Vector Flows and the Capacity of a Discrete Memoryless Channel

Author:

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

Keyword:

Computer Science, Information Theory, Information Theory (cs.IT)

journal:

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date:

2023-12-27 00:00:00

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.