Expurgated Random-Coding Ensembles: Exponents, Refinements, and Connections

This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and nonasymptotic bounds on the error probability for an arbitrary codeword distribu...

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Bibliographic Details
Published in:IEEE transactions on information theory 2014-08, Vol.60 (8), p.4449-4462
Main Authors: Scarlett, Jonathan, Peng, Li, Merhav, Neri, Martinez, Alfonso, Guillen i Fabregas, Albert
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic methods
Asymptotic properties
Channels
Codes
Coding
Coding, codes
Decoding
Derivation
Electronic mail
Encoding
Error analysis
Error probability
Exact sciences and technology
Exponents
Expurgated error exponents
Information theory
Information, signal and communications theory
IP networks
Joints
Lagrange multiplier
Maximum-likelihood decoding
Measurement
Mismatched decoding
Permissible error
Probability distribution
Random coding
Reliability function
Signal and communications theory
Telecommunications and information theory
Type class enumeration
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Summary:This paper studies expurgated random-coding bounds and exponents for channel coding with a given (possibly suboptimal) decoding rule. Variations of Gallager's analysis are presented, yielding several asymptotic and nonasymptotic bounds on the error probability for an arbitrary codeword distribution. A simple nonasymptotic bound is shown to attain an exponent of Csiszár and Körner under constant-composition coding. Using Lagrange duality, this exponent is expressed in several forms, one of which is shown to permit a direct derivation via cost-constrained coding that extends to infinite and continuous alphabets. The method of type class enumeration is studied, and it is shown that this approach can yield improved exponents and better tightness guarantees for some codeword distributions. A generalization of this approach is shown to provide a multiletter exponent that extends immediately to channels with memory.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2322033