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

Bounds on the minimum code distance for nonbinary codes based on bipartite graphs 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 ≤ 32. 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 ≤ 32) 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

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

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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2011 by Pleiades Publishing, Ltd.
Subject
Engineering; Systems Theory, Control; Information Storage and Retrieval; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946011040028
Publisher site
See Article on Publisher Site

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 ≤ 32. 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 ≤ 32) 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.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jan 20, 2012

References

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