Limiting distribution of Lempel Ziv´78 redundancy

We show that the Lempel Ziv´78 redundancy rate tends to a Gaussian distribution for memoryless sources. We accomplish it by extending findings from our 1995 paper [3]. We present a new simplified proof of the Central Limit Theorem for the number of phrases in the LZ´78 algorithm. As in our 1995 paper, here we first analyze the asymptotic behavior of the total path length in a digital search tree (a DST) built from independent sequences. Then we present simplified proofs and extend our analysis of LZ´78 algorithm to include new results on the convergence of moments, moderate and large deviations, and redundancy analysis.