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2020

Strong data processing constant is achieved by binary inputs

Ordentlich, Or, Polyanskiy, Yury

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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).

Strong data processing constant is achieved by binary inputs · Around

Built on

I. Csiszár, “Information-type measures of difference of probability distributions and indirect observation,” studia scientiarum Mathematicarum Hungarica , vol. 2, pp. 229–318, 1967
1967
Earlier work this paper cites.
R. Ahlswede and P. Gács, “Spreading of sets in product spaces and hypercontraction of the markov operator,” The annals of probability , pp. 925–939, 1976
1976
Earlier work this paper cites.

Similar

J. Cohen, J. H. Kempermann, and G. Zbaganu, Comparisons of stochastic matrices with applications in information theory, statistics, economics and population . Springer Science & Business Media, 1998
1998
Cited alongside, same era.
Y. Polyanskiy and Y. Wu, “Strong data-processing inequalities for channels and Bayesian networks,” in Convexity and Concentration . Springer, 2017, pp. 211–249
2017
Cited alongside, same era.

Then

Y. Polyanskiy, “Post-SDPI and distributed estimation”, Lecture 5, Information-Theoretic Methods in Statistics and Computer Science , EPFL, 2019. http://people.lids.mit.edu/yp/homepage/data/LN_sdpi3.pdf
2019
Later among the works it cites.
——, “Application of the information-percolation method to reconstruction problems on graphs,” Mathematical Statistics and Learning , vol. 2, no. 1, pp. 1–24, 2020
2020
Closest in time.

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