Strong Data Processing Constant Is Achieved by Binary Inputs

For any channel P-Y vertical bar X the strong data processing constant is defined as the smallest number eta(KL) is an element of [0,1] such that I(U;Y) <= eta I-KL(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 vertical bar X. The same result holds for any f-divergence, verifying a conjecture of Cohen, Kemperman and Zbaganu (1998).

Automated summary

The strong data processing constant is defined as the smallest number eta(KL) within [0,1] such that certain conditions hold for any Markov chain U - X - Y. The value of eta(KL) is determined by the best binary-input subchannel of P-Y vertical bar X, which also applies for any f-divergence, confirming a conjecture from Cohen, Kemperman, and Zbaganu (1998).