Abstract
—This paper investigates the maximal achievable rate for a given maximal error probability, and blocklength for the reconfigurable intelligent surface (RIS) assisted multiple-input and multiple-output (MIMO) system. The result consists of a finite blocklength and finite alphabet constraints channel coding achievability and converse bounds based on the Berry-Esseen theorem, the Mellin transform and the closed-form expression of the mutual information and the unconditional variance. The numerical evaluation shows a fast speed of convergence to the maximal achievable rate as the blocklength increases and also proves that the channel variance is a sound measurement of the backoff from the maximal achievable rate due to finite blocklength. Index Terms—RIS, MIMO, finite blocklength, achievable rate, achievablility bound, converse bound.