TY - GEN

T1 - The Compound Information Bottleneck Program

AU - Dikshtein, Michael

AU - Weinberger, Nir

AU - Shitz, Shlomo Shamai

N1 - Publisher Copyright:
© 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - Motivated by the emerging technology of oblivious processing in remote radio heads with universal decoders, we formulate and analyze in this paper a compound version of the information bottleneck problem. In this problem, a Markov chain X→Y→ Z is assumed, and the marginals PX and PY are set. The mutual information between X and Z is sought to be maximized over the choice of the conditional probability of Z given Y from a given class, under the worst choice of the joint probability of the pair (X,Y) from a different class. We provide values, bounds, and various characterizations for specific instances of this problem: the binary symmetric case, the scalar Gaussian case, the vector Gaussian case, the symmetric modulo-additive case, and the total variation constraints case. Finally, for the general case, we propose a Blahut-Arimoto type of alternating iterations algorithm to find a consistent solution to this problem.

AB - Motivated by the emerging technology of oblivious processing in remote radio heads with universal decoders, we formulate and analyze in this paper a compound version of the information bottleneck problem. In this problem, a Markov chain X→Y→ Z is assumed, and the marginals PX and PY are set. The mutual information between X and Z is sought to be maximized over the choice of the conditional probability of Z given Y from a given class, under the worst choice of the joint probability of the pair (X,Y) from a different class. We provide values, bounds, and various characterizations for specific instances of this problem: the binary symmetric case, the scalar Gaussian case, the vector Gaussian case, the symmetric modulo-additive case, and the total variation constraints case. Finally, for the general case, we propose a Blahut-Arimoto type of alternating iterations algorithm to find a consistent solution to this problem.

UR - http://www.scopus.com/inward/record.url?scp=85136301229&partnerID=8YFLogxK

U2 - 10.1109/ISIT50566.2022.9834812

DO - 10.1109/ISIT50566.2022.9834812

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AN - SCOPUS:85136301229

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2475

EP - 2480

BT - 2022 IEEE International Symposium on Information Theory, ISIT 2022

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2022 IEEE International Symposium on Information Theory, ISIT 2022

Y2 - 26 June 2022 through 1 July 2022

ER -