By harnessing compressed-sensing principles, sparse vector coding (SVC) compresses and delivers data with ultra-low latency and near-instantaneous reliability, making it a vital enabler of next-generation ultra-reliable and low-latency communications (xURLLC) services in sixth generation (6G) wireless communication systems. A fundamental challenge in SVC systems is developing a generalized sparse mapping mechanism that does not rely on either an index table or constellation labels. To meet such a requirement, this work proposes a base conversion index modulation (IM) that uses a novel mapping strategy for sparse vector construction. The proposed design achieves higher resource efficiency, requiring fewer positional resources for bit representation than conventional combination-based IM. Building on this foundation, a generalized SVC (GSVC) scheme is developed to enable fully pipelined bit-stream mapping and demapping. A further extension, termed enhanced GSVC (EGSVC), adopts a pairwise-grouped constellation assignment to improve the transmission performance of GSVC. Simulation results confirm that GSVC achieves block error rate (BLER) performance comparable to conventional SVC in single-block coding modes, yet significantly improves BLER under high-coding-rate multi-block coding modes. By balancing the constellation label count and the sparse vector length, EGSVC delivers superior BLER compared to conventional SVC schemes while maintaining lower latency.

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 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 vector coding (SVC) is emerging as a feasible solution for short packet transmission, which can provide better reliability and lower latency. In this article, a uniquely decomposable constellation group (UDCG)-based SVC called UDCG-SVC is proposed. The important idea of UDCG-SVC is to map the bits into the nonzero elements of the sparse vector by using the sub-constellations in the UDCG. After random spreading, the resource blocks carry the unique decomposable superimposed constellations, which ensures that the minimum Euclidean distance (MED) of the superimposed constellation is large. This results in an improved block error rate (BLER) performance of SVC. Numerical results demonstrate the advanced BLER simulation of UDCG-SVC, and the proposed UDCG-SVC scheme is better than constellation rotation-based SVC (CR-SVC) scheme.

In-home health networks greatly rely on the massive connected monitoring devices. Compared to orthogonal multiple access (OMA), non-orthogonal multiple access (NOMA) can connect more monitoring devices and enhance the spectrum efficiency (SE) performance, which makes it an ideal solution to in-home health networks. However, conventional NOMA (C-NOMA) is mostly constrained to single-carrier scenario. The problem of multi-carrier NOMA lies in the inter-carrier interference (ICI) from neighboring carriers. In this article, we propose a sparse vector coding-based NOMA (SVC-NOMA) to suppress the ICI. We give closed-form expressions of capacity and symbol error rate (SER) performances for both C-NOMA and SVC-NOMA within the considered multi-carrier scenario. Simulation results demonstrate that compared to C-NOMA, SVC-NOMA has better capacity and SER performances. In addition, we find from our results that there is a trade-off between SVC-NOMA's ICI suppression ability and the system capacity 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.