In this letter, we present a design framework for fixed-point implementation of the log-domain message passing algorithm (Log-MPA) for sparse code multiple access signals, and make a detailed comparative analysis on the complexity of Log-MPA and traditional MPA. We also investigate the impact of the number of massage-passing iterations within the Log-MPA decoding process on the performance of Log-MPA. Simulation results demonstrate that Log-MPA achieves favorable performance with low-complexity hardware implementation as compared to MPA. We also implement Log-MPA on FPGA evaluation board to verify the performance of Log-MPA.