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The modern data compression is mainly based on two approaches to entropycoding: Huffman (HC) and arithmetic/range coding (AC). The former is muchfaster, but approximates probabilities with powers of 2, usually leading torelatively low compression rates. The latter uses nearly exact probabilities -easily approaching theoretical compression rate limit (Shannon entropy), but atcost of much larger computational cost.  Asymmetric numeral systems (ANS) is a new approach to accurate entropycoding, which allows to end this trade-off between speed and rate: the recentimplementation [1] provides about $50\%$ faster decoding than HC for 256 sizealphabet, with compression rate similar to provided by AC. This advantage isdue to being simpler than AC: using single natural number as the state, insteadof two to represent a range. Beside simplifying renormalization, it allows toput the entire behavior for given probability distribution into a relativelysmall table: defining entropy coding automaton. The memory cost of such tablefor 256 size alphabet is a few kilobytes. There is a large freedom whilechoosing a specific table - using pseudorandom number generator initializedwith cryptographic key for this purpose allows to simultaneously encrypt thedata.  This article also introduces and discusses many other variants of this newentropy coding approach, which can provide direct alternatives for standard AC,for large alphabet range coding, or for approximated quasi arithmetic coding.

Asymmetric numeral systems: entropy coding combining speed of Huffman coding with compression rate of arithmetic coding