Parameter Estimation of Mutual Information Maximized Channels

Hassan Tavakoli; Thinh Nguyen; Bella Bose

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arXiv · 2605.11352

Parameter Estimation of Mutual Information Maximized Channels

Hassan Tavakoli·Thinh Nguyen·Bella Bose

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Abstract

We study the problem of estimating a parametric discrete memoryless channel $ p(y \mid x; \boldsymbol{\theta}) $ when the transmitter selects its input distribution $ \pi $ to maximize mutual information under the true parameter $ \boldsymbol{\theta}^* $. Using only i.i.d.\ observations of the channel output, we aim to jointly estimate the capacity-achieving input distribution $ \boldsymbol{\pi}^* $ and the true channel parameter $ \boldsymbol{\theta}^* $. In general, recovery of $ \boldsymbol{\pi}^* $ and $ \boldsymbol{\theta}^* $ can be challenging. To that end, we propose two efficient algorithms based on the Blahut--Arimoto (BA) optimality conditions: (i) a bilevel fixed-point method and (ii) an augmented Lagrangian method. Empirical results demonstrate that both proposed algorithms successfully recover the true $ \boldsymbol{\theta}^* $ and $ \boldsymbol{\pi}^* $, whereas a naive maximum-likelihood approach that ignores the mutual-information maximization constraint fails to do so.

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Hassan Tavakoli, Thinh Nguyen, Bella Bose. 2026-05-12. Parameter Estimation of Mutual Information Maximized Channels. https://arxiv.org/abs/2605.11352

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