Common-Message Broadcast Channels With Feedback in the Nonasymptotic Regime: Stop Feedback

We investigate the maximum coding rate for a given average blocklength and error probability over a <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula>-user discrete memoryless broadcast channel for the scenario where a common message is trans...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 64; no. 12; pp. 7686 - 7718
Main Authors: Trillingsgaard, Kasper Floe, Yang, Wei, Durisi, Giuseppe, Popovski, Petar
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Asymptotic series
Broadcast channel with common-message
channel dispersion
Channels
Codes
Coding
Communication channels
Convergence
decision feedback
Decoding
Dispersion
Electronic mail
Encoding
Error probability
Feedback
finite blocklength regime
Probability distribution
stop feedback
variable-length coding
ISSN:0018-9448, 1557-9654, 1557-9654
Online Access:Get full text
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Summary:We investigate the maximum coding rate for a given average blocklength and error probability over a <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula>-user discrete memoryless broadcast channel for the scenario where a common message is transmitted using variable-length stop-feedback codes. For the point-to-point case, Polyanskiy et al. (2011) demonstrated that variable-length coding combined with stop-feedback significantly increases the speed of convergence of the maximum coding rate to capacity. This speed-up manifests itself in the absence of a square-root penalty in the asymptotic expansion of the maximum coding rate for large blocklengths, i.e., zero dispersion . In this paper, we present nonasymptotic achievability and converse bounds on the maximum coding rate of the common-message <inline-formula> <tex-math notation="LaTeX">K </tex-math></inline-formula>-user discrete memoryless broadcast channel, which strengthen and generalize the ones reported in Trillingsgaard et al. (2015) for the two-user case. An asymptotic analysis of these bounds reveals that zero dispersion cannot be achieved for certain common-message broadcast channels (e.g., the binary symmetric broadcast channel). Furthermore, we identify conditions under which our converse and achievability bounds are tight up to the second order. Through numerical evaluations, we illustrate that our second-order expansions approximate accurately the maximum coding rate and that the speed of convergence to capacity is indeed slower than for the point-to-point case.
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ISSN:0018-9448
1557-9654
1557-9654
DOI:10.1109/TIT.2018.2868953