Universal Decoding for Arbitrary Channels Relative to a Given Class of Decoding Metrics

We consider the problem of universal decoding for arbitrary, finite-alphabet unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average error probability is, within a subexponential m...

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Veröffentlicht in:IEEE transactions on information theory Jg. 59; H. 9; S. 5566 - 5576
1. Verfasser: Merhav, Neri
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.09.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Access methods and protocols, osi model
Applied sciences
Channel coding
Codes
Coding, codes
Entropy
Error exponents
Exact sciences and technology
feedback
finite-state machines
Information theory
Information, signal and communications theory
Lempel-Ziv algorithm
Maximum likelihood decoding
Maximum likelihood method
Measurement
mismatched decoding
multiple access channel (MAC)
Probability distribution
Signal and communications theory
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Teleprocessing networks. Isdn
Transmission and modulation (techniques and equipments)
universal decoding
Vectors
Alphabet
Access control
Multiple access
Error probability
multiple access channel (MAC)
Lempel Ziv algorithm
Finite state machine
Feedback regulation
Random coding
Random distribution
Mismatching
Maximum likelihood decoding
Lempel―Ziv algorithm
feedback
Universal coding
Error exponents
Metric
finite―state machines
Deterministic approach
Multiple channel
mismatched decoding
universal decoding
ISSN:0018-9448, 1557-9654
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Zusammenfassung:We consider the problem of universal decoding for arbitrary, finite-alphabet unknown channels in the random coding regime. For a given random coding distribution and a given class of metric decoders, we propose a generic universal decoder whose average error probability is, within a subexponential multiplicative factor, no larger than that of the best decoder within this class of decoders. Since the optimum, maximum likelihood (ML) decoder of the underlying channel is not necessarily assumed to belong to the given class of decoders, this setting suggests a common generalized framework for: 1) mismatched decoding, 2) universal decoding for a given family of channels, and 3) universal coding and decoding for deterministic channels using the individual sequence approach. The proof of our universality result is fairly simple, and it is demonstrated how some earlier results on universal decoding are obtained as special cases. We also demonstrate how our method extends to more complicated scenarios, like incorporation of noiseless feedback, the multiple access channel, and continuous alphabet channels.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2266657