Shannon Meets Turing: Non-Computability and Non-Approximability of the Finite State Channel Capacity

Boche, Holger; Schaefer, Rafael F.; Poor, H. Vincent

doi:10.48550/arxiv.2008.13270

Cited by 1 publication

(1 citation statement)

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“…However, this optimization is challenging since analytic computation of DI requires knowledge of the underlying probability law, which is typically unavailable in practice. Furthermore, even when the probability law is given, tractable DI characterizations that lend well for optimization are rare [17,18], as it is generally given by a multiletter expression. To address this, the goal of the paper is to develop a computable and provably accurate estimate of DI.…”

Section: Introductionmentioning

confidence: 99%

Neural Estimation and Optimization of Directed Information over Continuous Spaces

Tsur¹,

Aharoni²,

Goldfeld³

et al. 2022

Preprint

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This work develops a new method for estimating and optimizing the directed information rate between two jointly stationary and ergodic stochastic processes. Building upon recent advances in machine learning, we propose a recurrent neural network (RNN)-based estimator which is optimized via gradient ascent over the RNN parameters. The estimator does not require prior knowledge of the underlying joint and marginal distributions. The estimator is also readily optimized over continuous input processes realized by a deep generative model. We prove consistency of the proposed estimation and optimization methods and combine them to obtain end-to-end performance guarantees. Applications for channel capacity estimation of continuous channels with memory are explored, and empirical results demonstrating the scalability and accuracy of our method are provided. When the channel is memoryless, we investigate the mapping learned by the optimized input generator.

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Section: Introductionmentioning

confidence: 99%