On Coset Leader Graphs of LDPC Codes

Eran Iceland; Alex Samorodnitsky

doi:10.1109/TIT.2015.2438716

On Coset Leader Graphs of LDPC Codes

Eran Iceland, Alex Samorodnitsky

The Rachel and Selim Benin School of Engineering and Computer Science

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

3 Scopus citations

Abstract

Our main technical result is that, in the coset leader graph of a linear binary code of block length n , the metric balls spanned by constant-weight vectors grow exponentially slower than those in \{0,1\}^{n}. Following the approach of Friedman and Tillich, we use this fact to improve on the first linear programming bound on the rate of low-density parity check (LDPC) codes, as the function of their minimal relative distance. This improvement, combined with the techniques of Ben-Haim and Litsyn, improves the rate versus distance bounds for LDPC codes in a significant subrange of relative distances.

Original language	English
Article number	7114293
Pages (from-to)	4158-4163
Number of pages	6
Journal	IEEE Transactions on Information Theory
Volume	61
Issue number	8
DOIs	https://doi.org/10.1109/TIT.2015.2438716
State	Published - Aug 2015

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

Hamming weight
Indexes
Linear codes
Measurement
Parity check codes
Probability
Upper bound

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10.1109/TIT.2015.2438716

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KW - Indexes

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KW - Measurement

KW - Parity check codes

KW - Probability

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On Coset Leader Graphs of LDPC Codes

Abstract

Bibliographical note

Keywords

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