An Achievability Bound for Variable-Length Stop-Feedback Coding over the Gaussian Channel

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.