  In this paper, we study a concatenate coding scheme based on sparse
regression code (SPARC) and tree code for unsourced random access in massive
multiple-input and multiple-output systems. Our focus is concentrated on
efficient decoding for the inner SPARC with practical concerns. A two-stage
method is proposed to achieve near-optimal performance while maintaining low
computational complexity. Specifically, a one-step thresholding-based algorithm
is first used for reducing large dimensions of the SPARC decoding, after which
a relaxed maximum-likelihood estimator is employed for refinement. Adequate
simulation results are provided to validate the near-optimal performance and
the low computational complexity. Besides, for covariance-based sparse recovery
method, theoretical analyses are given to characterize the upper bound of the
number of active users supported when convex relaxation is considered, and the
probability of successful dimension reduction by the one-step
thresholding-based algorithm.
