Sparse code multiple access(SCMA)is a new non-orthogonal multiple access scheme,which effectively exploits the shaping gain of multi-dimensional codebook.Recently,the method of SCMA codebook design has drawn increasing attention.Previous works presented method to design SCMA codebooks based on the design principle of constellation.However,it is difficult to design a multi-dimensional SCMA codebook in this way.In this paper,a multi-dimensional SCMA(MD-SCMA)codebook design method based on multi-dimensional mother codebook and Latin structure constellation operator is proposed for downlink and uplink SCMA systems.In particular,the multi-dimensional mother codebook codebook is constructed by constellation rotation and interleaving,and the constellation operators are based on phases of users signal.Furthermore,the average energy,the minimum square Euclidean distance and the Peak to Average Power Ratio(PAPR)of mother codebook are derived and discussed.Simulation results show that the BER performance of MD-SCMA codebooks outperforms that of the existing SCMA codebooks and LDS in both uplink and downlink,especially in uplink where 3dB improvement can be achieved.