Improved redundancy of a version of the Lempel-Ziv algorithm
نویسندگان
چکیده
منابع مشابه
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...
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Abstract: If x is a string of nite length over a nite alphabet A, let LZ(x) denote the length of the binary codeword assigned to x by the 1978 version of the Lempel-Ziv data compression algorithm, let t(x) be the number of phrases in the Lempel-Ziv parsing of x, and let (x) be the probability assigned to x by a memoryless source model. Using a very simple technique, we prove the pointwise redun...
متن کاملOn 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...
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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...
متن کاملAn Implementable Lossy Version of the Lempel - Ziv Algorithm { Part I : Optimality for Memoryless
{ A new lossy variant of the Fixed-Database Lempel-Ziv coding algorithm for encoding at a xed distortion level is proposed, and its asymptotic optimality and universality for memoryless sources (with respect to bounded single-letter distortion measures) is demonstrated: As the database size m increases to innnity, the expected compression ratio approaches the rate-distortion function. The compl...
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عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 41 شماره
صفحات -
تاریخ انتشار 1995