Codeword or Noise? Exact Random Coding Exponents for Joint Detection and Decoding

We consider the problem of coded communication, where in each time frame, the transmitter is either silent or transmits a codeword from a given (randomly selected) codebook. The task of the decoder is to decide whether transmission has taken place, and if so, to decode the message. We derive the opt...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 60; no. 9; pp. 5077 - 5094
Main Authors: Weinberger, Nir, Merhav, Neri
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.09.2014
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Coding theory
Coding, codes
Communications networks
Decoding
Detectors
Encoding
Exact sciences and technology
Information theory
Information, signal and communications theory
Joints
Noise
Radiocommunications
Signal and communications theory
Telecommunications
Telecommunications and information theory
Transmitters
Transmitters. Receivers
Vectors
unequal error protection
error exponent
false alarm
misdetection
Joint detection/decoding
synchronization
random coding
Transmitter
Decoding
Random coding
Optimal detection
Synchronization
Joint detection
False alarm rate
Codebook
Error correction
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:We consider the problem of coded communication, where in each time frame, the transmitter is either silent or transmits a codeword from a given (randomly selected) codebook. The task of the decoder is to decide whether transmission has taken place, and if so, to decode the message. We derive the optimum detection/decoding rule in the sense of the best tradeoff among the probabilities of decoding error, false alarm, and misdetection. For this detection/decoding rule, we then derive single-letter characterizations of the exact exponential rates of these probabilities for the average code in the ensemble. It is shown that previously proposed decoders are in general strictly suboptimal.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2014.2335733