Variable-length coding with feedback in the non-asymptotic regime
Yury Polyanskiy H Vincent Poor Sergio Verdú
Proceedings of the IEEE International Symposium on Information Theory, Austin, TX, USA, June 2010

Without  feedback , the backoff from capacity due to  non - asymptotic  block  length  can be quite substantial for block lengths and error probabilities of interest in many practical applications. In this paper, novel achievability bounds are used to demonstrate that in the  non - asymptotic   regime , the maximal achievable rate improves dramatically thanks to  variable - length   coding  with  feedback . For example, for the binary symmetric channel with capacity 1/2 the blocklength required to achieve 90% of the capacity is smaller than 200, compared to at least 3100 for the best fixed-blocklength,  non - feedback   code . Virtually all the advantages of noiseless  feedback  are shown to be achievable with decision- feedback  only. It is demonstrated that the  non - asymptotic  behavior of the fundamental limit depends crucially on the particular model chosen for the “end-of-packet” control signal.