DECODING ALGORITHMS FOR ERROR-CORRECTING PRODUCT-CODES BASED ON PROJECT GEOMETRY LOW-DENSITY PARITY-CHECK CODES
Lev E. Nazarov
Kotelnikov Institute of Radioengineering and Electronics of RAS, Fryazino Branch, http://fire.relarn.ru/
1,Vvedensky area, Fryazino 141190, Moscow region, Russian Federation
Received May 24, 2020; peer reviewed Juni 15, 2020; accepted August 22, 2020
The focus of this paper is directed towards the investigation of the characteristics of symbol-by-symbol iterative decoding algorithms for error-correcting block product-codes (block turbo-codes) which enable to reliable information transfer at relatively low received signal/noise and provide high power efficiency. Specific feature of investigated product codes is construction with usage of low-density parity-check codes (LDPC) and these code constructions are in the class of LDPC too. According to this fact the considered code constructions have symbol-by-symbol decoding algorithms developed for total class LDPC codes, namely BP (belief propagation) and its modification MIN_SUM_BP. The BP decoding algorithm is iterative and for implementation the signal/noise is required, for implementation of MIN_SUM_BP decoding algorithm the signal/noise is not required. The resulted characteristics of product codes constructed with usage of LDPC based on project geometry (length of code words, information volume, code rate, error performances) are presented in this paper. These component LDPC codes are cyclic and have encoding and decoding algorithms with low complexity implementation. The computer simulations for encoding and iterative symbol-by-symbol decoding algorithms for the number of turbo-codes with different code rate and information volumes are performed. The results of computer simulations have shown that MIN_SUM_BP decoding algorithm is more effective than BP decoding algorithm for channel with additive white gaussian noise concerning error-performances.
: noise-immune, product codes, error-correcting low density parity-check codes, signals, noise, iterative symbol-by-symbol decoding
, 2020, 12(3):399-406.
Full-text electronic version of this article - web site http://en.rensit.ru/vypuski/article/348/12(3)399-406e.pdf