On the design of LDPC code ensembles for BIAWGN channels

• Published in: IEEE transactions on communications 2010-05, Vol.58 (5), p.1376-1382
• Main Authors: Saeedi, Hamid, Banihashemi, Amir H
• Format: Article
• Language: English
• Subjects: Additive white noise; Algorithms; AWGN channel; AWGN channels; code design; Codes; Design; Design methodology; Design optimization; irregular LDPC codes; Iterative algorithms; Iterative decoding; LDPC codes; Low-density parity-check codes; Optimization methods; Parity check codes; Stability; stability condition; Studies; systematic design; Upper bound
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2010.05.080299

Existing design methods for irregular Low-Density Parity-Check (LDPC) codes over the additive white Gaussian noise channel are based on using asymptotic analysis tools such as density evolution in an optimization process. Such a process is computationally expensive particularly when a large number of constituent variable node degrees are involved in the design. In this paper, we propose a systematic approach for the design of irregular LDPC codes. The proposed method, which is based on a pre-computed upper bound on the fraction of edges connected to variable nodes of degree 3, is considerably less complex than the conventional optimization approach. Through a number of examples, we demonstrate that using our method, ensembles with performance very close to those devised based on optimization, can be designed. In addition to having very good performance, the number of constituent variable node degrees in the designed ensembles is only three or four. This, in some cases, is much smaller than the corresponding number for optimization-based designs with similar performance.