Weight Distribution of Low-Density Parity-Check Codes

Author

Changyan Di ; Richardson, Thomas J. ; Urbanke, Rudiger L.

Author_Institution

Swiss Fed. Inst. of Technol., Lausanne

Volume

52

Issue

11

fYear

2006

Firstpage

4839

Lastpage

4855

Abstract

We derive the average weight distribution function and its asymptotic growth rate for low-density parity-check (LDPC) code ensembles. We show that the growth rate of the minimum distance of LDPC codes depends only on the degree distribution pair. It turns out that capacity-achieving sequences of standard (unstructured) LDPC codes under iterative decoding over the binary erasure channel (BEC) known to date have sublinearly growing minimum distance in the block length

Keywords

block codes; channel capacity; channel coding; iterative decoding; parity check codes; sequences; BEC; LDPC; binary erasure channel; block length; capacity-achieving sequence; iterative decoding; low-density parity-check code; weight distribution function; Aerospace materials; Code standards; Distribution functions; Hamming distance; Iterative algorithms; Iterative decoding; Joining processes; Linear code; Parity check codes; Sparse matrices; Binary erasure channel (BEC); capacity-achieving sequences; growth rate; irregular repeat–accumulate (IRA) codes; low-density parity-check (LDPC) codes; minimum distance; weight distribution;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2006.883541

Filename

1715529