Vector Flows and the Capacity of a Discrete Memoryless Channel

G. Beretta; G. Chiarot; A. E. Cinà; M. Pelillo

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arXiv · 2312.16472

Vector Flows and the Capacity of a Discrete Memoryless Channel

G. Beretta·G. Chiarot·A. E. Cinà·M. Pelillo

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Abstract

One of the fundamental problems of information theory, since its foundation by Shannon in 1948, has been the computation of the capacity of a discrete memoryless channel, a quantity expressing the maximum rate at which information can travel through the channel. In the literature, several algorithms were proposed to approximately compute the capacity of a discrete memoryless channel, being an analytical solution unavailable for the general discrete memoryless channel. This paper presents a novel approach to compute the capacity, which is based on a continuous-time dynamical system. Such a dynamical system can indeed be regarded as a continuous-time version of the Blahut-Arimoto algorithm. In fact, the updating map appearing in the Blahut-Arimoto algorithm is here obtained as a suitable discretization of the vector flow presented, using an analogy with some game-theoretical models. Finally, this analogy suggests a high-level hardware circuit design enabling analog computation to estimate the capacity.

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G. Beretta, G. Chiarot, A. E. Cinà, M. Pelillo. 2023-12-27. Vector Flows and the Capacity of a Discrete Memoryless Channel. https://arxiv.org/abs/2312.16472

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