Farnoud (Hassanzadeh), Farzad and Schwartz, Moshe and Bruck, Jehoshua (2016) Bounds for Permutation Rate-Distortion. IEEE Transactions on Information Theory, 62 (2). pp. 703-712. ISSN 0018-9448. doi:10.1109/TIT.2015.2504521. https://resolver.caltech.edu/CaltechAUTHORS:20160119-151223798
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Abstract
We study the rate-distortion relationship in the set of permutations endowed with the Kendall t-metric and the Chebyshev metric. Our study is motivated by the application of permutation rate-distortion to the average-case and worst-case distortion analysis of algorithms for ranking with incomplete information and approximate sorting algorithms. For the Kendall τ-metric we provide bounds for small, medium, and large distortion regimes, while for the Chebyshev metric we present bounds that are valid for all distortions and are especially accurate for small distortions. In addition, for the Chebyshev metric, we provide a construction for covering codes.
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| Additional Information: | © 2015 IEEE. Manuscript received November 19, 2014; revised September 13, 2015; accepted November 16, 2015. Date of publication December 4, 2015; date of current version January 18, 2016. This work was supported in part by the National Science Foundation under Grant CIF-1218005 and in part by the Israel Science Foundation under Grant 130/14. This paper was presented in part at the 2014 IEEE International Symposium on Information Theory. The authors would like to thank the associate editor and anonymous reviewers, whose comments helped improve the presentation of the paper. | ||||||||||||
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| Subject Keywords: | Rank modulation, rate-distortion, covering codes, permutations, Kendall τ-metric, Chebyshev metric, ℓ∞-metric | ||||||||||||
| Issue or Number: | 2 | ||||||||||||
| DOI: | 10.1109/TIT.2015.2504521 | ||||||||||||
| Record Number: | CaltechAUTHORS:20160119-151223798 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160119-151223798 | ||||||||||||
| Official Citation: | Farnoud Hassanzadeh, F.; Schwartz, M.; Bruck, J., "Bounds for Permutation Rate-Distortion," in Information Theory, IEEE Transactions on , vol.62, no.2, pp.703-712, Feb. 2016 doi: 10.1109/TIT.2015.2504521 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 63776 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||
| Deposited On: | 19 Jan 2016 23:35 | ||||||||||||
| Last Modified: | 10 Nov 2021 23:21 |
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