Dissipation of Information in Channels With Input Constraints

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Dissipation of Information in Channels With Input Constraints
One of the basic tenets in information theory, the data processing inequality states that output divergence does not exceed the input divergence for any channel. For channels without input constraints, various estimates on the amount of such contraction are known, Dobrushin’s coefficient for the total variation being perhaps the most well-known. This work investigates channels with average input cost constraint. It is found that while the contraction coefficient typically equals one (no contraction), the information nevertheless dissipates. A certain nonlinear function, the Dobrushin curve of the channel, is proposed to quantify the amount of dissipation. Tools for evaluating the Dobrushin curve of additive-noise channels are developed based on coupling arguments. Some basic applications in stochastic control, uniqueness of Gibbs measures and fundamental limits of noisy circuits are discussed. As an application, it shown that in the chain of n power-constrained relays and Gaussian c...
Yury Polyanskiy, Yihong Wu 0001
Added 11 Apr 2016
Updated 11 Apr 2016
Type Journal
Year 2016
Where TIT
Authors Yury Polyanskiy, Yihong Wu 0001
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