LDPC-Coded 16-Dimensional Modulation Based on the Nordstrom-Robinson Nonlinear Block Code

Recent forward error correction (FEC) codes based on low-density parity-check (LDPC) codes have shown capacity-achieving performance in practice. To support various modulation formats in conjunction with LDPC codes, bit-interleaved coded modulation (BICM) has been widely used. To achieve better performance, BICM iterative demodulation (BICM-ID), multi-layer coding (MLC), and nonbinary-interleaved coded modulation (NBICM) have been studied for high-order modulation and high-dimensional modulation (HDM). In particular, HDM has received much interest because of its high sensitivity. In this paper, we propose a new 16-dimensional (16D) modulation based on the Nordstrom-Robinson (NR) nonlinear code. The NR code is an optimal binary code, whose minimum Hamming distance is 6, whereas the best-known linear code (BKLC) has a minimum distance of 5. We optimize LDPC codes for BICM-ID with various HDM formats, and show the benefit of the NR-coded 16D modulation.