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.

翻译：信息论奠基人香农于1948年创立该学科以来，其核心问题之一便是计算离散无记忆信道的容量——该量表示信息通过信道传输的最大速率。文献中已提出多种算法用以近似计算离散无记忆信道容量，但一般性离散无记忆信道的解析解仍不可得。本文提出一种基于连续时间动力系统的新颖方法，该动力系统可视为Blahut-Arimoto算法的连续时间形式。具体而言，Blahut-Arimoto算法中的更新映射通过适当离散化本文提出的向量流获得，其间借鉴了博弈论模型的类比关系。最后，这一类比启发了用于模拟计算容量估计的高层次硬件电路设计方案。