Collision Diversity SCRAM: Beyond the Sphere-Packing Bound

TL;DR

Collision Diversity SCRAM (CoD-SCRAM) reframes collisions in Slotted Coded Random Access Multiplexing as a source of diversity to boost spectral efficiency in 6G-like URLLC scenarios. It extends SCRAM with a uniform interleaved access design across multiple subgraphs, seeded by LFSRs, to minimize detrimental global cycles and trapping sets on a three-layer Tanner graph, while preserving LDPC decoding synergy. The approach leverages information-theoretic capacity insights to favor uniform-like access over random access, and demonstrates substantial PER improvements over SCRAM, NOMA, and RA-SPB bounds, effectively increasing the block-length gain through collision-induced diversity. With cycle-profile analysis and extensive simulations, CoD-SCRAM shows reduced global 8-cycles and enhanced decoding robustness, making it a promising candidate for scalable, low-latency multi-user access in future wireless networks.

Abstract

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.

Figures (7)

• Figure 1: Three-Layer Tanner graph example of SCRAM system with $N_{u}=4$ users, each tranmitting $n_{n_{u}}=6$ LDPC encoded symbols over a system with $N_{s}=12$ SA slots
• Figure 2: Simulated degree distribution of an SA system with $N_{s}=8064$ slots, incorporating $N_{u}=10$ users, each transmitting $n_{n_{u}}=4320$ bits
• Figure 3: Node degree distribution comparison of Random and Uniform Channel Access
• Figure 4: Interleaved Uniform Access with Collision Diversity example, of a SCRAM system with $N_{u}=4$ users, $n_{n_{u}}=6$ modulated symbols per user, and $N_{s}=12$ SA slots
• Figure 5: Flowchart of Interleaved Uniform Access SCRAM with Collision Diversity, on each user terminal, $U_{n_{u}}$, in the uplink scenario