期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 60, 期 2, 页码 777-795出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2013.2291007
关键词
Lossless data compression; fixed-to-variable source coding; fixed-to-fixed source coding; entropy; finite-block length fundamental limits; central limit theorem; Markov sources; varentropy; minimal coding variance; source dispersion
资金
- National Science Foundation [CCF- 1016625]
- Center for Science of Information
- NSF Science and Technology Center [CCF-0939370]
- European Union
- Greek National Funds through the Operational Program Education and Lifelong Learning of the National Strategic Reference Framework Research Funding Program THALES: Investing in knowledge society through the European Social Fund
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1319304] Funding Source: National Science Foundation
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1016625] Funding Source: National Science Foundation
This paper provides an extensive study of the behavior of the best achievable rate (and other related fundamental limits) in variable-length strictly lossless compression. In the nonasymptotic regime, the fundamental limits of fixed-to-variable lossless compression with and without prefix constraints are shown to be tightly coupled. Several precise, quantitative bounds are derived, connecting the distribution of the optimal code lengths to the source information spectrum, and an exact analysis of the best achievable rate for arbitrary sources is given. Fine asymptotic results are proved for arbitrary (not necessarily prefix) compressors on general mixing sources. Nonasymptotic, explicit Gaussian approximation bounds are established for the best achievable rate on Markov sources. The source dispersion and the source varentropy rate are defined and characterized. Together with the entropy rate, the varentropy rate serves to tightly approximate the fundamental nonasymptotic limits of fixed-to-variable compression for all but very small block lengths.
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