Common-message broadcast channels with feedback in the nonasymptotic regime: Stop feedback
Journal article, 2018

We investigate the maximum coding rate for a given average blocklength and error probability over a $K$-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 $K$-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.

Broadcast channel with common-message

decision feedback

finite blocklength regime

stop feedback

channel dispersion

variable-length coding

Author

Kasper Fløe Trillingsgaard

Aalborg University

Wei Yang

Qualcomm Technologies

Giuseppe Durisi

Chalmers, Electrical Engineering, Communication and Antenna Systems, Communication Systems

Petar Popovski

Aalborg University

IEEE Transactions on Information Theory

0018-9448 (ISSN)

Vol. 64 12 7686-7718 8456639

Subject Categories

Telecommunications

Communication Systems

Signal Processing

DOI

10.1109/TIT.2018.2868953

More information

Latest update

12/10/2018