An approximate analytical model of the message passing decoder of LDPC codes

Author

Lehmann, Frederic ; Maggio, Gian Mario

Author_Institution

CWC, California Univ., San Diego, La Jolla, CA, USA

fYear

2002

fDate

2002

Firstpage

31

Abstract

In this paper we introduce a novel one-dimensional model of the message passing decoding algorithm of low-density parity-check (LDPC) codes, based on Gaussian densities. The model consists of a closed-form 1-D map whose iterates directly represent the error probability. This map allows a qualitative analysis of the nonlinear dynamics of the decoding algorithm. Moreover, it is shown that our approach leads to the correct stability condition and that the corresponding threshold values are in good agreement with density evolution.

Keywords

Gaussian distribution; error statistics; iterative decoding; message passing; parity check codes; Gaussian approximation; Gaussian densities; LDPC codes; approximate analytical model; closed-form 1D map; convergence properties; density evolution; error probability; low-density parity-check codes; message passing decoding algorithm; nonlinear dynamics; one-dimensional model; stability condition; threshold values; Algorithm design and analysis; Analytical models; Closed-form solution; Electronic mail; Error probability; Gaussian approximation; Iterative decoding; Message passing; Parity check codes; Stability;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory, 2002. Proceedings. 2002 IEEE International Symposium on

Print_ISBN

0-7803-7501-7

Type

conf

DOI

10.1109/ISIT.2002.1023303

Filename

1023303