This paper studies a cooperative relaying communication scheme that employs a single passive reconfigurable intelligent surface (RIS), utilizing integer forcing (IF) as a multiple-input multiple-output (MIMO) technique. In the case of IF-based transceivers, the transmitter sends independently encoded data streams using the same lattice code, and the receiver decodes integer-linear combinations of codewords instead of decoding each codeword separately. Although the flexible decoding provided by IF improves achievable rates compared to conventional separate decoding, the integer-linear combinations observed at the IF-based receiver must remain unchanged throughout the codeword's duration, even in the presence of channel variations, to enable the decoding of summed codewords. Motivated by this fact, we introduce a novel strategy tailored for IF that involves adjusting the reflection matrix of the RIS to reduce fluctuations in the resulting end-to-end channel between the transmitter and receiver throughout codeword transmission, which we refer to as channel stabilization. Furthermore, we develop a novel IF-based transceiver scheme called successive cancellation IF (SC-IF), which effectively integrates successive IF (S-IF) sum decoding with minimum mean square error-successive interference cancellation (MMSE-SIC) individual decoding within a unified MIMO framework to achieve improved performance. Simulation results demonstrate that when a large number of reflective elements are employed in the RIS, the proposed channel stabilization scheme significantly outperforms benchmark schemes that aim to individually optimize the reflection matrix for each sub-block, and the proposed SC-IF can achieve a rate comparable to the theoretical upper bound represented by the joint maximal likelihood (ML) receiver.
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