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Redundancy of the Lempel-Ziv incremental parsing rule

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1 Author(s)
Savari, S.A. ; Lab. for Inf. & Decision Syst., MIT, Cambridge, MA, USA

The Lempel-Ziv codes are universal variable-to-fixed 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 or Markov sources, the redundancy of encoding the first n letters of the source output with the Lempel-Ziv incremental parsing rule (LZ'78), the Welch modification (LZW), or a new variant is O((ln n)-1), and we upper-bound the exact form of convergence. We conclude by considering the relationship between the code length and the empirical entropy associated with a string

Published in:

Information Theory, IEEE Transactions on  (Volume:43 ,  Issue: 1 )