In this letter, a reconfigurable intelligent surface (RIS)-based symbiotic radio is addressed, which enables parasite communication through the passive reflection characteristics of the RIS. In RIS-assisted parasite communication where the information is embedded in the phase of the legacy signal, the receiver estimates the signal without the modulation scheme information of the legacy signal. In decoding the information conveyed via phase, the use of automatic modulation classification (MC) for the legacy signal is required, along with demodulation of the phase-shifted signal. To characterize the impacts of automatic MC and demodulation, the performance of parasite communication is analyzed in terms of the symbol error rate. Simulation results are presented to verify the accuracy of the analysis and the validity of parasite communication in the presence of a practical range of the number of RIS elements.