A Simple Technique for Bounding the Pointwise Redundancy of the 1978 Lempel-Ziv Algorithm

The Redundancy and Distribution of the PhraseLengths of the Fixed - Database

The Fixed-Database version of the Lempel Ziv algorithm closely resembles many versions that appear in practice. In this paper, we ascertain several key asymptotic properties of the algorithm as applied to sources with nite memory. First, we determine that for a dictionary of size n, the algorithm achieves a redundancy n = H log log n log n + o(log log n log n), where H is the entropy of the pro...

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 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...

Improved redundancy of a version of the Lempel-Ziv algorithm

To compress or not to compress ?

| For practical communications which transmit nite blocks of source data over noisy channels, we question the common practice to compress (C) the source and then to add redundancy for error control. Rather we exploit the redundancy of the non-compressed source (NC) at the channel decoder by source-controlled channel decoding. For a simple binary Markov source and a Rayleigh fading channel we si...