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 lossless and lossy variable-length compression, allowing a nonzero error probability ε, for lossless compression. We give nonasymptotic 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: (1 - ε) k H(S) - ((V(S)/2π))1/2 exp[-((Q-1 (ε))2/2)], where Q-1(·) is the functional inverse of the standard Gaussian complementary cumulative distribution 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 this asymptotic limit is approached from below, i.e., larger source dispersions and shorter blocklengths are beneficial. Variable-length lossy compression under an excess distortion constraint is shown to exhibit similar properties.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
IEEE Transactions on Information Theory
Institute of Electrical and Electronics Engineers (IEEE)
Kostina, Victoria, Yury Polyanskiy and Sergio Verdú. "Variable-Length Compression Allowing Errors." IEEE Transactions on Information Theory 61, no. 8 (August 2015): pp. 4316-4330.
Author's final manuscript