Information Theory of Blockchain Systems

Abstract: In this paper, we apply the information theory to provide an approximate expression of the steady-state probability distribution for blockchain systems. We achieve this goal by maximizing an entropy function subject to specific constraints. These constraints are based on some prior information, including the average numbers of transactions in the block and the transaction pool, respectively. Furthermore, we use some numerical experiments to analyze how the key factors in this approximate expression depend on the crucial parameters of the blockchain system. As a result, this approximate expression has important theoretical significance in promoting practical applications of blockchain technology. At the same time, not only do the method and results given in this paper provide a new line in the study of blockchain queueing systems, but they also provide the theoretical basis and technical support for how to apply the information theory to the investigation of blockchain queueing networks and stochastic models more broadly.