Design of Enhanced Protograph Codes and Codebooks for IDD-SCMA Systems

This paper investigates the design of protograph low-density parity-check (PLDPC) codes and Gray-labeling codebooks (CBs) for the sparse code multiple access systems with iterative detection and decoding receiver (IDD-SCMA). Specifically, leveraging the protograph extrinsic information transfer (PEXIT) analysis, we first propose two types of PLDPC codes (i.e., an unpunctured Code-W and a punctured Code-V) which achieve the lowest decoding thresholds for the IDD-SCMA systems over AWGN and Rayleigh fading channels. To further enhance system performance, we focus on the critical role of Gray-labeling in the PLDPC-coded-IDD-SCMA systems, which are regarded as specific types of bit-interleaved coded modulation with iterative decoding (BICM-ID) systems. Subsequently, we devise a simple SCMA CB design scheme, referred to as the MPSK-based Gray-labeling CB design. This scheme is composed of the factor graph matrix design, the constellation set design, and Gray-labeling for the constellation set. Furthermore, with the aid of the PEXIT algorithm, the proposed CBs exhibit superior compatibility with the PLDPC-coded-IDD-SCMA systems. Analytical and simulation results demonstrate significant performance gains from the proposed PLDPC codes and CBs compared to existing counterparts. Consequently, the PLDPC-coded-IDD-SCMA systems with the proposed design emerge as a promising solution to satisfy the high-reliability requirements for SCMA applications.