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