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

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2 Author(s)
Yury Polyanskiy ; Department of Electrical Engineering and Computer Science, MIT, Cambridge, MA, 02139 USA ; Sergio VerdĂș

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).

Published in:

Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on

Date of Conference:

28-30 Sept. 2011