Abstract
Abstract In this paper we examine the average redundancy rate of a Lempel–Ziv'78 code with the k-error protocol. Storer and Reif have studied this modification of the Lempel–Ziv (LZ) 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 memoryless sources. Using analytic methods, we establish our result by exploiting a relationship between a parsing scheme of the LZ encoder with the k-error protocol and a generalization of the digital search tree (DST) structure. We accompany our analysis with a number of experiments that test the validity of our theoretical result and demonstrate the effects of various additional modifications of the LZ algorithm.
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