Multiuser Transmission via Spatially-Coupled Non-Binary Factor Graphs

Toward next-generation multiple access, we propose a multiuser transmission framework via non-binary factor graphs defined over Galois field GF(
q
). The non-orthogonal multiuser transmission is realized by applying the GF(
q
) multiplication and superposition. In coordination with the high-order modulation, the proposed GF(
q
) codebook improves the cardinality of the superimposed constellation and reduces interference at each resource element. The proposed structure also characters for flexibility by spatially coupling the base graph when applying to different user scales. We have theoretically proved that both the system capacity and the error performance are improved due to the GF(
q
) operations. We utilize the simulated annealing algorithm to optimize both the base factor graph and the spatially-coupled graph, therefore short girths are eliminated or mitigated. The detection of the proposed scheme can be performed through iterative belief-propagation (BP) based on symbol-level log-domain probability vectors derived on the GF(
q
) factor graph. The numerical results in terms of upper bounds of maximum likelihood (ML) detection and symbol error rates through BP detection are both provided, which demonstrate the superiority of the GF(
q
) factor graphs to their binary counterparts. The performance can be further improved by increasing the field order
q
and/or by spatially coupling the non-binary factor graph.