Journal
IEEE TRANSACTIONS ON COMMUNICATIONS
Volume 70, Issue 5, Pages 2964-2976Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCOMM.2022.3160176
Keywords
Parity check codes; Maximum likelihood decoding; Optimization; Encoding; Block codes; Simulated annealing; Finite element analysis; AWGN channel; error-correcting codes; low-density parity-check codes; nonbinary quasi-cyclic LDPC codes; iterative decoding; error probability
Funding
- Huawei Technologies Co., Ltd.
- Estonian Research Council [PRG49]
- Ministry of Science and Higher Education of Russian Federation [2019-0898]
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This article proposes a novel approach to optimizing nonbinary quasi-cyclic LDPC codes by constructing check matrices and labeling field elements. It analyzes the performance of the codes and compares them with other related LDPC codes. The results show that this method accurately predicts the decoding performance of LDPC codes in practical applications.
We propose a novel approach to optimization of irregular nonbinary (NB) quasi-cyclic (QC)-LDPC codes over small alphabets. In this approach, first, the base parity-check matrices are constructed by a simulated annealing method, and then these matrices are labeled by the field elements while maximizing the so- called generalized girth of the Tanner graph. In order to analyze the performance of the constructed irregular NB LDPC codes, a new ensemble of irregular NB LDPC codes over the extensions of the binary Galois field is introduced. A finite-length random coding bound on the error probability of the maximum-likelihood (ML) decoding over the binary phase shift keying (BPSK) input AWGN channel for the new code ensemble is derived. The frame error rate (FER) performance of the sum-product belief-propagation (BP) decoding of the constructed NB QC-LDPC block codes is compared to that of both the optimized binary QC-LDPC block codes in the 5G standard and the best known NB QC-LDPC codes as well as to the derived random coding bound on the ML decoding error probability. It is shown that the obtained bound predicts the behavior of BP decoding performance of practical NB QC-LDPC codes more accurately than the BP decoding thresholds do.
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