Sparse code multiple access (SCMA) is a promising uplink multiple access technique that can achieve superior spectral efficiency, provided that multidimensional codebooks are carefully designed. In this letter, we investigate the multiuser codebook design for SCMA systems over Rayleigh fading channels. The criterion of the proposed design is derived from the cutoff rate analysis of the equivalent multiple-input multiple-output system. Furthermore, new codebooks with signal-space diversity are suggested, while simulations show that this criterion is efficient in developing codebooks with substantial performance improvement, compared with the existing ones.