On the Average Redundancy Rate of the Lempel-Ziv Code with K-Error Protocol
DCC '00 Proceedings of the Conference on Data Compression
Precise Average Redundancy Of An Idealized Arithmetic Coding
DCC '02 Proceedings of the Data Compression Conference
Lower Bounding the Optimal LZ78-Parsing
DCC '01 Proceedings of the Data Compression Conference
Redundancy estimates for the Lempel-Ziv algorithm of data compression
Discrete Applied Mathematics
Superior Guarantees for Sequential Prediction and Lossless Compression via Alphabet Decomposition
The Journal of Machine Learning Research
On the Value of Multiple Read/Write Streams for Data Compression
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
On prediction using variable order Markov models
Journal of Artificial Intelligence Research
IEEE Transactions on Information Theory
Reducing coding redundancy in LZW
Information Sciences: an International Journal
Sensor fusion: from dependence analysis via matroid bases to online synthesis
ALGOSENSORS'11 Proceedings of the 7th international conference on Algorithms for Sensor Systems, Wireless Ad Hoc Networks and Autonomous Mobile Entities
On the value of multiple read/write streams for data compression
Information Theory, Combinatorics, and Search Theory
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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