Collision Diversity SCRAM: Beyond the Sphere-Packing Bound

This paper presents a novel scheme dubbed Collision Diversity (CoD) SCRAM, which is provisioned to meet the challenging requirements of the future 6G, portrayed in massive connectivity, reliability, and ultra-low latency. The conventional SCRAM mechanism, which stands for Slotted Coded Random Access Multiplexing, is a hybrid decoding scheme, that jointly resolves collisions and decodes the Low Density Parity Check (LDPC) codewords, in a similar analogy to Belief Propagation (BP) decoding on a joint three-layer Tanner graph. The CoD SCRAM proposed herein tends to enhance the performance of SCRAM by adopting an information-theoretic approach that tends to maximize the attainable Spectral Efficiency. Besides, due to the analogy between the two-layer Tanner graph of classical LDPC codes, and the three-layer Tanner graph of SCRAM, the CoD SCRAM adopts the well-developed tools utilized to design powerful LDPC codes. Finally, the proposed CoD scheme tends to leverage the collisions among the users in order to induce diversity. Results show that the proposed CoD SCRAM scheme surpasses the conventional SCRAM scheme, which is superior to the state-of-the-art Non-Orthogonal Multiple Access (NOMA) schemes. Additionally, by leveraging the collisions, the CoD SCRAM tends to surpass the Sphere-Packing Bound (SPB) at the respective information block length of the underlying LDPC codes of the accommodated users.