Maximal-Capacity Discrete Memoryless Channel Identification
ISIT(2024)
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
capacity estimator is proposed and tight confidence bounds on the estimator
error are derived. Based on this capacity estimator, a gap-elimination
algorithm termed BestChanID is proposed, which is oblivious to the
capacity-achieving input distribution and is guaranteed to output the DMC with
the largest capacity, with a desired confidence. Furthermore, two additional
algorithms NaiveChanSel and MedianChanEl, that output with certain confidence a
DMC with capacity close to the maximal, are introduced. Each of those
algorithms is beneficial in a different regime and can be used as a subroutine
in BestChanID. The sample complexity of all 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 for the required number of channel senses to identify
the best channel with a certain confidence is derived.
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Key words
alphabet size,arm identification problem,candidate DMCs,capacity estimator,capacity-achieving input distribution,channel identification scales,channel senses,channel sensing,channel statistics,derive associated concentration results,discrete memoryless channels,DMC,gap-elimination algorithm,input-output alphabet sizes,maximal-capacity discrete memoryless channel identification,multiarmed bandits
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