Performance Analysis of RIS-Assisted Coded Cooperation System Based on Polar Codes With Finite Code Length

In this letter, we propose a novel reconfigurable intelligent surface (RIS)-assisted coded cooperation system based on polar codes to pursue the ultra-reliable and global coverage transmission. Firstly, we establish the RIS-assisted coded cooperation system based on polar codes. The polar codes employed at the source and relay are jointly designed by Plotkin construction method, and the joint decoding is performed at the destination. Subsequently, we derive the theoretical expressions for ergodic capacity (EC) under Nakagami- $m$ fading channel model with central limit theorem (CLT) and Gamma approximation (GA). Specially, the closed-form expression for EC with finite code length is obtained by approximating its tight upper and lower bounds. Finally, theoretical analysis and simulation results demonstrate the superiorities of the proposed system compared to the existing schemes, and also reveal that the EC of the proposed system with finite code length approaches the ideal EC as the code length of polar codes increases.