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 Vol. 60; no. 8; pp. 4449 - 4462
Main Authors: Scarlett, Jonathan, Peng, Li, Merhav, Neri, Martinez, Alfonso, Guillen i Fabregas, Albert
Format: Journal Article Conference Proceeding
Language:English
Published: New York, NY IEEE 01.08.2014
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers (IEEE)
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
maximum-likelihood decoding
reliability function
random coding
type class enumeration
mismatched decoding
Expurgated error exponents
Alphabet
Channel with memory
Error probability
Refinement method
Random coding
Channel coding
Mismatching
Maximum likelihood decoding
Reliability
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2322033