How to use several noisy channels with unknown error probabilities

Abstract

Consider a sender transmitting a given sequence of bits simultaneously through m binary symmetric channels with error probabilities ε1,…,εm such that 0⩽εi<1/2 for each i=1,…,m. The receiver can base its guess for the true transmitted bit on the m channel noisy outputs. Knowing the channel error probabilities, the receiver could apply the maximum likelihood estimator (MLE). What if the receiver does not know the channel error probabilities? In the paper, a strategy is derived whose error probability converges to that of the MLE with rate O(ln(n)/n), where n is the number of bits transmitted so far, whenever m⩾3.