Zhurnal Radioelektroniki - Journal of Radio Electronics. eISSN 1684-1719. 2022. №10
ContentsFull text in Russian (pdf)
DOI: https://doi.org/10.30898/1684-1719.2022.10.6
ALGORITHM FOR OPTIMAL SYMBOL-BY-SYMBOL RECEPTION OF FREQUENCY-EFFICIENT SIGNALS
WITH CORRECTION CODES IN NON-BINARY GALOIS FIELDS
L.E. Nazarov
Fryazino branch of the Kotelnikov Institute of Radioegineering and Electronics of RAS,
141120, Moscow region, Fryazino, Vvedensky Sq. 1
The paper was received September 16, 2022
Abstract. The description of the developed algorithm for optimal symbol-by-symbol reception of signal structures based on frequency-efficient signals with two-dimensional «constellations» intensively used in applications and block correction codes in non-binary Galois fields is given. It is shown that symbol-by-symbol reception minimizes the error probability for code symbol or for information bit in contrast to the well-known maximum likelihood rule which minimizes the error-probability for code word. It is proved that the basis of this decoding algorithm is the spectral transform in the Walsh-Hadamard basis and the resulting complexity of the algorithm is determined by the dimension of the dual code which makes it promising for block correction codes with a high code rate (with low redundancy). The study of the error-performance characteristics (probability of erroneous reception for information bit) of the considered symbol-by-symbol reception algorithm was carried out by simulating it for signal structures based on signals with multilevel phase shift keying (PSK-16 signals) and on signals with quadrature amplitude manipulation (QAM-16 signals) and on simple correcting code with a general parity check in non-binary Galois field of size 16. It is shown that the use of the symbol-by-symbol reception algorithm provides an energy gain for the bit error probability from 0.00001 to 1.25…1.5 in relation to the considered signals without coding. As the bit error probability decreases the energy gains increase.
Key words: error-correcting codes, signal constructions, symbol-by-symbol reception, frequency-efficient signals
Financing: This study was supported by the Russian Foundation for Basic Research, project 20-07-00525
Corresponding author: Nazarov Lev Evgenievich, levnaz2018@mail.ru
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For citation:
Nazarov L.E. Algorithm for optimal symbol-by-symbol reception of frequency-efficient signals with correction codes in non-binary Galois fields. Zhurnal radioelektroniki [Journal of Radio Electronics] [online]. 2022. №10. https://doi.org/10.30898/1684-1719.2022.10.6 (In Russian)