Strong data processing constant is achieved by binary inputs

Abstract

For any channel $P_{Y|X}$ the strong data processing constant is defined as the smallest number ${\eta }_{KL}\in [0,1]$ such that $I(U;Y)\le {\eta }_{KL}I(U;X)$ holds for any Markov chain $U-X-Y$. It is shown that the value of ${\eta }_{KL}$ is given by that of the best binary-input subchannel of $P_{Y|X}$. The same result holds for any $f$-divergence, verifying a conjecture of Cohen, Kemperman and Zbaganu (1998).

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