On the Performance of Short Tail-Biting Convolutional Codes for Ultra-Reliable Communications

Motivated by the increasing interest in powerful short channel codes for low-latency ultra-reliable communications, we analyze the performance of tail-biting convolutional codes with different memories, block lengths and code rates over the additive white Gaussian noise channel. The analysis is carried out both through Monte Carlo simulations and by upper bounding the error probability via Poltyrev’s tangential sphere bound at very low error rates. For the simulations, the near maximum likelihood wrap-around Viterbi algorithm is considered. We then compare the performance of tail-biting convolutional codes both with finite-length performance bounds and with that of other channel codes that have been recently considered for ultra-reliable satellite telecommand links. For the shortest block lengths, tail-biting convolutional codes outperform significantly state-of-the-art iterative coding schemes, while as expected their performance degrades visibly with increasing block lengths. Keywords—Convolutional codes, tail-biting, ultra-reliable communications, finite-length bounds