Sparse vector coding (SVC) is emerging as a key enabler for short-packet ultrareliable and low-latency communications (URLLCs), since it displays good block error rate (BLER) performance and can achieve low transmission latency. In this article, we propose an SVC-based sparse superimposed transmission (SVC-ST) coding scheme to further enhance the BLER performance of the SVC scheme. At the encoding side, a portion of transmission bits is represented by nonzero position indices of the sparse vector. The remaining bits are equally split into multiple streams and then mapped into the nonzero positions of sparse vector via quadrature amplitude modulation (QAM) with constellation rotation (CR). We afterward adopt the multipath matching pursuit-based soft decoding (MMP-SD) to recover the transmission packet. The BLER and bit error rate (BER) analyses of the SVC-ST scheme demonstrate the validity and rationality of our study. Moreover, we find from the simulation results that the proposed SVC-ST scheme outperforms SVC and its enhanced version (ESVC) schemes in terms of BLER and latency performance.

Sparse code multiple access (SCMA), which helps improve spectrum efficiency (SE) and enhance connectivity, has been proposed as a non-orthogonal multiple access (NOMA) scheme for 5G systems. In SCMA, codebook design determines system overload ratio and detection performance at a receiver. In this paper, an SCMA codebook design approach is proposed based on uniquely decomposable constellation group (UDCG). We show that there are N+1 ( N ≥ 1) constellations in the proposed UDCG, each of which has M (M ≥ 2) constellation points. These constellations are allocated to users sharing the same resource. Combining the constellations allocated on multiple resources of each user, we can obtain UDCG-based codebook sets. Bit error ratio (BER) performance will be discussed in terms of coding gain maximization with superimposed constellations and UDCG-based codebooks. Simulation results demonstrate that the superimposed constellation of each resource has large minimum Euclidean distance (MED) and meets uniquely decodable constraint. Thus, BER performance of the proposed codebook design approach outperforms that of the existing codebook design schemes in both uncoded and coded SCMA systems, especially for large-size codebooks.

Different from traditional communication systems, information-centric Internet of things (IC-IoT) as a novel smart paradigm needs to guarantee end-to-end connectivity for rapidly growing smart devices. How to meet the demands of massive connection has become a key problem for IC-IoT. Sparse code multiple access (SCMA) as a code-domain non-orthogonal multiple access (NOMA) technique has been intensively investigated. With SCMA, each user employs different sub-carrier frequencies for transmission, and different users can share the same sub-carrier frequency via superposition coding. The spectrum efficiency is thus improved. However, designing large-scale codebook sets is still an open problem for SCMA. In this paper, a new lattice-based codebook design method is proposed via mother constellation optimization. First, the optimization problem of the mother constellation is formulated. Through analysis, the problem can be converted into two sub-problems. Accordingly, we first use the lattice theory to find a constellation containing infinite points with large coding gain. After that, we search for a boundary that contains a set of points via spherical packing. Such an approach enables us to obtain a real constellation satisfying a power saving criterion. Secondly, the mother constellation with large power variance is obtained from the real multi-dimensional constellation. Finally, lattice-based codebooks are generated by combining the mother constellation and the mapping matrices with constellation rotation. Simulations demonstrate that the designed codebooks have improved bit error rate (BER) performance with large codebook size, especially at high signal to noise ratio (SNR).

Sparse superimposed coding (SSC) is a promising coding technique to achieve high reliability and low latency for short packet communications. To further improve its performance, an index redefinition-based SSC (IR-SSC) is proposed, in which the sparse vector can represent N index bit streams and N modulation bit streams. The index redefinition is introduced to avoid index collisions of N index bit streams. Meanwhile, constellation rotation-based constellations are adopted as modulation constellations for N modulation bit streams and as identification tags of these N index bit streams. Correspondingly, a constellation matching-based multipath matching pursuit decoder is designed to recover the order of these N index bit streams and to decode all transmitted bits. Simulation results show that the proposed IR-SSC scheme can improve both the reliability and latency performance, compared with conventional SSC schemes.

Sparse vector coding (SVC) is a promising coding technique to achieve high transmission reliability and low latency for short packet communications. However, for SVC with conventional combination-based sparse mapping, a small increase of transmitted bits may lead to excessively long sparse vectors, resulting in unsatisfactory transmission performance when coding efficiency is high. In this paper, we propose a generalized index redefinition (IR)-based SVC (GIR-SVC) to significantly enhance the efficiency of SVC. The IR mechanism enables multiple index bit streams to share position resources in SVC, with the help of constellation labels. GIR-SVC constructs the sparse vector using a hybrid IR mechanism that integrates the unlabeled IR and the pairwise-grouping-based labeled IR, which allows efficient mapping and de-mapping of index bits without requiring index tables. Consequently, the proposed GIR-SVC can be efficiently decoded without the index table using sparse recovery algorithms. Theoretical analysis is conducted to validate the block error rate (BLER) performance of GIR-SVC. Simulations show that GIR-SVC can significantly reduce the decoding delay compared to existing approaches, while maintaining the high transmission reliability.

Sparse vector coding (SVC) is a promising transmission scheme in ultra-reliable and low-latency communications (URLLC) scenario. Its transmission performance primarily depends on the sparse vector construction, namely sparse mapping. In this letter, we first demonstrate the relationship between combination-based and index redefinition (IR)-based sparse mapping of SVC, from which we conclude that the latter has obtained the shortest sparse vectors with the aid of multiple constellation allocation. There is a trade-off between sparse vector length and the number of allocated constellations to construct an SVC scheme with the optimal performance. Based on this, we propose a pairwise grouping-based SVC (PG-SVC) scheme by grouping multiple constellations in pairs to reduce the number of allocated constellations, in which the constellation allocation is determined by specific transmitted bits. This approach ensures sparse vectors of moderate length, as the number of bits determining the sparse vector length is reduced. Simulation results show that the PG-SVC scheme can achieve higher transmission reliability compared to the existing SVC schemes, especially when coding efficiency is high.