Efficient methods for bounding the fractional distance of LDPC codes and obtaining fundamental polytopes of nonbinary and generalized codes

David Burshtein; Idan Goldenberg

doi:10.1109/ISIT.2011.6033739

Efficient methods for bounding the fractional distance of LDPC codes and obtaining fundamental polytopes of nonbinary and generalized codes

David Burshtein^*, Idan Goldenberg

^*Corresponding author for this work

School of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A method which obtains a tight lower bound on the fractional distance of LDPC codes is proposed. This algorithm exhibits complexity which scales quadratically with the block length, and thus less than currently-known methods. We also show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.

Original language	English
Title of host publication	2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages	1263-1267
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2011.6033739
State	Published - 2011
Event	2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation Duration: 31 Jul 2011 → 5 Aug 2011

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
ISSN (Print)	2157-8104

Conference

Conference	2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Country/Territory	Russian Federation
City	St. Petersburg
Period	31/07/11 → 5/08/11

Keywords

Linear programming decoding
fractional distance
fundamental polytope
low-density parity-check (LDPC) codes

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10.1109/ISIT.2011.6033739

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Burshtein, D., & Goldenberg, I. (2011). Efficient methods for bounding the fractional distance of LDPC codes and obtaining fundamental polytopes of nonbinary and generalized codes. In 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 (pp. 1263-1267). Article 6033739 (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2011.6033739

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abstract = "A method which obtains a tight lower bound on the fractional distance of LDPC codes is proposed. This algorithm exhibits complexity which scales quadratically with the block length, and thus less than currently-known methods. We also show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.",

keywords = "Linear programming decoding, fractional distance, fundamental polytope, low-density parity-check (LDPC) codes",

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Burshtein, D & Goldenberg, I 2011, Efficient methods for bounding the fractional distance of LDPC codes and obtaining fundamental polytopes of nonbinary and generalized codes. in 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011., 6033739, IEEE International Symposium on Information Theory - Proceedings, pp. 1263-1267, 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011, St. Petersburg, Russian Federation, 31/07/11. https://doi.org/10.1109/ISIT.2011.6033739

Efficient methods for bounding the fractional distance of LDPC codes and obtaining fundamental polytopes of nonbinary and generalized codes. / Burshtein, David; Goldenberg, Idan.
2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011. 2011. p. 1263-1267 6033739 (IEEE International Symposium on Information Theory - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Burshtein D, Goldenberg I. Efficient methods for bounding the fractional distance of LDPC codes and obtaining fundamental polytopes of nonbinary and generalized codes. In 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011. 2011. p. 1263-1267. 6033739. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2011.6033739

Efficient methods for bounding the fractional distance of LDPC codes and obtaining fundamental polytopes of nonbinary and generalized codes

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Keywords

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