Simple Gray Coding and LLR Calculation for MDS Modulation Systems

Due to dependence between codeword elements, index modulation (IM) and related modulation techniques struggle to provide simple solutions for practical problems such as Gray coding between information bits and constellation points; and low-complexity log-likelihood ratio (LLR) calculations for channel-encoded information bits. In this paper, we show that a modulation technique based on a simple maximum distance separable (MDS) code, in other words, MDS modulation, can provide simple yet effective solutions to these problems, rendering the MDS techniques more beneficial in the presence of coding. We also compare the coded error performance of the MDS methods with that of the IM methods and demonstrate that MDS modulation outperforms IM.

Modulation Based On A Simple MDS Code: Achieving Better Error Performance Than Index Modulation and Related Schemes

In this paper, we propose two novel modulation concepts based on a simple maximum distance separable (MDS) code { and show that these concepts can achieve better error performance than index modulation (IM) and related schemes.} In the first concept, we use amplitude and phase levels to form a simple MDS code, whereas, in the second one, in-phase and quadrature components of codeword elements are used to construct the MDS code. We depict practical schemes for using the proposed concepts with orthogonal frequency division multiplexing (OFDM). We analyze the performance in terms of the minimum Euclidean distance and bit error rate. We also show that the proposed techniques exhibit desirable properties such as efficient low-complexity detection, very simple bits-to-symbols, and symbols-to-bits mappings, and a better error performance when compared to the OFDM-IM and related schemes. More importantly, contrary to the vast majority of IM studies that focus on showing the superiority of the IM techniques against conventional modulation techniques, we show that modulation concepts based on a well-known MDS code can achieve better error performance than the IM and related schemes while exhibiting a structure as simple as these schemes.