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.
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