Currently, sparse code multiple access (SCMA) is a commonly used multiple-access technique, and it is a strong candidate for implementation as part of the fifth generation (5G) of wireless mobile communications. Although several design methods are available for SCMA codebooks, we propose a new method that optimizes point-to-point distances within the same codeword and from codebook-to-codebook for the same carrier based on singular value decomposition (SVD). A neural network-based receiver is proposed for detecting and decoding SVD–SCMA codewords. The simulation results show an improvement in the bit error rate (BER) compared to that for methods such as low-density signatures (LDS), SCMA, and multidimensional SCMA (MD-SCMA).