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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Vydáno v:	IEEE transactions on information theory Ročník 59; číslo 9; s. 5566 - 5576
Hlavní autor:	Merhav, Neri
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.09.2013 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	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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Popis
Shrnutí:	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.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2013.2266657