# Vector Flows That Compute the Capacity of Discrete Memoryless Channels

## TL;DR

This paper introduces a new continuous-time method to compute the capacity of communication channels, inspired by the Blahut–Arimoto algorithm and suitable for analog computation.

## Contribution

A novel continuous-time dynamical system for computing channel capacity with proven convergence properties and an analog circuit implementation.

## Key findings

- The proposed system is a continuous-time version of the Blahut–Arimoto algorithm with exponential convergence under certain conditions.
- An analog circuit design is presented to implement the dynamics for estimating channel capacity.
- The method bridges classical information theory with continuous-time computation and hardware implementation.

## Abstract

One of the fundamental problems of information theory, since its foundation by C. Shannon, 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 this paper, we investigate the properties of a novel approach to computing the capacity, based on a continuous-time dynamical system. Interestingly, the proposed dynamical system can be regarded as a continuous-time version of the classical Blahut–Arimoto algorithm, and we can prove that the former shares with the latter an exponential rate of convergence if certain conditions are met. Moreover, a circuit design is presented to implement the dynamics, hence enabling analog computation to estimate the capacity.