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On the Achievable Rate Under Finite Codelength for RIS-Aided Systems

The ideal Shannon channel capacity can only be achieved by infinite codelength, so it is not accurate for practical finite codelength. The codelength of channel coding schemes heavily affects the performance of communication systems, but it cannot be too long to ensure affordable decoding complexity and latency. Unfortunately, existing performance analysis for systems aided by reconfigurable intelligent surface (RIS) only focus on the ideal channel capacity and neglect the achievable rate loss caused by finite codelength. To fill in this gap, this paper analyzes the achievable rate under finite codelength in a time-coherent RIS-aided systems, and gives an approximate analytic solution based on Taylor expansion and multi-dimensional central limit theorem. To be more specific, the closed form approximated achievable rate is given based on Taylor expansion, and it is shown that the required codelength decreases superlinearly with the increase of the number of RIS elements. Simulation results verify the analysis, and demonstrate the advantage of RIS-aided systems over the traditional large antenna array schemes.