Average Coset Weight Distribution of Multi-Edge Type LDPC Code Ensembles

Kenta KASAI  Yuji SHIMOYAMA  Tomoharu SHIBUYA  Kohichi SAKANIWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.10   pp.2519-2525
Publication Date: 2006/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.10.2519
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
Keyword: 
average coset weight distribution,  low-density parity-check codes,  multi-edge type low-density parity-check codes,  symmetry,  weight distribution,  

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Summary: 
Multi-Edge type Low-Density Parity-Check codes (MET-LDPC codes) introduced by Richardson and Urbanke are generalized LDPC codes which can be seen as LDPC codes obtained by concatenating several standard (ir)regular LDPC codes. We prove in this paper that MET-LDPC code ensembles possess a certain symmetry with respect to their Average Coset Weight Distributions (ACWD). Using this symmetry, we drive ACWD of MET-LDPC code ensembles from ACWD of their constituent ensembles.