Channel Coding Rate in the Finite Blocklength Regime

Abstract

This paper investigates the maximal channel coding rate achievable at a given blocklength and error probability. For general classes of channels new achievability and converse bounds are given, which are tighter than existing bounds for wide ranges of parameters of interest, and lead to tight approximations of the maximal achievable rate for blocklengths <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> as short as 100. It is also shown analytically that the maximal rate achievable with error probability <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</i> isclosely approximated by C - ¿(V/n) Q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> (¿) where C is the capacity, V is a characteristic of the channel referred to as channel dispersion , and Q is the complementary Gaussian cumulative distribution function.