Variable-length compression allowing errors
This paper studies the fundamental limits of the minimum average length of variable-length compression when a nonzero error probability ε is tolerated. We give non-asymptotic bounds on the minimum average length in terms of Erokhin's rate-distortion function and we use those bounds to obtain a...
Main Authors: | , , |
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Other Authors: | |
Format: | Article |
Language: | English |
Published: |
Institute of Electrical and Electronics Engineers (IEEE),
2016-01-27T15:07:34Z.
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Subjects: | |
Online Access: | Get fulltext |
Summary: | This paper studies the fundamental limits of the minimum average length of variable-length compression when a nonzero error probability ε is tolerated. We give non-asymptotic bounds on the minimum average length in terms of Erokhin's rate-distortion function and we use those bounds to obtain a Gaussian approximation on the speed of approach to the limit which is quite accurate for all but small blocklengths: equation where Q[superscript -1] (·) is the functional inverse of the Q-function and V (S) is the source dispersion. A nonzero error probability thus not only reduces the asymptotically achievable rate by a factor of 1-ε, but also this asymptotic limit is approached from below, i.e. a larger source dispersion and shorter blocklengths are beneficial. Further, we show that variable-length lossy compression under excess distortion constraint also exhibits similar properties. National Science Foundation (U.S.). Science and Technology Center (Grant CCF-0939370) |
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