Relative entropy at the channel output of a capacity-achieving code

In this paper we establish a new inequality tying together the coding rate, the probability of error and the relative entropy between the channel and the auxiliary output distribution. This inequality is then used to show the strong converse, and to prove that the output distribution of a code must be close, in relative entropy, to the capacity achieving output distribution (for DMC and AWGN). One of the key tools in our analysis is the concentration of measure (isoperimetry).