An Extension of Gallager Ensemble of Low Density Parity Check Codes

Tadashi WADAYAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A   No.5   pp.1161-1171
Publication Date: 2002/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
LDPC code,  typical minimum distance ratio,  code ensemble,  iterative decoding,  

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Gallager has defined an ensemble of regular low density parity check (LDPC) codes for deriving the ensemble performance of regular LDPC codes. The ensemble is called the Gallager ensemble. In this paper, we define a new ensemble of LDPC codes, called extended Gallager ensemble, which is a natural extension of the Gallager ensemble. It is shown that an extended Gallager ensemble has potential to achieve larger typical minimum distance ratio than that of the original Gallager ensemble. In particular, the extended Gallager ensembles based on the Hamming and extended Hamming codes have typical minimum distance ratio which is very close to the asymptotic Gilbert-Varshamov bound. Furthermore, decoding performance of an instance of an extended Gallager ensemble, called an extended LDPC code, has been examined by simulation. The results show good block error performance of extended LDPC codes.