  Sparse Code Multiple Access (SCMA) has been recently proposed for the future
generation of wireless communication standards. SCMA system design involves
specifying several parameters. In order to simplify the procedure, most works
consider a multistage design approach. Two main stages are usually emphasized
in these methods: sparse signatures design (equivalently, resource allocation)
and codebook design. In this paper, we present a novel SCMA codebook design
method. The proposed method considers SCMA codebooks structured with an
underlying vector space obtained from classical block codes. In particular,
when using maximum distance separable (MDS) codes, our proposed design provides
maximum signal-space diversity with a relatively small alphabet. The use of
small alphabets also helps to maintain desired properties in the codebooks,
such as low peak-to-average power ratio and low-complexity detection.
