Channel Detection in Coded Communication

The problem of block-coded communication where in each block the channel law belongs to one of two disjoint sets is considered. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to detect the set which contains the underlying channel. The s...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 63; no. 10; pp. 6364 - 6392
Main Authors: Weinberger, Nir, Merhav, Neri
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Channels
Coding
Decoding
Detection complexity
Detectors
Encoding
Error analysis
Error detection
error exponents
Error probability
Exponents
expurgated bounds
false alarm
False alarms
joint detection/decoding
Maximum likelihood decoding
misdetection
mismatch detection
Optimization
random coding
Receivers
Transmitters
universal detection
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
Summary:The problem of block-coded communication where in each block the channel law belongs to one of two disjoint sets is considered. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to detect the set which contains the underlying channel. The simplified case where each of the sets is a singleton is studied first. The decoding error, false alarm, and misdetection probabilities of a given code are defined, and the optimum detection/decoding rule in a generalized Neyman-Pearson sense is derived. Sub-optimal detection/decoding rules are also introduced which are simpler to implement. Then, various achievable bounds on the error exponents are derived, including the exact single-letter characterization of the random coding exponents for the optimal detector/decoder. The random coding analysis is then extended to general sets of channels, and an asymptotically optimal detector/decoder under a worst case formulation of the error probabilities is derived, as well as its random coding exponents. The case of a pair of binary symmetric channels is discussed in detail.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2017.2732356