  Sparse code multiple access (SCMA), which helps improve spectrum efficiency
(SE) and enhance connectivity, has been proposed as a non-orthogonal multiple
access (NOMA) scheme for 5G systems. In SCMA, codebook design determines system
overload ratio and detection performance at a receiver. In this paper, an SCMA
codebook design approach is proposed based on uniquely decomposable
constellation group (UDCG). We show that there are $N+1 (N \geq 1)$
constellations in the proposed UDCG, each of which has $M (M \geq 2)$
constellation points. These constellations are allocated to users sharing the
same resource. Combining the constellations allocated on multiple resources of
each user, we can obtain UDCG-based codebook sets. Bit error ratio (BER)
performance will be discussed in terms of coding gain maximization with
superimposed constellations and UDCG-based codebooks. Simulation results
demonstrate that the superimposed constellation of each resource has large
minimum Euclidean distance (MED) and meets uniquely decodable constraint. Thus,
BER performance of the proposed codebook design approach outperforms that of
the existing codebook design schemes in both uncoded and coded SCMA systems,
especially for large-size codebooks.
