Maximal-capacity discrete memoryless channel identification
File(s)
Author(s)
Egger, Maximilian
Bitar, Rawad
Wachter-Zeh, Antonia
Gündüz, Deniz
Weinberger, Nir
Type
Journal Article
Abstract
The problem of identifying the channel with the highest capacity among several discrete memoryless channels (DMCs) is considered. The problem is cast as a pure-exploration multi-armed bandit problem, which follows the practical use of training sequences to sense the communication channel statistics. A gap-elimination algorithm termed BestChanID is proposed, which is oblivious to the capacity-achieving input distributions, and is guaranteed to output the DMC with the largest capacity, with a desired confidence. Furthermore, two additional algorithms NaiveChanSel and MedianChanEl, which output with certain confidence a DMC with capacity close to the maximal, are also presented. Each of these algorithms is shown to be beneficial in a different regime and can be used as a subroutine of BestChanID. To analyze the algorithms’ guarantees, a capacity estimator is proposed and tight confidence bounds on the estimator error are derived. Based on this estimator, the sample complexity of all the proposed algorithms is analyzed as a function of the desired confidence parameter, the number of channels, and the channels’ input and output alphabet sizes. The cost of best channel identification is shown to scale quadratically with the alphabet size, and a fundamental lower bound is derived on the number of channel senses required to identify the best channel with a certain confidence.
Date Issued
2025-02-01
Date Acceptance
2024-12-08
Citation
IEEE Transactions on Information Theory, 2025, 71 (2), pp.1248-1265
ISSN
0018-9448
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Start Page
1248
End Page
1265
Journal / Book Title
IEEE Transactions on Information Theory
Volume
71
Issue
2
Copyright Statement
© 2024 The Authors. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/
Identifier
10.1109/ISIT54713.2023.10206461].
Publication Status
Published
Date Publish Online
2024-12-24