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 Probl. Peredachi Inf., 2011, Volume 47, Issue 4, Pages 27–42 (Mi ppi2058)

Coding Theory

Bounds on the minimum code distance for nonbinary codes based on bipartite graphs

A. Frolov, V. V. Zyablov

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: The minimum distance of codes on bipartite graphs (BG codes) over $GF(q)$ is studied. A new upper bound on the minimum distance of BG codes is derived. The bound is shown to lie below the Gilbert–Varshamov bound when $q\ge32$. Since the codes based on bipartite expander graphs (BEG codes) are a special case of BG codes and the resulting bound is valid for any BG code, it is also valid for BEG codes. Thus, nonbinary ($q\ge32$) BG codes are worse than the best known linear codes. This is the key result of the work. We also obtain a lower bound on the minimum distance of BG codes with a Reed-Solomon constituent code and a lower bound on the minimum distance of low-density parity-check (LDPC) codes with a Reed–Solomon constituent code. The bound for LDPC codes is very close to the Gilbert–Varshamov bound and lies above the upper bound for BG codes.

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English version:
Problems of Information Transmission, 2011, 47:4, 327–341

Bibliographic databases:

UDC: 621.391.15
Revised: 19.09.2011

Citation: A. Frolov, V. V. Zyablov, “Bounds on the minimum code distance for nonbinary codes based on bipartite graphs”, Probl. Peredachi Inf., 47:4 (2011), 27–42; Problems Inform. Transmission, 47:4 (2011), 327–341

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. A. Frolov, “Upper bound on the minimum distance of LDPC codes over $GF(q)$ based on counting the number of syndromes”, Problems Inform. Transmission, 52:1 (2016), 6–13
2. I. V. Zhilin, F. I. Ivanov, “Vectorizing computations at decoding of nonbinary codes with small density of checks”, Autom. Remote Control, 77:10 (2016), 1781–1791
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