Geodesic
On correctness conditions of a soft-decisions decoder for ternary Reed–Muller codes of second order
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 23-33 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{VMJ_2016_18_4_a2,
     author = {V. M. Deundyak and N. S. Mogilevskaya},
     title = {On correctness conditions of a soft-decisions decoder for ternary {Reed{\textendash}Muller} codes of second order},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {23--33},
     year = {2016},
     volume = {18},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a2/}
}
TY  - JOUR
AU  - V. M. Deundyak
AU  - N. S. Mogilevskaya
TI  - On correctness conditions of a soft-decisions decoder for ternary Reed–Muller codes of second order
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2016
SP  - 23
EP  - 33
VL  - 18
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a2/
LA  - ru
ID  - VMJ_2016_18_4_a2
ER  - 
%0 Journal Article
%A V. M. Deundyak
%A N. S. Mogilevskaya
%T On correctness conditions of a soft-decisions decoder for ternary Reed–Muller codes of second order
%J Vladikavkazskij matematičeskij žurnal
%D 2016
%P 23-33
%V 18
%N 4
%U http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a2/
%G ru
%F VMJ_2016_18_4_a2
V. M. Deundyak; N. S. Mogilevskaya. On correctness conditions of a soft-decisions decoder for ternary Reed–Muller codes of second order. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 23-33. http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a2/

[1] Deundyak V. M., Maevskii A. E., Mogilevskaya N. S., Metody pomekhoustoichivoi zaschity dannykh, Ucheb., Izd-vo Yuzhnogo federalnogo un-ta, Rostov n/D., 2014, 309 pp.

[2] Prokis Dzh., Tsifrovaya svyaz, Radio i svyaz, M., 2000, 800 pp.

[3] Sidelnikov V. M., Pershakov A. S., “Dekodirovanie kodov Rida–Mallera pri bolshom chisle oshibok”, Problemy peredachi informatsii, 28:3 (1992), 80–94 | Zbl

[4] Loidreau P., Sakkour B., “Modified version of Sidel'nikov–Pershakov decoding algorithm for binary second order Reed–Muller codes”, Ninth International Workshop on Algebraic and Combinatorial Coding theory (ACCT-9) (Kranevo, 2004), 266–271

[5] Mogilevskaya N. S., Skorobogat V. R., Chudakov V. S., “Eksperimentalnoe issledovanie dekoderov kodov Rida — Mallera vtorogo poryadka”, Vestn. Donskogo gos. tekh. un-ta, 8:3 (2008), 231–237 | Zbl

[6] Deundyak V. M., Mogilevskaya N. S., “Model troichnogo kanala peredachi dannykh s ispolzovaniem dekodera myagkikh reshenii kodov Rida–Mallera vtorogo poryadka”, Izv. vuzov. Sev.-Kavk. region. Tekhn. nauki, 2015, no. 1(182), 3–10

[7] Teilor M., Psevdodifferentsialnye operatory, Mir, M., 1985, 25 pp.

[8] Mogilevskaya N. S., “Korrektiruyuschaya sposobnost dekodera myagkikh reshenii troichnykh kodov Rida–Mallera vtorogo poryadka pri bolshom chisle oshibok”, Vestn. Donskogo gos. tekh. un-ta, 2015, no. 1, 121–130

[9] Deundyak V. M., Kosolapov Yu. V., “O stoikosti kodovogo zashumleniya k statisticheskomu analizu nablyudaemykh dannykh mnogokratnogo povtoreniya”, Model. i analiz inform. sistem, 19:4 (2012), 110–127

[10] Bukashkin S. A., “Metod sluchainogo kodirovaniya”, Radiotekhnika, 2014, no. 4, 30–36

[11] Kosolapov Yu. V., “Kody dlya obobschennoi modeli kanala s podslushivaniem”, Problemy peredachi informatsii, 51:1 (2015), 23–28

[12] Logachev O. A., Salnikov A. P., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2004, 470 pp.

[13] Pellikaan R., Wu X.-W., “List decoding of $q$-ary Reed–Muller codes”, IEEE. Trans. Infor. Theory, 50:4 (2004), 679–682 | DOI | MR | Zbl

[14] Khirsh M., Differentsialnaya topologiya, Mir, M., 1979, 280 pp.