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Vladikavkaz. Mat. Zh., 2016, Volume 18, Number 4, Pages 23–33 (Mi vmj594)  

On correctness conditions of a soft-decisions decoder for ternary Reed–Muller codes of second order

V. M. Deundyaka, N. S. Mogilevskayab

a Southern Federal University, Rostov-on-Don
b Don State Technical University, Rostov-on-Don

Abstract: We study theoretically conditions of correct operation of a new soft decisions decoder of Reed–Muller second order codes over the field $\mathbb F_3$, whose experimental research showed that its corrective ability exceeds that of the decoder of the minimum Hamming's distance. For discrete data channel allocated we indicated the smoothness condition under which the decoder guarantees correction of all errors, the number of which does not exceed the permissible number of errors referred to the code design.

Key words: Reed–Muller codes, soft decoder, decoder correctness proof.

Full text: PDF file (246 kB)
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UDC: 519.725
Received: 11.10.2015

Citation: V. M. Deundyak, N. S. Mogilevskaya, “On correctness conditions of a soft-decisions decoder for ternary Reed–Muller codes of second order”, Vladikavkaz. Mat. Zh., 18:4 (2016), 23–33

Citation in format AMSBIB
\Bibitem{DeuMog16}
\by V.~M.~Deundyak, N.~S.~Mogilevskaya
\paper On correctness conditions of a soft-decisions decoder for ternary Reed--Muller codes of second order
\jour Vladikavkaz. Mat. Zh.
\yr 2016
\vol 18
\issue 4
\pages 23--33
\mathnet{http://mi.mathnet.ru/vmj594}


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