Data-Driven Optimization of Directed Information over Discrete Alphabets

TL;DR

This paper introduces a novel reinforcement learning-based framework for estimating and optimizing directed information over discrete alphabets, enabling capacity estimation and probabilistic shaping without requiring explicit channel models.

Contribution

It develops an end-to-end estimation-optimization method combining neural estimators and reinforcement learning to optimize directed information over discrete channels with memory.

Findings

Successfully estimates channel capacity using the proposed method.

Provides theoretical bounds on feedback capacity of finite-state channels.

Enables probabilistic shaping in power-constrained Gaussian channels.

Abstract

Directed information (DI) is a fundamental measure for the study and analysis of sequential stochastic models. In particular, when optimized over input distributions it characterizes the capacity of general communication channels. However, analytic computation of DI is typically intractable and existing optimization techniques over discrete input alphabets require knowledge of the channel model, which renders them inapplicable when only samples are available. To overcome these limitations, we propose a novel estimation-optimization framework for DI over discrete input spaces. We formulate DI optimization as a Markov decision process and leverage reinforcement learning techniques to optimize a deep generative model of the input process probability mass function (PMF). Combining this optimizer with the recently developed DI neural estimator, we obtain an end-to-end estimation-optimization algorithm which is applied to estimating the (feedforward and feedback) capacity of various discrete channels with memory. Furthermore, we demonstrate how to use the optimized PMF model to (i) obtain theoretical bounds on the feedback capacity of unifilar finite-state channels; and (ii) perform probabilistic shaping of constellations in the peak power-constrained additive white Gaussian noise channel.