Computer Science – Information Theory
Scientific paper
2008-08-05
Computer Science
Information Theory
13 pages, 1 figure, submitted to the International Workshop on Statistical-Mechanical Informatics (IW-SMI2008), Sendai
Scientific paper
10.1088/1742-6596/143/1/012018
We explore the relation between the techniques of statistical mechanics and information theory for assessing the performance of channel coding. We base our study on a framework developed by Gallager in {\em IEEE Trans. Inform. Theory} {\bf 11}, 3 (1965), where the minimum decoding error probability is upper-bounded by an average of a generalized Chernoff's bound over a code ensemble. We show that the resulting bound in the framework can be directly assessed by the replica method, which has been developed in statistical mechanics of disordered systems, whereas in Gallager's original methodology further replacement by another bound utilizing Jensen's inequality is necessary. Our approach associates a seemingly {\em ad hoc} restriction with respect to an adjustable parameter for optimizing the bound with a phase transition between two replica symmetric solutions, and can improve the accuracy of performance assessments of general code ensembles including low density parity check codes, although its mathematical justification is still open.
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