2013 IEEE International Symposium on Information Theory 2013
DOI: 10.1109/isit.2013.6620689
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A rate-distortion theory for permutation spaces

Abstract: Abstract-We investigate the lossy compression of the permutation space by analyzing the trade-off between the size of a source code and the distortion with respect to either Kendall tau distance or 1 distance of the inversion vectors. For both distortion measures, we characterize the rate-distortion functions and provide explicit code designs that achieve them. Finally, we provide bounds on the higher order terms in the codebook size when the distortion levels lead to degenerate code rates (0 or 1).

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Cited by 12 publications
(23 citation statements)
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“…For a permutation σ, we denote its permutation inverse by σ −1 , where σ −1 (x) = i when σ(i) = x. and σ(i) is the i-th element in array σ. For example, the permutation inverse of σ = [2,5,4,3,1] …”
Section: A Notationmentioning
confidence: 99%
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“…For a permutation σ, we denote its permutation inverse by σ −1 , where σ −1 (x) = i when σ(i) = x. and σ(i) is the i-th element in array σ. For example, the permutation inverse of σ = [2,5,4,3,1] …”
Section: A Notationmentioning
confidence: 99%
“…For the vector representation of permutation, compression based on Kendall tau distance is essentially optimal, which can be achieved by partitioning each permutation vector into subsequences with proper sizes and sorting them accordingly [3]. For the inversion vector representation of permutation, a simple component-wise scalar quantization achieves the optimal rate distortion trade-off, as shown in [3].…”
Section: Theorem 6 (Rate Distortion Functions For Distortion Measuresmentioning
confidence: 99%
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