  Reconfigurable intelligent surface (RIS) is considered as one of the key
technologies for future 6G communications. To fully unleash the performance of
RIS, accurate channel state information (CSI) is crucial. Beam training is
widely utilized to acquire the CSI. However, before aligning the beam correctly
to establish stable connections, the signal-to-noise ratio (SNR) at UE is
inevitably low, which reduces the beam training accuracy. To deal with this
problem, we exploit the coded beam training framework for RIS systems, which
leverages the error correction capability of channel coding to improve the beam
training accuracy under low SNR. Specifically, we first extend the coded beam
training framework to RIS systems by decoupling the base station-RIS channel
and the RIS-user channel. For this framework, codewords that accurately steer
to multiple angles is essential for fully unleashing the error correction
capability. In order to realize effective codeword design in RIS systems, we
then propose a new codeword design criterion, based on which we propose a
relaxed Gerchberg-Saxton (GS) based codeword design scheme by considering the
constant modulus constraints of RIS elements. In addition, considering the two
dimensional structure of RIS, we further propose a dimension reduced encoder
design scheme, which can not only guarentee a better beam shape, but also
enable a stronger error correction capability. Simulation results reveal that
the proposed scheme can realize effective and accurate beam training in low SNR
scenarios.
