This paper investigates the reconfigurable intelligent surface (RIS) assisted spatial scattering modulation (SSM) scheme for millimeter-wave (mmWave) multiple-input multiple-output (MIMO) systems, in which line-of-sight (LoS) and non-line-of-sight (NLoS) paths are respectively considered in the transmitter-RIS and RIS-receiver channels. Based on the maximum likelihood detector, the conditional pairwise error probability (CPEP) expression for the RIS-SSM scheme is derived under the two cases of received beam correct and demodulation error. Furthermore, we derive the closed-form expressions of the unconditional pairwise error probability (UPEP) by employing two different methods: the probability density function and the moment-generating function expressions with a descending order of scatterer gains. To provide more useful insights, we derive the asymptotic UPEP and the diversity gain of the RIS-SSM scheme in the high SNR region. Depending on UPEP and the corresponding Euclidean distance, we get the union upper bound of the average bit error probability (ABEP). A new framework for ergodic capacity analysis is also provided to acquire the proposed system's effective capacity. Finally, all derivation results are validated via extensive Monte Carlo simulations, revealing that the proposed RIS-SSM scheme outperforms the benchmarks in terms of reliability.

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