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

Index and composition modulation

In this paper, we propose a novel modulation concept which we call index and composition modulation (ICM). In the proposed concept, we use indices of active/deactive codeword elements and compositions of an integer to encode information. In this regard, we first determine the activated codeword elements, then we exploit energy levels of these elements to identify the compositions. We depict a practical scheme for using ICM with orthogonal frequency division multiplexing (OFDM) and show that OFDM with ICM (OFDM-ICM) can enhance the spectral efficiency (SE) and error performance of OFDM-IM. We design an efficient low-complexity detector for the proposed technique. Moreover, we analyze the error and SE performance of the OFDM-ICM technique and show that it is capable of outperforming existing OFDM benchmarks in terms of error and SE performance

Comparing minimum codeword distances and error performance for index modulation and maximum distance separable coded modulation

Index modulation (IM) that embeds information into combinations of activated codeword elements have desirable properties in terms of error performance, low-complexity implementation, and compatibility with existing communication techniques. However, a recent modulation concept based on a simple maximum distance separable (MDS) code, i.e., MDS modulation, achieves better performance than IM while preserving a low-complexity structure. In this paper, we conduct further numerical comparisons among the MDS and IM techniques to comprehend to what extent the MDS methods can outperform the IM methods in terms of distance properties and bit error rate (BER) performance. Our numerical distance comparisons show that the MDS techniques are more beneficial than the IM techniques when η > 2, where η is spectral efficiency (SE) per codeword element. Moreover, our BER results support the distance results and show the effectiveness of the MDS techniques against the IM techniques for a wide range of SE

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 and complexity of the MDS methods with those of the IM methods and demonstrate that MDS modulation outperforms IM

Set partition modulation

In this paper, a novel modulation scheme called set partition modulation (SPM) is proposed. In this scheme, set partitioning and ordered subsets in the set partitions are used to form codewords. We define different SPM variants and depict a practical model for using SPM with orthogonal frequency division multiplexing (OFDM). For the OFDM-SPM schemes, different constellations are used to distinguish between different subsets in a set partition. To achieve good distance properties as well as better error performance for the OFDM-SPM codewords, we define a codebook selection problem and formulate such a problem as a clique problem in graph theory. In this regard, we propose a fast and efficient codebook selection algorithm. We analyze error and achievable rate performance of the proposed schemes and provide asymptotic results for the performance. It is shown that the proposed SPM variants are general schemes, which encompass multi-mode OFDM with index modulation (MM-OFDM-IM) and dual-mode OFDM with index modulation (DM-OFDM-IM) as special cases. It is also shown that OFDM-SPM schemes are capable of exhibiting better error performance and improved achievable rate than conventional OFDM, OFDM-IM, DM-OFDM-IM, and MM-OFDM-IM

Q-ary multi-mode OFDM with index modulation

In this paper, we propose a novel orthogonal frequency division multiplexing with index modulation (OFDM-IM) scheme, which we call Q-ary multi-mode OFDM-IM (Q-MM-OFDM-IM). In the proposed scheme, Q disjoint M-ary constellations are used repeatedly on each subcarrier, and a maximum-distance separable code is applied to the indices of these constellations to achieve the highest number of index symbols. A low-complexity subcarrier-wise detection is shown possible for the proposed scheme. Spectral efficiency (SE) and the error rate performance of the proposed scheme are further analyzed. It is shown that the proposed scheme exhibits a very flexible structure that is capable of encompassing conventional OFDM as a special case. It is also shown that the proposed scheme is capable of considerably outperforming the other OFDM-IM schemes and conventional OFDM in terms of error and SE performance while preserving a low-complexity structure

Index and composition modulation

In this paper, we propose a novel modulation concept which we call index and composition modulation (ICM). In the proposed concept, we use indices of active/deactive codeword elements and compositions of an integer to encode information. In this regard, we first determine the activated codeword elements, then we exploit energy levels of these elements to identify the compositions. We depict a practical scheme for using ICM with orthogonal frequency division multiplexing (OFDM) and show that OFDM with ICM (OFDM-ICM) can enhance the spectral efficiency (SE) and error performance of OFDM-IM. We design an efficient low-complexity detector for the proposed technique. Moreover, we analyze the error and SE performance of the OFDM-ICM technique and show that it is capable of outperforming existing OFDM benchmarks in terms of error and SE performance