Sparse Vector Coding via Base Conversion Index Modulation for Short-Packet xURLLC

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.