On channel rate discovery for discrete memoryless binary output channels

This paper introduces an online active learning style algorithm that iteratively probes a discrete memoryless binary output channel (DMBOC), where the channel transition probability mass functions are not known, to establish a communication rate (close to the channel capacity C) with high probability. Techniques from pure-exploration multi-arm bandit problems are adapted to economically sample the channel as few times as possible to determine an assured lower bound rate RL such that RL⩾η R>U, where P{RL ⩾ C} < δL and P{RU ⩽ C} < δU for η ϵ[0, 1). After developing an O(N) lower bound on the minimum number of input-output sample pairs required for any algorithm to check whether a DMBOC channel supports rate RL given apriori channel knowledge, we show (empirically) that the proposed channel rate discovery (CDR) algorithm can achieve the same result with a sample complexity of O (N log (log N)) chosen channel-input probes and associated channel-output observations