Semi-Tensor Sparse Vector Coding for Short-Packet URLLC with Low Storage Overhead

Sparse vector coding (SVC) is a promising short-packet transmission method for ultra reliable low latency communication (URLLC) in next generation mobile communication systems. However, the storage burden of codebook and high decoding complexity limit its application in Internet of Things (loT) devices with constrained storage space and computational capabilities. To tackle this challenge, a semi-tensor SVC (ST-SVC)-based short-packet transmission scheme is proposed in this paper. The core idea behind ST-SVC is that it utilizes the semi-tensor product (STP) model in random spreading process, replacing the matrix multiplication model used in traditional SVC schemes. At the transmitter, a low-dimensional codebook is utilized to perform random spreading on a high-dimensional sparse vector carrying information bits. At the receiver, by exploiting the Kronecker structure induced by the STP model, a low-complexity parallel support identification algorithm is proposed for ST-SVC decoding. The proposed scheme breaks through the dimension matching condition required between the codebook matrix and high-dimensional sparse vector in traditional SVC schemes, allowing the loT devices to store an ultra-low-dimensional codebook, which significantly reduces storage overhead. Simulation results demonstrate that the proposed ST-SVC scheme can achieve a substantial reduction in both storage overhead and decoding latency compared to state-of-the-art SVC schemes, with only a slight performance loss in block error rate.