Near-optimal Sampling to Optimize Communication Over Discrete Memoryless Channels

Abstract

This paper develops a strategy to minimize the number of channel probes required to recover the components of the channel law and maximize the reliable communication rate across a discrete memoryless channel (DMC). Based on the aggregate set of observed input-output pairs over time, the algorithm sequentially probes subsets of channel input values. We leverage a non-asymptotic probably approximately correct (PAC) bounds to establish the rate of convergence towards channel capacity as $O(\sqrt{\log(\log(N))\log(N)/N)}s$, where $N$ is the number of channel probes. For a discrete channel with $\vert \mathcal{X}\vert$ input values and $\vert \mathcal{Y}\vert$ output values, the sampling strategy may reduce the sample complexity by a factor of nearly $\min(\vert \mathcal{X}\vert /\vert \mathcal{Y}\vert, 1)$ relative to previous methods.