Sparse code multiple access (SCMA) is a code domain non-orthogonal multiple-access technique introduced for future 5G wireless networks. This paper describes the basic ideas of SCMA, the SCMA codebook design, the encoder and decoder, as well as the SCMA enabled transmission schemes for different application scenarios, including uplink grant-free contention-based transmission, downlink multi-user superposition, and downlink open-loop CoMP for ultra-dense networks even with moving users. We shall show from design principles and application examples that SCMA can resolve some major issues of current wireless systems and establish itself as a strong candidate for 5G networks.

Multicarrier CDMA is a multiple access scheme in which modulated QAM symbols are spread over OFDMA tones by using a generally complex spreading sequence. Effectively, a QAM symbol is repeated over multiple tones. Low density signature (LDS) is a version of CDMA with low density spreading sequences allowing us to take advantage of a near optimal message passing algorithm (MPA) receiver with practically feasible complexity. Sparse code multiple access (SCMA) is a multi-dimensional codebook-based non-orthogonal spreading technique. In SCMA, the procedure of bit to QAM symbol mapping and spreading are combined together and incoming bits are directly mapped to multi-dimensional codewords of SCMA codebook sets. Each layer has its dedicated codebook. Shaping gain of a multi-dimensional constellation is one of the main sources of the performance improvement in comparison to the simple repetition of QAM symbols in LDS. Meanwhile, like LDS, SCMA enjoys the low complexity reception techniques due to the sparsity of SCMA codewords. In this paper a systematic approach is proposed to design SCMA codebooks mainly based on the design principles of lattice constellations. Simulation results are presented to show the performance gain of SCMA compared to LDS and OFDMA.

In this paper, we consider the problem of zero-delay (encoding a single-source sample) robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme that, unlike previously known coding schemes, achieves the optimal scaling of the source signal-to-distortion ratio (SDR) versus channel signal-to-noise ratio (SNR). Also, we propose a family of robust codes, which together maintain a bounded gap with the optimum SDR curve (in terms of decibel). To show the importance of this result, we derive some theoretical bounds on the asymptotic performance of a widely used class of delay-limited hybrid digital-analog (HDA) coding schemes based on superposition of analog and digital components. We show that, unlike the delay-unlimited case, for this class of delay-limited HDA codes, the asymptotic performance loss is unbounded (in terms of decibels). Although the main focus of this paper is on uniform sources, it is also shown that the results are also valid for a more general class of well-behaved distributions.

In this paper, the inherent drawbacks of the naive lattice decoding (NLD) for MIMO fading systems is investigated. We show that using the NLD for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the nonvanishing determinant property cannot achieve the optimal diversity-multiplexing tradeoff. Indeed, we show that in the case of NLD, when we fix the underlying lattice, all the codes based on full-rate lattices have the same diversity-multiplexing tradeoff as V-BLAST. Also, we derive a lower bound on the symbol error probability of the NLD for the fixed-rate MIMO systems (with equal numbers of receive and transmit antennas). This bound shows that asymptotically, the NLD has an unbounded loss in terms of the required SNR, compared to the maximum likelihood decoding.

In this paper, the inherent drawbacks of the naive lattice decoding for MIMO fading systems is investigated. We show that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the rate-diversity tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal rate-diversity trade-off. Indeed, we show that in the case of naive lattice decoding, all the codes based on full-rate lattices have the same rate-diversity trade-off as V-BLAST. Also, we drive a lower bound on the symbol error probability of the naive lattice decoding for the fixed-rate MIMO systems (with equal numbers of receive and transmit antennas). This bound shows that asymptotically, the naive lattice decoding has an unbounded loss in terms of the required SNR, compared to the maximum likelihood decoding.

In this paper, we consider the problem of robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme which achieves the optimal slope for the signal-to-distortion (SDR) curve (unlike the previous known coding schemes). We also drive some theoretical bounds on the asymptotic performance of delay-limited hybrid digital-analog (HDA) coding schemes. We show that, unlike the delay-unlimited case, for any family of HDA codes, the asymptotic performance loss is unbounded (in terms of dB).

In multiple-input multiple-output (MIMO) systems, maximum-likelihood (ML) decoding is equivalent to finding the closest lattice point in an$N$-dimensional complex space. In general, this problem is known to be NP-hard. In this paper, a quasi-ML algorithm based on semi-definite programming (SDP) is proposed. We introduce several SDP relaxation models for MIMO systems, with increasing complexity. We use interior-point methods for solving the models and obtain a near-ML performance with polynomial computational complexity. Lattice basis reduction is applied to further reduce the computational complexity of solving these models. The proposed relaxation models are also used for soft output decoding in MIMO systems.

A new viewpoint for adopting the lattice reduction in communication over multiple-input multiple-output (MIMO) broadcast channels is introduced. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. The new viewpoint helps us to generalize the idea of lattice-reduction-aided (LRA) preceding for the case of unequal-rate transmission, and obtain analytic results for the asymptotic behavior (signal-to-noise ratio (SNR) rarr infin) of the symbol error rate for the LRA precoding and the perturbation technique. Also, the outage probability for both cases of fixed-rate users and fixed sum rate is analyzed. It is shown that the LRA method, using the Lenstra-Lenstra-Lovasz (LLL) algorithm, achieves the optimum asymptotic slope of symbol error rate (called the precoding diversity).

Diversity order is an important measure for the performance of communication systems over multiple-input-multiple-output (MIMO) fading channels. In this correspondence, we prove that in MIMO multiple- access systems (or MIMO point-to-point systems with V-BLAST transmission), lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, we prove that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity.

In this paper, a method is proposed to construct spectral-efficient unitary space–time codes for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods, which are designed to maximize the diversity product (the minimum determinant distance), our objective is to increase the spectral efficiency. The simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the existing alternatives. In the special case of two transmit antennas, which is the main focus of this paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum-likelihood decoding algorithm. Also, we demonstrate that similar ideas can be applied for designing codes for more than two transmit antennas. As an example, we present a construction for a 4$times$4 unitary constellations which has a good performance, as compared with the other known codes.

In this paper, a method is proposed to construct spectrally efficient unitary space-time codes for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods which are designed to maximize the diversity product (the minimum determinant distance), our objective is to increase the spectral efficiency. The simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the existing alternatives. In the special case of two transmit antennas, which is the main focus of this paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum-likelihood (ML) decoding algorithm. Also, we demonstrate that similar ideas can be applied to designing codes for more than two transmit antennas. As an example, we present a construction for 4-by-4 unitary constellations which has a good performance, compared with the other known codes

In multi-input multi-output (MIMO) systems, maximum-likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a quasi-maximum likelihood algorithm based on semi-definite programming (SDP). We introduce several SDP relaxation models for MIMO systems, with increasing complexity. We use interior-point methods for solving the models and obtain a near-ML performance with polynomial computational complexity. Lattice basis reduction is applied to further reduce the computational complexity of solving these models

Diversity order is an important measure for the performance of different communication systems over MIMO fading channels. In this paper, we define the preceding diversity for the fixed-rate MIMO broadcast systems and we prove that in these systems, lattice-reduction-aided preceding achieves the preceding diversity. Also, we prove that lattice-reduction-aided decoding achieves the receive diversity in MIMO point-to-point and multiple-access systems

A method to construct spectrally-efficient unitary space-time codes is proposed for high-rate differential communications over multiple-antenna channels. Unlike most of the known methods which are designed to maximize the diversity product (minimum determinant distance), we aim at increasing the spectral efficiency. Simulation results indicate that for high spectral efficiency and for more than one receive antenna, the new method significantly outperforms the known alternatives. In the special case of two transmit antennas, which is the main focus of the paper, the relation between the proposed code and the Alamouti scheme helps us to provide an efficient maximum likelihood decoding algorithm. We also show that similar ideas can be applied to more than two transmit antennas. As an example, we present a construction for 4 by 4 unitary constellations which has good performance as compared to the other known codes.