Communicating using feedback over a binary channel with arbitrary noise sequence

Communications over a binary channel with an additive (modulo 2) individual noise sequence and a full causal feedback link is explored. A randomized sequential transmission scheme that adapts its rate to the individual noise realization is presented. The decoding rate is analyzed for a special case, and shown to asymptotically approach 1 - h_b (p_emp) with a vanishing probability of error w.r.t. the scheme´s randomization, where h_b (p_emp) is the empirical entropy of the noise sequence. Therefore, while the classical capacity of this channel is zero, information may be reliably transmitted over the channel by not committing to a rate in advance, but rather decoding at a rate dictated by the realized noise sequence