Dual-Mapping Sparse Vector Coding for Phase Noise-Resilient Short-Packet Transmission

Sparse vector transmission (SVT) has emerged as a promising technique for ultra-reliable low-latency short-packet communications. However, existing SVT schemes typically assume negligible phase noise (PN), an assumption that rarely holds in practical wireless systems. In this paper, a dual-mapping sparse vector coding (DM-SVC) scheme is proposed for short-packet communications subject to PN. In DM-SVC, pilot symbols are mapped onto multiple non-zero blocks and data symbols onto isolated non-zero elements within a single sparse vector, thereby enabling pilot-data separation through distinct sparsity patterns rather than explicit resource partitioning. Moreover, the indices of pilot blocks convey additional information bits, further improving spectral efficiency. A basis expansion model is adopted to represent the PN process, substantially reducing the number of parameters to be estimated. Furthermore, an iterative joint PN estimation and data decoding algorithm is developed, where pilot block indices are first detected exploiting block-sparse priors, after which PN estimation and data decoding proceed iteratively. Simulation results show that DM-SVC could achieve block error rate performance close to that of perfect PN compensation, while offering improved spectral efficiency and reduced codebook storage overhead compared to state-of-the-art SVT schemes.