SCMA Codebook Design Based on Uniquely Decomposable Constellation Groups

Xuewan Zhang, Dalong Zhang, Liuqing Yang, Gangtao Han, Hsiao Hwa Chen, DI Zhang

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 ( Nge 1 ) constellations in the proposed UDCG, each of which has M (Mge 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.

Original languageEnglish (US)
Article number9371420
Pages (from-to)4828-4842
Number of pages15
JournalIEEE Transactions on Wireless Communications
Issue number8
StatePublished - Aug 2021

Bibliographical note

Funding Information:
Manuscript received April 1, 2020; revised September 2, 2020 and December 10, 2020; accepted February 17, 2021. Date of publication March 5, 2021; date of current version August 12, 2021. This work was supported in part by the National Science Foundation of China (NSFC) under Grant 62001423, in part by the Henan Provincial Key Research, Development and Promotion Project under Grant 212102210175 and Grant 202102210123, and in part by the Henan Provincial Key Scientific Research Project for College and University under Grant 21A510011. The associate editor coordinating the review of this article and approving it for publication was H. Pishro-Nik. (Corresponding author: Di Zhang.) Xuewan Zhang, Dalong Zhang, Gangtao Han, and Di Zhang are with the School of Information Engineering, Zhengzhou University, Zhengzhou 450001, China (e-mail:;;;

Publisher Copyright:
© 2002-2012 IEEE.


  • Sparse code multiple access (SCMA)
  • codebook design
  • non-orthogonal multiple access (NOMA)
  • uniquely decomposable constellation group (UDCG)


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