Notes on Conditional Entropy and Commitment Capacity

. The so-called commitment capacity of a discrete memoryless channel is given by the maximum of the conditional Shannon entropy H ( X | Y ) over all input distributions. We examine in detail this optimization problem, motivated by its relevance in information-theoretic cryptography. In particular, we study the role of the channel’s connected components in attaining the commitment capacity, and the questions of uniqueness and support of the optimal (capacity-achieving) input and output distributions. We also describe an iterative algorithm for computing the commitment capacity and the optimal input distribution.