This study presents a novel technique to estimate the computational complexity of sequential decoding using the Berry-Esseen theorem. Unlike the theoretical bounds determined by the conventional central limit theorem argument, which often holds only for sufficiently large codeword length, the new bound obtained from the Berry-Esseen theorem is valid for any blocklength. The accuracy of the new ...

A new asymptotic expansion is obtained in Lyapunov's Central Limit Theorem for distribution functions of centered and normed sums of independent random variables which are not necessary identically distributed. It is applied to determine the asymptotically best constants in the Berry{Esseen inequality, thus solving problems about their optimal values raised by Kolmogorov and Zolotarev.

Applying Stein's method, an inductive technique and size bias coupling yields a Berry–Esseen theorem for normal approximation without the usual restriction that the coupling be bounded. The theorem is applied to counting the number of vertices in the Erd˝ os–Rényi random graph of a given degree. 1. Introduction. We present a new Berry–Esseen theorem for sums Y of dependent variables by combinin...