Multiuser Sum-Pattern Check Assisted Filtering Logic Decoding for Full-Rank Overloaded Spreading Multiple-Access Systems

The most popular multiuser detection (MUD) algorithm of overloaded spreading multiple-access is message passing algorithm (MPA) which can provide well-behaved error performance. Nevertheless, the MPA suffers from exponentially increasing complexity, and most existing techniques reduce complexity at the cost of degraded error performance. To tackle this issue, inspired by the concept of cyclic redundancy check (CRC), we propose a multiuser sum-pattern check (MSC) criterion based on the multiuser sum-pattern (MSP). Using MSC as an assistant, we develop a filtering logic decoding (FLD) algorithm that reduces detection complexity across different modulation formats and codebook structures, including both sparse and dense codebooks, without sacrificing error performance. In the high-SNR regime, FLD outputs low-complexity decisions that, with overwhelming probability, coincide with maximum likelihood (ML) decisions, implying asymptotic optimality. Simulation results show that FLD combined with MPA (FLD-MPA) achieves the same error performance as the original MPA detector, with significant complexity reductions, e.g., 66% fewer multiplications at E_b/N₀ = 13 dB for the SCMA/QPSK scenario.