Variable-Length Sparse Feedback Codes for Point-to-Point, Multiple Access, and Random Access Channels

This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> de...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 70; no. 4; pp. 2367 - 2394
Main Authors: Yavas, Recep Can, Kostina, Victoria, Effros, Michelle
Format: Journal Article
Language:English
Published: New York IEEE 01.04.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
channel dispersion
Channels
Codes
Convergence
Decoding
Encoding
Error probability
Feedback
feedback codes
moderate deviations
Multiple access
Random access
Receivers
second-order analysis
sequential hypothesis testing
sparse feedback
Transmitters
Variable-length coding
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> decoding times <inline-formula> <tex-math notation="LaTeX">n_{1}, n_{2}, {\dots }, n_{L} </tex-math></inline-formula> for the point-to-point and multiple access channels and <inline-formula> <tex-math notation="LaTeX">KL + 1 </tex-math></inline-formula> decoding times for the random access channel with at most <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula> active transmitters. In the point-to-point and multiple access channels, the decoder uses the observed channel outputs to decide whether to decode at each of the allowed decoding times <inline-formula> <tex-math notation="LaTeX">n_{1}, {\dots }, n_{L} </tex-math></inline-formula>, at each time telling the encoder whether or not to stop transmitting using a single bit of feedback. In the random access scenario, the decoder estimates the number of active transmitters at time <inline-formula> <tex-math notation="LaTeX">n_{0} </tex-math></inline-formula> and then chooses among decoding times <inline-formula> <tex-math notation="LaTeX">n_{k, 1}, {\dots }, n_{k, L} </tex-math></inline-formula> if it believes that there are <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> active transmitters. In all cases, the choice of allowed decoding times is part of the code design; given fixed value <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula>, allowed decoding times are chosen to minimize the expected decoding time for a given codebook size and target average error probability. The number <inline-formula> <tex-math notation="LaTeX">L </tex-math></inline-formula> in each scenario is assumed to be constant even when the blocklength is allowed to grow; the resulting code therefore requires only sparse feedback. The central results are asymptotic approximations of achievable rates as a function of the error probability, the expected decoding time, and the number of decoding times. A converse for variable-length stop-feedback codes with uniformly-spaced decoding times is included for the point-to-point channel.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2023.3338632