Sparse Code Multiple Access (SCMA) and Blind Interference Alignment (BIA) are key enablers for multi-user communication, yet each suffers from distinct limitations: SCMA faces high complexity and limited multiplexing gain, while BIA requires a long temporal channel pattern and incurs significant decoding delay. This paper proposes SBMA (Sparsecode-and-BIA-based Multiple Access), a novel framework that synergizes SCMA's diversity and BIA's multiplexing while addressing their drawbacks. We design two decoders: a low-complexity two-stage decoder (Zero-forcing + Message Passing Algorithm (MPA)) and a Joint MPA (JMPA) decoder leveraging a virtual factor graph for improved BER. Theoretical analysis derives closed-form BER expressions for a 6-user 2x1 MISO system, validated by simulations. Compared to existing schemes, SBMA with JMPA achieves a diversity gain equivalent to STBC-SCMA and a multiplexing gain comparable to BIA, while simultaneously offering enhanced privacy (relative to STBC-SCMA) and reduced reliance on channel coherence time (compared to BIA). These advancements position SBMA as a compelling solution for next-generation wireless communication systems, particularly in IoT applications demanding high throughput, robust data privacy, and adaptability to dynamic channel conditions.