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.