Interleaver Design for Small-Coupling-Length Spatially Coupled Protograph LDPC-Coded BICM Systems over Wireless Fading Channels

As a class of convolutional error-correction codes (ECCs), spatially coupled protograph low-density parity-check (SC-PLDPC) codes with a sufficiently large coupling length can approach the channel capacity under belief propagation (BP) decoding. However, such codes suffer from poor performance in the case of small coupling lengths. To address the above weakness, we investigate the optimization and analysis of SC-PLDPC-coded bit-interleaved coded modulation (BICM) systems over Rayleigh fading channels. Specially, inspired by the unequal-error-protection (UEP) mechanism of $M$ -ary phase-shift keying/quadrature amplitude modulation ( $M$ -PSK/QAM), we put forward a novel interleaver design scheme, referred to as spatial position match mapping (SPMM) scheme . Based on the mutual information (MI) analysis, the proposed interleaver can be used to significantly boost the performance of the SC-PLDPC codes in BICM systems. Furthermore, we propose a block-scheduling protograph-based extrinsic information transfer (BS-PEXIT) algorithm to estimate the convergence performance (i.e, decoding threshold) of the SPMM-aided SC-PLDPC codes in BICM scenarios. Simulation results are well consistent with the theoretical analyses, and show that the proposed SPMM-aided SC-PLDPC-coded BICM systems are superior to the state-of-the-art counterparts.