Elements of information theory
Elements of information theory
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Generalized Shannon Code Minimizes the Maximal Redundancy
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
On the average redundancy rate of the Lempel-Ziv code
IEEE Transactions on Information Theory
Redundancy of the Lempel-Ziv incremental parsing rule
IEEE Transactions on Information Theory
The minimum description length principle in coding and modeling
IEEE Transactions on Information Theory
Asymptotic average redundancy of Huffman (and other) block codes
IEEE Transactions on Information Theory
The context-tree weighting method: basic properties
IEEE Transactions on Information Theory
Compression of graphical structures
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Minimum expected length of fixed-to-variable lossless compression of memoryless sources
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
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Redundancy is defined as the excess of the code length over the optimal (ideal) code length. We study the average redundancy of an idealized arithmetic coding (for memoryless sources with unknown distributions) in which the Krichevsky and Trofimov estimator is followed by the Shannon-Fano code. We shall ignore here important practical implementation issues such as finite precisions and finite buffer sizes. In fact, our idealized arithmetic code can be viewed as an adaptive infinite precision implementation of arithmetic encoder that resembles Elias coding. However, we provide very precise results for the average redundancy that takes into account integer-length constraints. These findings are obtained by analytic methods of analysis of algorithms such as theory of distribution of sequences modulo 1 and Fourier series. These estimates can be used to study the average redundancy of codes for tree sources, and ultimately the context-tree weighting algorithms.