Strong data processing constant is achieved by binary inputs

09/16/2020

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by   Or Ordentlich, et al.

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For any channel P_Y|X the strong data processing constant is defined as the smallest number η_KL∈[0,1] such that I(U;Y)≤η_KL I(U;X) holds for any Markov chain U-X-Y. It is shown that the value of η_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).