On the average redundancy rate of the Lempel-Ziv code

On the Average Redundancy Rate of the Lempel-Ziv Code

Wojciech Szpankowski'" Department of Computer Science Purdue University W. Lafayette, IN 47907 U.S.A. It was conjectured that the average redundancy rate, Tnl for the Lempel-Ziv code (LZ78) is 0(loglognflogn) where n is the length of the database sequence. However, it was also known that for infinitely many n the redundancy Tn is bounded from the below by 2/ log n. In this paper we settle the a...

Redundancy of the Lempel-Ziv incremental parsing rule

The Lempel-Ziv codes are universal variable-tofixed length codes that have become virtually standard in practical lossless data compression. For any given source output string from a Markov or unifilar source, we upper-bound the difference between the number of binary digits needed to encode the string and the self-information of the string. We use this result to demonstrate that for unifilar o...

Improved redundancy of a version of the Lempel-Ziv algorithm

Redundancy estimates for the Lempel-Ziv algorithm of data compression

The problem of non-distorting compression (or coding) of sequences of symbols is considered. For sequences of asymptotically zero empirical entropy, a modi0cation of the Lempel–Ziv coding rule is o1ered whose coding cost is at most a 0nite number of times worse than the optimum. A combinatorial proof is o1ered for the well-known redundancy estimate of the Lempel–Ziv coding algorithm for sequenc...

Average Profile of the Lempel - Ziv Parsing Scheme for Amarkovian

For a Markovian source, we analyze the Lempel-Ziv parsing scheme that partitions sequences into phrases such that a new phrase is the shortest phrase not seen in the past. We consider three models: In the Markov Independent model, several sequences are generated independently by Markovian sources, and the ith phrase is the shortest preex of the ith sequence that was not seen before as a phrase ...