Low-Density Spreading Codes for NOMA Systems and a Gaussian Separability-Based Design

Abstract

Improved low-density spreading (LDS) code designs based on the Gaussian separability criterion are conceived. We show that the bit error rate (BER) hinges not only on the minimum distance criterion, but also on the average Gaussian separability margin. If two code sets have the same minimum distance, the code set having the highest Gaussian separability margin will lead to a lower BER. Based on the latter criterion, we develop an iterative algorithm that converges to the best known solution having the lowest BER. Our improved LDS code set outperforms the existing LDS designs in terms of its BER performance both for binary phase-shift keying (BPSK) and for quadrature amplitude modulation (QAM) transmissions. Furthermore, we use an appallingly low-complexity minimum mean-square estimation (MMSE) and parallel interference cancellation (PIC) (MMSE-PIC) technique, which is shown to have comparable BER performance to the potentially excessive-complexity maximum-likelihood (ML) detector. This MMSE-PIC algorithm has a much lower computational complexity than the message passing algorithm (MPA).Code sets for MPA are designed similar to low-density parity-check (LDPC) codes to avoid cycles and to increase girth of the Tanner graph, code sets that are 'optimal' for MMSE-PIC might not be optimal for MPA.