Protograph LDPC Code and Shaped Index Modulation Design for Multi-Mode OAM Systems

Orbital angular momentum (OAM) is a mode division multiplexing (MDM) technique enabling simpler implementation and higher capacity than conventional multiple-input multiple-output (MIMO) over line-of-sight (LoS) channels. This paper studies the joint design of protograph low-density parity-check (PLDPC) codes and shaping index modulation (IM) in OAM systems. To begin with, we analyze the distribution of extrinsic log-likelihood-ratios (LLRs) for coded bits output from channel detector, and then propose a customized Box-Cox transformation (CBCT) to make the distribution achieve symmetry and Gaussian features. We also devise a CBCT-based protograph extrinsic information transfer (CBCT-PEXIT) algorithm to predict the convergence performance of PLDPC-coded OAM systems. Furthermore, with the aid of such an algorithm, we construct two new types of improved PLDPC codes tailored for OAM systems, including unpunctured codes and rate-compatible punctured codes. In addition, we present a two-step design method, which seamlessly combines the shaping technique and index rule into a novel modulation scheme, called shaping index. Both theoretical analyses and simulation results demonstrate that the proposed PLDPC-coded OAM systems with shaping index significantly outperform state-of-the-art counterparts.