Channel input adaptation via natural type selection

We propose an algorithm for computation of the optimal correct-decoding exponent, and its corresponding optimal input. The computation algorithm translates into a stochastic iterative algorithm for adaptation of the codebook distribution to an unknown discrete memoryless channel in the limit of a large block length. The adaptation scheme uses i.i.d. random block codes, and it relies on one bit of feedback per transmitted block. Throughout the adaptation process, the communication itself is assumed reliable at a constant rate R below the channel capacity C. In the end of the iterations, the resulting codebook distribution guarantees reliable communication for all rates below R + Δ, where 0 < Δ ≤ C-R is a predetermined reliability parameter affecting the speed of adaptation.