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.
翻译:直接信息(DI)是研究和分析相继随机分析模型的一项基本措施。特别是,当对一般通信渠道的能力进行优化的输入分布优化时,一般通信渠道的能力特征是优化输入分布,但是,对DI的分析计算通常是棘手的,对于离散输入字母而言,现有优化技术要求了解频道模型,因此在只有样本的情况下无法适用。为了克服这些限制,我们提议了一个用于对离散输入空间进行数据交换的新颖的估计-优化框架。我们制定数据优化作为Markov决定程序,并利用强化学习技术优化输入过程概率质量功能的深层基因化模型(PMF)。将这一优化模型与最近开发的DI神经测量仪结合起来,我们获得一种终端到终端估计-优化算法,用于估计具有记忆的各种离散渠道的(前进和反馈)能力。此外,我们演示如何使用优化的 PMF模型来(i) 获得关于非固定状态有限频道反馈能力的理论约束;(ii) 进行高压级的星座峰级变压;以及(ii) 进行高压级级级级变动。