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Abstract: We explore the relation between the techniques of statistical mechanics andinformation theory for assessing the performance of channel coding. We base ourstudy on a framework developed by Gallager in {\em IEEE Trans. Inform. Theory}{\bf 11}, 3 1965, where the minimum decoding error probability isupper-bounded by an average of a generalized Chernoff-s bound over a codeensemble. We show that the resulting bound in the framework can be directlyassessed by the replica method, which has been developed in statisticalmechanics of disordered systems, whereas in Gallager-s original methodologyfurther replacement by another bound utilizing Jensen-s inequality isnecessary. Our approach associates a seemingly {\em ad hoc} restriction withrespect to an adjustable parameter for optimizing the bound with a phasetransition between two replica symmetric solutions, and can improve theaccuracy of performance assessments of general code ensembles including lowdensity parity check codes, although its mathematical justification is stillopen.



Author: Yoshiyuki Kabashima

Source: https://arxiv.org/



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