A Class of Nonbinary Symmetric Information Bottleneck Problems

10/03/2021

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by   Michael Dikshtein, et al.

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We study two dual settings of information processing. Let 𝖸→𝖷→𝖶 be a Markov chain with fixed joint probability mass function 𝖯_𝖷𝖸 and a mutual information constraint on the pair (𝖶,𝖷). For the first problem, known as Information Bottleneck, we aim to maximize the mutual information between the random variables 𝖸 and 𝖶, while for the second problem, termed as Privacy Funnel, our goal is to minimize it. In particular, we analyze the scenario for which 𝖷 is the input, and 𝖸 is the output of modulo-additive noise channel. We provide analytical characterization of the optimal information rates and the achieving distributions.