Gallager´s decoding algorithm Α over high order modulations

Author

Yang, Hyun-Koo ; Lee, Myung-Kyu ; Yang, Kyeongcheol

Author_Institution

Dept. of Electron. & Electr. Eng., Pohang Univ. of Sci. & Technol. (POSTECH), Pohang

Volume

13

Issue

5

fYear

2009

fDate

5/1/2009 12:00:00 AM

Firstpage

336

Lastpage

338

Abstract

Gallager´s decoding algorithm A (GDA) for low density parity check (LDPC) codes is of interest mainly due to its good performance with extremely low complexity. In this paper, we analyze GDA over 2^m-ary pulse-amplitude modulation (2^m-PAM). Firstly, we represent its average error probability by means of a recursion formula. We then define its threshold for additive white Gaussian noise (AWGN) channels and derive its stability condition. The bit-to-symbol mapping strategies have a strong influence on the performance of LDPC-coded modulation systems. Finally, we show that the bit-reliability mapping strategy proposed by Li and Ryan maximizes the threshold of the LDPC coded modulation system with GDA over Gray-mapped 2^m-PAM in the AWGN channel.

Keywords

AWGN channels; decoding; error statistics; parity check codes; pulse amplitude modulation; 2^m-ary pulse amplitude modulation; Gallagers decoding algorithm; additive white Gaussian noise channel; average error probability; bit-to-symbol mapping strategy; high order modulation; low density parity check code; recursion formula; stability condition derivation; AWGN channels; Additive white noise; Closed-form solution; Constellation diagram; Demodulation; Error probability; Gaussian noise; H infinity control; Iterative decoding; Parity check codes; Density evolution, GallagerÂ¿s decoding algorithm A, low-density parity-check (LDPC) codes, LDPC-coded modulation, optimal bit-to-symbol mapping.;

fLanguage

English

Journal_Title

Communications Letters, IEEE

Publisher

ieee

ISSN

1089-7798

Type

jour

DOI

10.1109/LCOMM.2009.090070

Filename

4939344