On Coset Leader Graphs of LDPC Codes

Author

Iceland, Eran ; Samorodnitsky, Alex

Author_Institution

Sch. of Eng. & Comput. Sci., Hebrew Univ. of Jerusalem, Jerusalem, Israel

Volume

61

Issue

8

fYear

2015

fDate

Aug. 2015

Firstpage

4158

Lastpage

4163

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, 11n. 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.

Keywords

binary codes; graph theory; linear codes; linear programming; parity check codes; vectors; LDPC codes; block length; constant weight vectors; coset leader graph; linear binary code; linear programming bound; low-density parity check; metric ball; minimal relative distance; Hamming weight; Indexes; Linear codes; Measurement; Parity check codes; Probability; Upper bound; Low-density parity-check (LDPC) code; minimum distance;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2015.2438716

Filename

7114293