Asymptotic enumeration methods for analyzing LDPC codes

Author

Burshtein, David ; Miller, Gadi

Author_Institution

Sch. of Electr. Eng., Tel-Aviv Univ., Israel

Volume

50

Issue

6

fYear

2004

fDate

6/1/2004 12:00:00 AM

Firstpage

1115

Lastpage

1131

Abstract

We show how asymptotic estimates of powers of polynomials with nonnegative coefficients can be used in the analysis of low-density parity-check (LDPC) codes. In particular, we show how these estimates can be used to derive the asymptotic distance spectrum of both regular and irregular LDPC code ensembles. We then consider the binary erasure channel (BEC). Using these estimates we derive lower bounds on the error exponent, under iterative decoding, of LDPC codes used over the BEC. Both regular and irregular code structures are considered. These bounds are compared to the corresponding bounds when optimal (maximum-likelihood (ML)) decoding is applied.

Keywords

error statistics; iterative decoding; maximum likelihood decoding; parity check codes; telecommunication channels; LDPC code; asymptotic enumeration method; binary erasure channel; code ensembles; error probability; iterative decoding; low density parity check codes; maximum-likelihood decoding; nonnegative coefficient polynomials; Belief propagation; Bipartite graph; Communication system control; Error analysis; Error probability; Iterative decoding; Maximum likelihood decoding; Maximum likelihood estimation; Parity check codes; Polynomials; BEC; Binary erasure channel; LDPC; code ensembles; code spectrum; codes; iterative decoding; low-density parity-check;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2004.828064

Filename

1302293