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This paper provides an extensive study of the behavior of the best achievable rate (and other related fundamental limits) in variable-length lossless compression. In the non-asymptotic 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 codelengths 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. Non-asymptotic, 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 non-asymptotic limits of fixed-to-variable compression for all but very small blocklengths.
Many information sources are not just sequences of distinguishable symbols but rather have invariances governed by alternative counting paradigms such as permutations, combinations, and partitions. We consider an entire classification of these invari
The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs, the condi
Soft compression is a lossless image compression method, which is committed to eliminating coding redundancy and spatial redundancy at the same time by adopting locations and shapes of codebook to encode an image from the perspective of information t
Suppose there is a large file which should be transmitted (or stored) and there are several (say, m) admissible data-compressors. It seems natural to try all the compressors and then choose the best, i.e. the one that gives the shortest compressed fi
Probabilistic shaping based on constant composition distribution matching (CCDM) has received considerable attention as a way to increase the capacity of fiber optical communication systems. CCDM suffers from significant rate loss at short blocklengt