Characterization of Factor Graph by Mooij's Sufficient Condition for Convergence of the Sum-Product Algorithm

Tomoharu SHIBUYA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A    No.11    pp.2083-2088
Publication Date: 2010/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.2083
Print ISSN: 0916-8508
Type of Manuscript: Special Section LETTER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
convergence of the sum-product algorithm,  factor graph,  message-passing,  sum-product decoding,  LDPC codes,  

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Recently, Mooij et al. proposed new sufficient conditions for convergence of the sum-product algorithm, and it was also shown that if the factor graph is a tree, Mooij's sufficient condition for convergence is always activated. In this letter, we show that the converse of the above statement is also true under some assumption, and that the assumption holds for the sum-product decoding. These newly obtained fact implies that Mooij's sufficient condition for convergence of the sum-product decoding is activated if and only if the factor graph of the a posteriori probability of the transmitted codeword is a tree.