Channel Input Adaptation via Natural Type Selection

We propose an on-line algorithm for adapting the input of an unknown or slowly varying channel, while keeping reliable communication at some fixed rate R during the adaptation process. The purpose of the algorithm is to push the generating distribution of an i.i.d. random code toward the input that achieves the channel capacity C. The algorithm uses one bit feedback per each transmission block, that acknowledges whether the decoded codeword crossed some pre-determined threshold T > R, with respect to some 'fitness' metric. In the rare event of threshold crossing, the encoder and decoder update the input distribution according to the type of the current codeword, while the decoder updates the fitness metric. We show that for a large block length, this algorithm simulates computation of the channel correct-decoding exponent, and it leads to the capacity-achieving input if we set T = C.¹