• Citer

On the average redundancy rate of the Lempel-Ziv code

par Louchard, Guy ;Szpankowski, Wojciech
Référence IEEE transactions on information theory, 43, 1, page (2-8)
Publication Publié, 1997

Article révisé par les pairs

• Détails
• Contenu

Résumé :

In this paper, we settle a long-standing open problem concerning the average redundancy rn of the Lempel-Ziv'78 (LZ78) code. We prove that for a memoryless source the average redundancy rate attains asymptotically Ern = (A+δ(n))/log n+ O(log log n/log2 n), where A is an explicitly given constant that depends on source characteristics, and δ(x) is a fluctuating function with a small amplitude. We also derive the leading term for the kth moment of the number of phrases. We conclude by conjecturing a precise formula on the expected redundancy for a Markovian source. The main result of this paper is a consequence of recently obtained second-order properties of the Lempel-Ziv algorithm by Jacquet and Szpankowski. These findings have been established by analytical techniques of the precise analysis of algorithms. We give a brief survey of these results since they are interesting in their own right, and shed some light on the probabilistic behavior of pattern matching based data compression. © 1997 IEEE.