Digital search trees revisited
SIAM Journal on Computing
Data compression: methods and theory
Data compression: methods and theory
Text compression
Elements of information theory
Elements of information theory
Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Error-Resilient Optimal Data Compression
SIAM Journal on Computing
Average Profile of the Generalized Digital Search Tree and the Generalized Lempel--Ziv Algorithm
SIAM Journal on Computing
Generalized Lempel-Ziv parsing scheme and its preliminary analysis of the average profile
DCC '95 Proceedings of the Conference on Data Compression
On the average redundancy rate of the Lempel-Ziv code
IEEE Transactions on Information Theory
Redundancy of the Lempel-Ziv incremental parsing rule
IEEE Transactions on Information Theory
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In this paper we examine the average redundancy rate of a Lempel-Ziv'78 code with k-error protocol. Storer and Reif have studied this modification of the Lempel-Ziv scheme and showed that it provides an efficient protection against error propagation while preserving the asymptotic optimality of the code.We refine this result by providing an asymptotic expression for the average redundancy rate of this code for memory-less sources. We have established our result by exploiting a relation between a parsing scheme of the Lempel-Ziv encoder with k-error protocol and a generalization of digital search tree structure (also known as b-DST), and using analytical techniques of the analysis of algorithms. We accompany our analysis by a number of experiments that test the validity of our asymptotic expression and demonstrate the effects of various additional modifications of the Lempel-Ziv algorithm.