A Pairwise Grouping-Based Sparse Mapping for Sparse Vector Transmission

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.