Parameter Estimation of Mutual Information Maximized Channels

2026-05-11

AI Summary

This work addresses the challenging problem of jointly estimating the true channel parameters and the capacity-achieving input distribution in discrete memoryless channels when only channel outputs are observed. To tackle this, the study formulates the task as a mutual information maximization problem and innovatively incorporates the Blahut–Arimoto optimality conditions into parameter estimation. The authors propose a bilevel fixed-point algorithm combined with an augmented Lagrangian method to effectively handle the mutual information constraint inherent in the formulation. Experimental results demonstrate that the proposed approach accurately recovers both the underlying channel parameters and the capacity-achieving input distribution, significantly outperforming naive maximum likelihood estimation that disregards the mutual information constraint.

Abstract

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.

Problem

• parameter estimation
• mutual information
• discrete memoryless channel
• capacity-achieving input distribution
• channel identification

Innovation

• mutual information maximization
• channel parameter estimation
• Blahut–Arimoto algorithm
• capacity-achieving input distribution
• augmented Lagrangian method