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Grant-free multiple-access (GFMA) is a valuable research topic, since it cansupport multiuser transmission with low latency. This paper constructs noveluniquely-decodable multi-amplitude sequence (UDAS) sets for GFMA systems, whichcan provide high spectrum efficiency (SE) with low-complexity active userdetection (AUD) algorithm. First of all, we propose an UDAS-basedmulti-dimensional bit interleaving coded modulation (MD-BICM) transmitter; thenintroduce the definition of UDAS and construct two kinds of UDAS sets based oncyclic and quasi-cyclic matrix modes. Besides, we present a statistic of UDASfeature based AUD algorithm (SoF-AUD), and a joint multiuser detection andimproved message passing algorithm for the proposed system. Finally, the activeuser error rate (AUER) and Shannon limits of the proposed system are deduced indetails. Simulation results show that our proposed system can simultaneouslysupport four users without additional redundancy, and the AUER can reach anextremely low value $10^{-5}$ when $E_b/N_0$ is $0$ dB and the length oftransmit block is larger than a given value, i.e., 784, verifying the validityand flexibility of the proposed UDAS sets.

Uniquely Decodable Multi-Amplitude Sequence for Grant-Free Multiple-Access Adder Channels