Construction of Universal Codes Using LDPC Matrices and Their Error Exponents

Shigeki MIYAKE  Mitsuru MARUYAMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E90-A   No.9   pp.1830-1839
Publication Date: 2007/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e90-a.9.1830
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: 
Keyword: 
LDPC matrices,  universal code,  minimum entropy decoding,  error exponent,  

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Summary: 
A universal coding scheme for information from i.i.d., arbitrarily varying sources, or memoryless correlated sources is constructed using LDPC matrices and shown to have an exponential upper bound of decoding error probability. As a corollary, we construct a universal code for the noisy channel model, which is not necessarily BSC. Simulation results show universality of the code with sum-product decoding, and presence of a gap between the error exponent obtained by simulation and that obtained theoretically.