Variable-length compression allowing errors
Author(s)Kostina, Victoria; Polyanskiy, Yury; Verdu, Sergio
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the 2014 IEEE International Symposium on Information Theory
Institute of Electrical and Electronics Engineers (IEEE)
Kostina, Victoria, Yury Polyanskiy, and Sergio Verdu. “Variable-Length Compression Allowing Errors.” 2014 IEEE International Symposium on Information Theory (June 2014).
Author's final manuscript