Abstract
In this paper, we consider a slot-controlled coded compressed sensing protocol for unsourced massive random access (URA) that concatenates a shared patterned Reed-Muller (PRM) inner codebook to an outer error-correction code. Due to the limitations of the geometry-based decoding algorithm in single-sequence settings and due to the message interference that may result in decreased decoding performance under multi-sequence circumstances, a list PRM projection algorithm and an iterative list PRM projection algorithm are proposed to supplant the signal detector associated with the inner PRM sequences in this paper. In detail, we first propose an enhanced path-saving algorithm, called list PRM projection detection, for use in single-user scenarios that maintains multiple candidates during the first few layers so as to remedy the risk of spreading errors. On this basis, we further propose an iterative list PRM projection algorithm for use in multi-user scenarios. The vectors for PRM codes and channel coefficients are jointly detected in an iterative manner, which offers significant improvements regarding the convergence rate for signal recovery. Furthermore, the performances of the proposed algorithms are analyzed mathematically, and we verify that the theoretical simulations are consistent with the numerical simulations. Finally, we concatenate the inner PRM codes that employ iterative list detection in two practical error-correction outer codes. According to the simulation results, we conclude that the packetized URA with the proposed iterative list projection detection works better than benchmarks in terms of the number of active users it can support in each slot and the amount of energy needed per bit to meet an expected error probability.