SYMBOL-BY-SYMBOL DECODING ALGORITHMS FOR SIGNALS BASED ON SINGLE-PARITY-CHECK CODES IN THE FIELD GF(2^m)

 

L. E. Nazarov, P. V. Shishkin

Fryazino Branch of Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences,
Vvedensky Sq.1, Fryazino Moscow region 141190, Russia

 

 The paper is received on December 3, 2018

 

Abstract. The focus of this paper is directed towards the development and investigation of the characteristics of symbol-by-symbol decoding algorithms for signal constructions based on partial signals and on single-parity-check codes in non-binary fields GF(2^m). The coherent and noncoherent symbol-by-symbol decoding algorithms for signal constructions based on partial signals and on single-parity-check codes are presented in the article. The non-binary fields GF(2^m) are construct on the base of module primitive polyneme arithmetic. The decisions evaluated with application of these decoding algorithms are equivalent to the output soft decisions used for block turbo-codes iterative decoding procedures. The base of developed symbol-by-symbol decoding algorithms is organization of set ^m independent channels that transmit information with usage of the component binary error-correcting single-parity-check codes in binary field. The decoding algorithms for these component codes use input soft symbol decisions. The coherent and noncoherent algorithms for evaluation input soft symbol decisions are developed for partial signals that equivalent Hadamard functions. The base of these algorithms is Fast Hadamard Transformation with dimension 2^m. The computer simulations for developed symbol-by-symbol decoding for investigated signal constructions with information volumes 200 bits for fields GF(2³), GF(2⁶), GF(2⁸)  and for Additive White Gaussian Noise are performed. It shown the error-performance degradations without code concerning with single-parity-check code are about 1 dB for bit-error 0.00001.

The work is performed with support by RFFI (project (¹16-07-00746).

Key words: non-binary fields, signals, symbol-by-symbol decoding, single-parity-check codes, block product codes, Fast Hadamard Transformation.

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For citation:
L. E. Nazarov, P. V. Shishkin. Symbol-by-symbol decoding algorithms for signals based on single-parity-check codes in the field GF(2^m). Zhurnal Radioelektroniki - Journal of Radio Electronics. 2018. No. 12. Available at http://jre.cplire.ru/jre/dec18/10/text.pdf

DOI  10.30898/1684-1719.2018.12.10