Arimoto Channel Coding Converse and Renyi Divergence
Arimoto proved a non-asymptotic upper bound on the probability of successful decoding achievable by any code on a given discrete memory-less channel. In this paper the authors present a simple derivation of the Arimoto converse based on the data-processing inequality for Renyi divergence. The method has two benefits. First, it generalizes to codes with feedback and gives the simplest proof of the strong converse for the DMC with feedback. Second, it demonstrates that the sphere-packing bound is strictly tighter than Arimoto converse for all channels, block-lengths and rates, since in fact they derive the latter from the former. Finally, they prove similar results for other (non-Renyi) divergence measures.