Trade-Off Between Frame Synchronization and Channel Decoding for Short Packets

We consider the transmission of successive packets where each packet consists of a frame synchronization word (SW), followed by coded symbols. For short packets, the header cost is no longer negligible and the SW design requires careful optimization. In particular, a trade-off arises depending on the way the total transmit power is split among the SW and the codeword. Assuming optimal finite-length codes, we develop tight approximations on the probability of false synchronization for several synchronization metrics and use them to characterize this trade-off. Simulation results and comparisons with 5G Polar codes show the relevance of the proposed optimization for short-packet communication system design.