An Achievability Bound for Variable-Length Stop-Feedback Coding over the Gaussian Channel
Abstract: Feedback holds a pivotal role in practical communication schemes, even though it does not enhance channel capacity. Its main attribute includes adaptability in transmission that allows for a higher rate of convergence of the error probability to zero with respect to blocklength. Motivated by this fact, we present a non-asymptotic achievability bound for variable-length coding with stop-feedback. Specifically, a general achievability bound is derived, that employs a random coding ensemble in combination with minimum distance decoding. The general bound is particularized for the Gaussian channel. Numerical evaluation of the bound confirms the significant value of feedback compared to transmission with fixed blocklength coding and without feedback.
- C. Shannon, “The zero error capacity of a noisy channel,” IRE Transactions on Information Theory, vol. 2, no. 3, pp. 8–19, 1956.
- M. Burnashev, “Data transmission over a discrete channel with feedback. Random transmission time,” Probl. Peredachi Inf., vol. 12, no. 4, pp. 10–30, 1976.
- Y. Polyanskiy, H. V. Poor, and S. Verdu, “Channel coding rate in the finite blocklength regime,” IEEE Transactions on Information Theory, vol. 56, pp. 2307–2359, May 2010.
- Y. Polyanskiy, H. V. Poor, and S. Verdu, “Feedback in the non-asymptotic regime,” IEEE Transactions on Information Theory, vol. 57, no. 8, pp. 4903–4925, 2011.
- J. Östman, R. Devassy, G. Durisi, and E. G. Ström, “Short-packet transmission via variable-length codes in the presence of noisy stop feedback,” IEEE Transactions on Wireless Communications, pp. 1–1, 2020.
- L. V. Truong and V. Y. F. Tan, “On gaussian macs with variable-length feedback and non-vanishing error probabilities,” IEEE Transactions on Information Theory, vol. 64, no. 4, pp. 2333–2346, 2018.
- I. Papoutsidakis, A. Doufexi, and R. J. Piechocki, “Efficient evaluation of the probability of error of random coding ensembles,” in 2023 IEEE International Symposium on Information Theory (ISIT), pp. 2117–2122, 2023.
- C. E. Shannon, “Probability of error for optimal codes in a gaussian channel,” The Bell System Technical Journal, vol. 38, no. 3, pp. 611–656, 1959.
- L. Devroye, Non-Uniform Random Variate Generation. Springer New York, 1986.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.