Upper bounds on the rate of LDPC codes

David Burshtein; Michael Krivelevich; Simon Litsyn; Gadi Miller

doi:10.1109/TIT.2002.801408

Upper bounds on the rate of LDPC codes

David Burshtein^*, Michael Krivelevich, Simon Litsyn, Gadi Miller

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

We derive upper bounds on the rate of low-density party-check (LDPC) codes for which reliable communication is achievable. We first generalize Gallager's bound to a general binary-input symmetric-output channel. We then proceed to derive tighter bounds. We also derive upper bounds on the rate as a function of the minimum distance of the code. We consider both individual codes and ensembles of codes.

Original language	English
Pages (from-to)	2437-2449
Number of pages	13
Journal	IEEE Transactions on Information Theory
Volume	48
Issue number	9
DOIs	https://doi.org/10.1109/TIT.2002.801408
State	Published - Sep 2002

Keywords

Error probability
Iterative decoding
Low-density parity-check (LDPC) codes
Maximum-likelihood (ML) decoding
Minimum distance

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10.1109/TIT.2002.801408

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abstract = "We derive upper bounds on the rate of low-density party-check (LDPC) codes for which reliable communication is achievable. We first generalize Gallager's bound to a general binary-input symmetric-output channel. We then proceed to derive tighter bounds. We also derive upper bounds on the rate as a function of the minimum distance of the code. We consider both individual codes and ensembles of codes.",

keywords = "Error probability, Iterative decoding, Low-density parity-check (LDPC) codes, Maximum-likelihood (ML) decoding, Minimum distance",

author = "David Burshtein and Michael Krivelevich and Simon Litsyn and Gadi Miller",

note = "Funding Information: Manuscript received May 9, 2001; revised February 16, 2002. This work was supported by the Israel Science Foundation under Grants 553/00 and 22/01-1. D. Burshtein, S. Litsyn, and G. Miller are with the Department of Electrical Engineering–Systems, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel (e-mail: [email protected]; [email protected]; [email protected]). M. Krivelevich is with the Department of Mathematics, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel (e-mail: [email protected]). Communicated by R. Koetter, Associate Editor for Coding Theory. Publisher Item Identifier 10.1109/TIT.2002.801408.",

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AB - We derive upper bounds on the rate of low-density party-check (LDPC) codes for which reliable communication is achievable. We first generalize Gallager's bound to a general binary-input symmetric-output channel. We then proceed to derive tighter bounds. We also derive upper bounds on the rate as a function of the minimum distance of the code. We consider both individual codes and ensembles of codes.

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KW - Iterative decoding

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KW - Maximum-likelihood (ML) decoding

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Upper bounds on the rate of LDPC codes

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Keywords

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