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.

Quantization plays a central role in digital communication by mapping continuous-valued signals to a finite set of levels with minimal distortion. Beyond mean-square error, mutual information between the channel input and the quantizer output provides a powerful metric for signal recovery. However, finding the quantizer that maximizes the mutual information is NP-complete for non-binary inputs. To that end, while not optimal, thresholding schemes, whether single-threshold or multi-threshold, are widely adopted. In this work, we study the parallel stochastic single-threshold quantizer architecture, provide some information-theoretic insights, and introduce a momentum-accelerated gradient ascent algorithm that efficiently tunes a single decision threshold to maximize the mutual information. We demonstrate convergence improvements over exhaustive search and quantify mutual information gains across binary and non-binary input distributions. We also validate our theoretical framework with simulations on the MNIST dataset, demonstrating that increasing the number of parallel quantization branches, i.e., mutual information, significantly improves classification accuracy, especially when quantization thresholds are learned and training data is limited.

In this study the authors design the optimal rate capacity approaching irregular low-density parity-check code ensemble over binary erasure channel, by using practical semi-definite programming approach. The method does not use any relaxation or any approximate solution unlike previous works. The simulation results include two parts. First, we present some codes and their degree distribution functions that their rates are close to the capacity. Second, the maximum achievable rate behaviour of codes in our method is illustrated through some figures.

In this paper, we introduce a new practical and general method for solving the main problem of designing the capacity approaching, optimal rate, irregular low-density parity-check (LDPC) code ensemble over binary erasure channel (BEC). Compared to some new researches, which are based on application of asymptotic analysis tools out of optimization process, the proposed method is much simpler, faster, accurate and practical. Because of not using any relaxation or any approximate solution like previous works, the found answer with this method is optimal. We can construct optimal variable node degree distribution for any given binary erasure rate, e, and any check node degree distribution. The presented method is implemented and it works well in practice. The time complexity of this method is of polynomial order. As a result, we obtain some degree distribution which their rates are close to the capacity.