Coding theorems using Rényi information measures

We present single-shot coding theorems for standard problems in information theory and show that the results retain the form of their asymptotic counterparts, with Rényi information measures replacing the corresponding Shannon information measures. In particular, the code sizes for fixed-length lossless source codes are bounded in terms of Rényi entropy and conditional Rényi entropy; code sizes for channel coding and for lossy source coding are bounded in terms of appropriate notions of Rényi mutual information. As a corollary, we identify simple sufficient conditions for asymptotic optimal rates to not depend on the probability of error, i.e., for the strong converse property to hold, in the lossless source coding and the channel coding problems.