An Over-the-Air Multi-User Convolutional Code for URLLC

URLLC applications impose stringent latency and reliability requirements, making its compliance challenging due to the inherent trade-off between them. These applications typically involve the exchange of small information blocks. Convolutional codes (CC) exhibit near-optimal performance when encoding short blocks. To enable packet-based transmissions, CCs require some kind of termination. A zero-terminated CC (ZTCC) enables efficient maximum likelihood (ML) decoding through the Viterbi algorithm, but suffers from a rate-loss particularly prominent in short blocks. A tail-biting CC (TBCC) avoids rate-loss but entails significantly higher ML decoding complexity. Despite the ZTCC having lower ML decoding complexity and similar error performance, TBCC has received preference by wireless standards, essentially due to ZTCC rate-loss. This work proposes a novel distributed multi-user ZTCC (MU-ZTCC) coding scheme, which eliminates rate-loss by encoding multiple physically separated users over-the-air. Local user data undergoes standard ZTCC encoding followed by multi-user encoding via over-the-air summation. Due to its zero termination, ML decoding of MU-ZTCC is accomplished with a single Viterbi execution. Simulation results show that MU-ZTCC approaches the performance of orthogonal transmissions as SNR increases, while increasing the transmission rate by up to 47% for the selected parameters. This scheme can be viewed as a non-orthogonal multiple access scheme, whose structure enables ML joint detection and decoding with the complexity of standard Viterbi algorithm.