Paper Info
Title
How Could The Replica Method Improve Accuracy Of Performance Assessment Of Channel Coding?
Abstract
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 IEEE Trans. Inform. Theory IT-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 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.
Year
DOI
Venue
2008
10.1088/1742-6596/143/1/012018
INTERNATIONAL WORKSHOP ON STATISTICAL-MECHANICAL INFORMATICS 2008 (IW-SMI 2008)
Keywords
Field
DocType
jensen s inequality,channel coding,statistical mechanics,error probability,information theory,upper bound,phase transition
Information theory,Channel code,Replica,Statistical mechanics,Binary symmetric channel,Decoding error probability,Low-density parity-check code,Theoretical computer science,Code (cryptography),Mathematics
Journal
Volume
Issue
ISSN
143
1
1742-6588
Citations 
PageRank 
References 
2
0.39
4
Authors
1
Name
Order
Citations
PageRank
Yoshiyuki Kabashima113627.83