  We compare dirty paper coding (DPC) and linear precoding methods in a
reconfigurable intelligent surface (RIS)- aided high-signal-to-noise ratio
(SNR) scenario, where the channel between the base station (BS) and the RIS is
dominated by a line-of-sight (LOS) component. Furthermore, we consider two
groups of users where one group can be efficiently served by the BS, whereas
the other one has a negligible direct channel and has to be served via the RIS.
Within this scenario, we analytically show fundamental differences between DPC
and linear methods. In particular, our analysis addresses two essential
aspects, i.e., the orthogonality of the BS-RIS channel with the direct channel
and a channel mitigation term, depending on the number of RIS elements, that is
present only for linear precoding techniques. The mitigation term generally
leads to strong limitations for the linear method, especially for random or
statistical phase shifts. Moreover, we discuss under which circumstances this
mitigation term is negligible and in which scenarios DPC and linear precoding
lead to the same performance.
