  Grant-free multiple-access (GFMA) is a valuable research topic, since it can
support multiuser transmission with low latency. This paper constructs novel
uniquely-decodable multi-amplitude sequence (UDAS) sets for GFMA systems, which
can provide high spectrum efficiency (SE) with low-complexity active user
detection (AUD) algorithm. First of all, we propose an UDAS-based
multi-dimensional bit interleaving coded modulation (MD-BICM) transmitter; then
introduce the definition of UDAS and construct two kinds of UDAS sets based on
cyclic and quasi-cyclic matrix modes. Besides, we present a statistic of UDAS
feature based AUD algorithm (SoF-AUD), and a joint multiuser detection and
improved message passing algorithm for the proposed system. Finally, the active
user error rate (AUER) and Shannon limits of the proposed system are deduced in
details. Simulation results show that our proposed system can simultaneously
support four users without additional redundancy, and the AUER can reach an
extremely low value $10^{-5}$ when $E_b/N_0$ is $0$ dB and the length of
transmit block is larger than a given value, i.e., 784, verifying the validity
and flexibility of the proposed UDAS sets.
