Noise-immunity of optimal symbol-by-symbol reception of signals with corrective coding in Galois fields for fading channels

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Abstract

A description of the algorithm for optimal symbol-by-symbol reception of signal structures based on correction coding in non-binary Galois fields is given. The results of modeling this algorithm are given in order to study its noise-immunity for transionospheric channels with fading due to scattering on ionospheric irregularities for a number of digital signals with multi-level phase shift keying in combination with a correction code with a parity check in Galois fields. It is shown that for these channels the use of a symbol-by-symbol reception algorithm provides an energy gain of up to 4.5...24 dB in relation to the reception of signals without coding.

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About the authors

L. E. Nazarov

Fryazino Branch Kotelnikov Institute of Radioengineering and Electronics RAS

Author for correspondence.
Email: levnaz2018@mail.ru
Russian Federation, Vvedenskogo Squar., 1 Fryazino, Moscow region, 141190

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Supplementary files

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2. Fig. 1. Error probabilities Pb for FM-4 (curve 1), FM-8 (curve 2), FM-16 (curve 3) signals when propagating through the ABGS channel.

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3. Fig. 2. Error probabilities at reception of the signal design based on FM-4 signals for the channel with fading (parameter S4 = 0.3 (a) and 0.6 (b)): 1 - without coding; 2 - using a correction code in the GF field (22).

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4. Fig. 3. Error probabilities at reception of the signal design based on FM-8 signals for the channel with fading (parameter S4 = 0.3 (a) and 0.6 (b)): 1 - without coding; 2 - using a correction code in the GF field (23).

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5. Fig. 4. Error probabilities at reception of the signal design based on FM-16 signals for the channel with fading (parameter S4 = 0.3 (a) and 0.6 (b)): 1 - without coding; 2 - using a correction code in the GF field (24).

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