codes based on an evolutionary algorithm, the Genetic Algorithm (GenAlg). By changing the positions and shift values of non-negative entries in the base matrix, the optimized codes can achieve better decoding performances. The optimized construction of the base matrix compatible for multiple lengths with different lifting sizes is discussed and a statistic metric used to measure the effectiveness of optimization is introduced to quantitatively evaluate the decoding performances with different code lengths. Simulation results of the proposed GenAlg optimized QC-LDPC codes with different lengths can significantly outperform those of the codes in various existing standards.
We propose an approach for optimizing nonbinary (NB) quasi-cyclic (QC) LDPC codes. This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the so-called generalized girth of the NB LDPC code Tanner graph. Tightened random coding bounds based on the average binary spectra for ensembles of "almost regular" NB LDPC codes of finite lengths over extensions of the binary Galois field are derived. The simulated FER performance of the sum-product BP decoding of "almost regular" NB QC-LDPC block codes are presented and compared with the derived finite-length random coding bounds as well as with the same performance of the optimized binary QC-LDPC block code in the 5G standard. In the waterfall region our finite-length bounds on the error probability of ML decoding are about 0.1--0.2 dB away from the simulated FER performance of BP decoding.
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). 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 order to explain the simulation results we also derive upper bounds on the minimum distance of NB QC-LDPC codes.
Short cycles in the Tanner graph of a given LDPC code has negative effect on the performance of iterative decoding. To improve the performance, we presented an approach for constructing Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes whose associated Tanner graph has large girth and a small amount of short cycles. Each column block of the parity check matrix was designed by adding circulant permutation sub-matrices one after another, provided the current parity check matrix has minimal number of short cycles. The condition for the proposed QC-LDPC codes to have girth at least 6 was also analyzed. Regular and irregular QC-LDPC codes with various lengths and rates can be constructed. Simulations show that the proposed QC-LDPC codes have less short cycles and better performance than existing progressive edge growth based QC-LDPC codes.
We propose a novel approach for optimization of nonbinary (NB) quasi-cyclic (QC)-LDPC codes. In this approach, the base parity-check matrices are constructed by the simulated annealing method, and then labeled while maximizing the so-called generalized girth of the NB LDPC code Tanner graph. Random coding bounds on the ML decoding error probability for ensembles of "almost regular" NB LDPC codes of finite lengths over extensions of the binary Galois field are derived. These bounds are based on the average bit weight spectra for the ensembles of NB LDPC codes. The observed FER performance of the sum-product BP decoding of "almost regular" NB QC-LDPC block codes is presented and compared to the finite-length random coding bounds, as well as to the performance of the optimized binary QC-LDPC block code in the 5G standard. In the waterfall region, the gap between the finite-length bounds on the error probability of the ML decoding and the simulation performance of the BP decoding is about 0.1 – 0.2 dB.