Variable-length compression allowing errors

• Main Authors: Kostina, Victoria (Author), Polyanskiy, Yury (Contributor), Verdu, Sergio (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers (IEEE), 2016-01-27T15:07:34Z.
• Subjects: Article
• Online Access: Get fulltext

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)