Strong Data Processing Inequalities for Input Constrained Additive Noise Channels

This paper quantifies the intuitive observation that adding noise reduces available information by means of nonlinear strong data processing inequalities. Consider the random variables W → X → Y forming a Markov chain, where Y = X+Z with X and Z real valued, independent and X bounded in Li-norm. It is shown that I(W; Y) ≤ FI(I(W; X)) with FI(t) 0, if and only if Z has a density w...