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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.11352 |
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| _version_ | 1866913115454570496 |
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| author | Tavakoli, Hassan Nguyen, Thinh Bose, Bella |
| author_facet | Tavakoli, Hassan Nguyen, Thinh Bose, Bella |
| contents | We study the problem of estimating a parametric discrete memoryless channel \( p(y \mid x; \boldsymbolθ) \) when the transmitter selects its input distribution \( π\) to maximize mutual information under the true parameter \( \boldsymbolθ^* \). Using only i.i.d.\ observations of the channel output, we aim to jointly estimate the capacity-achieving input distribution \( \boldsymbolπ^* \) and the true channel parameter \( \boldsymbolθ^* \). In general, recovery of \( \boldsymbolπ^* \) and \( \boldsymbolθ^* \) 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 \( \boldsymbolθ^* \) and \( \boldsymbolπ^* \), whereas a naive maximum-likelihood approach that ignores the mutual-information maximization constraint fails to do so. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11352 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parameter Estimation of Mutual Information Maximized Channels Tavakoli, Hassan Nguyen, Thinh Bose, Bella Information Theory Signal Processing We study the problem of estimating a parametric discrete memoryless channel \( p(y \mid x; \boldsymbolθ) \) when the transmitter selects its input distribution \( π\) to maximize mutual information under the true parameter \( \boldsymbolθ^* \). Using only i.i.d.\ observations of the channel output, we aim to jointly estimate the capacity-achieving input distribution \( \boldsymbolπ^* \) and the true channel parameter \( \boldsymbolθ^* \). In general, recovery of \( \boldsymbolπ^* \) and \( \boldsymbolθ^* \) 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 \( \boldsymbolθ^* \) and \( \boldsymbolπ^* \), whereas a naive maximum-likelihood approach that ignores the mutual-information maximization constraint fails to do so. |
| title | Parameter Estimation of Mutual Information Maximized Channels |
| topic | Information Theory Signal Processing |
| url | https://arxiv.org/abs/2605.11352 |