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 Probl. Peredachi Inf., 2016, Volume 52, Issue 1, Pages 8–15 (Mi ppi2193)

Coding Theory

Upper bound on the minimum distance of LDPC codes over $GF(q)$ based on counting the number of syndromes

A. A. Frolov

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: In [1] a syndrome counting based upper bound on the minimum distance of regular binary LDPC codes is given. In this paper we extend the bound to the case of irregular and generalized LDPC codes over $GF(q)$. A comparison with the lower bound for LDPC codes over $GF(q)$, upper bound for the codes over $GF(q)$, and the shortening upper bound for LDPC codes is made. The new bound is shown to lie under the Gilbert–Varshamov bound at high rates.

 Funding Agency Grant Number Russian Science Foundation 14-50-00150 The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.

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English version:
Problems of Information Transmission, 2016, 52:1, 6–13

Bibliographic databases:

UDC: 621.391.15
Revised: 17.11.2015

Citation: A. A. Frolov, “Upper bound on the minimum distance of LDPC codes over $GF(q)$ based on counting the number of syndromes”, Probl. Peredachi Inf., 52:1 (2016), 8–15; Problems Inform. Transmission, 52:1 (2016), 6–13

Citation in format AMSBIB
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