Patterned Reed-Muller Sequences with Outer A-Channel Codes and Projective Decoding for Slot-Controlled Unsourced Random Access.

We propose a novel slot-pattern-control based coded compressed sensing for unsourced random access with an outer A-channel code capable of correcting errors. Specifically, an RM extension code called patterned Reed-Muller (PRM) code is proposed. We demonstrate the high spectral efficiency due to its enormous sequence space and prove the geometry property in the complex domain that enhances the reliability and efficiency of detection. Accordingly, a projective decoder based on its geometry theorem is also proposed. Next, the "patterned" property of the PRM code, which partitions the binary vector space into several subspaces, is further extended as the primary principle for designing a slot control criterion that reduces the number of simultaneous transmissions in each slot. The factors affecting the chance of sequence collisions are identified. Finally, the proposed scheme is implemented in two practical outer A-channel codes: (i) the -tree code and (ii) the Reed-Solomon code with Guruswami-Sudan list decoding, and the optimal setups are determined to minimize SNR by optimizing the inner and outer codes jointly. In comparison with the existing counterpart, our simulation results confirm that the proposed scheme compares favorably with benchmark schemes regarding the energy-per-bit requirement to meet a target error probability as well as the number of accommodated active users in the system.