Large alphabets: Finite, infinite, and scaling models
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Dahleh_Large alphabets.pdf
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90.58 KB
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754ad55601a8588823042d57c708f941
Author(s)
Ohannessian, Mesrob I.
Dahleh, Munther A.
Date Issued
March 2012
Journal
Proceedings of the 2012 46th Annual Conference on Information Sciences and Systems (CISS)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Ohannessian, Mesrob I., and Munther A. Dahleh. “Large Alphabets: Finite, Infinite, and Scaling Models.” 2012 46th Annual Conference on Information Sciences and Systems (CISS) (n.d.).
Version
Author's final manuscript
Abstract
How can we effectively model situations with large alphabets? On a pragmatic level, any engineered system, be it for inference, communication, or encryption, requires working with a finite number of symbols. Therefore, the most straight-forward model is a finite alphabet. However, to emphasize the disproportionate size of the alphabet, one may want to compare its finite size with the length of data at hand. More generally, this gives rise to scaling models that strive to capture regimes of operation where one anticipates such imbalance. Large alphabets may also be idealized as infinite. The caveat then is that such generality strips away many of the convenient machinery of finite settings. However, some of it may be salvaged by refocusing the tasks of interest, such as by moving from sequence to pattern compression, or by minimally restricting the classes of infinite models, such as via tail properties. In this paper we present an overview of models for large alphabets, some recent results, and possible directions in this area.
MIT Department
Massachusetts Institute of Technology. Engineering Systems Division
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/CISS.2012.6310941
