As an advanced non-orthogonal multiple access (NOMA) technique, the low density signature (LDS) has never been used in filter bank multicarrier (FBMC) systems. In this paper, we model a low density weight matrix (LDWM) to utilize the intrinsic interference in FBMC systems, and propose a LDS-FBMC scheme which applies LDS to FBMC signals. In addition, a joint sparse graph for FBMC named JSG-FBMC is proposed to combine single graphs of LDS, LDWM and low density paritycheck (LDPC) codes which respectively represent techniques of NOMA, multicarrier modulation and channel coding. By employing the message passing algorithm (MPA), a joint receiver performing detection and decoding simultaneously on the joint sparse graph is designed. Extrinsic information transfer (EXIT) charts and construction guidelines of the joint sparse graph are studied. Simulations show the superiority of JSG-FBMC to stateof-the-art techniques such as OFDM, FBMC, LDS-OFDM, LDS-FBMC and turbo structured LDS-FBMC.