• Corpus ID: 13331542

Asymmetric numeral systems

@article{Duda2009AsymmetricNS,
  title={Asymmetric numeral systems},
  author={Jarek Duda},
  journal={ArXiv},
  year={2009},
  volume={abs/0902.0271},
  url={https://api.semanticscholar.org/CorpusID:13331542}
}
New approach to entropy coding is presented: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetricNumeral systems - optimal for freely chosen probability distributions of symbols.
[PDF] Semantic Reader
146 Citations
Highly Influential Citations
28
Background Citations
52
Methods Citations
65
Results Citations
2

Figures from this paper

146 Citations

Large-Alphabet Semi-Static Entropy Coding Via Asymmetric Numeral Systems

It is demonstrated that in applications in which semi-static compression is appropriate, ANS-based coders can provide an excellent balance between compression effectiveness and speed, even when the alphabet is large.

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

    J. Duda
    Computer Science, Mathematics
  • 2013
Asymmetric numeral systems (ANS) is a new approach to accurate entropy coding, which allows to end this trade-off between speed and rate and can provide direct alternatives for standard AC, for large alphabet range coding, or for approximated quasi arithmetic coding.

Probability Approximation in Asymmetric Numeral Systems

This paper proposes a new source approximation formula, and shows that it leads to an improvement of compression efficiency of ANS.

Lightweight Compression with Encryption Based on Asymmetric Numeral Systems

Asymmetric numeral systems— an innovative approach to entropy coding which can be used for compression with encryption provides a compression ratio comparable with arithmetic coding at a similar speed as Huffman coding; hence, this coding is starting to replace them in new compressors.

On the stationary distribution of asymmetric numeral systems

It is shown that the previous result in ABS, which deals only with binary sources, can be applied to ANS as it is and the rate of ANs asymptotically attains the source entropy.

Encoding of probability distributions for Asymmetric Numeral Systems

There is discussed encoding of probability distributions for such applications, especially using Pyramid Vector Quantizer(PVQ)-based approach with deformation, bucket approximation, prefix trees, improving accuracy with additional bits, also tuned symbol spread for tANS.

A tutorial on the range variant of asymmetric numeral systems

This paper is intended to be a brief and accessible introduction to the range variant of asymmetric numeral systems (ANS), a system for lossless compression of sequences which can be used as a drop…

Pseudorandom bit generation with asymmetric numeral systems

This work presents a construction of a PRBG based on the asymmetric numeral system (ANS) compression algorithm that is provably secure for large values of R and heuristically secure for smaller values and claims that it is secure against quantum adversaries.

Redundancy and Optimization of tANS Entropy Encoders

This paper presents a method that calculates encoder redundancies in almost linear time, which translates in practice to thousand-fold speedups in redundancy calculations for small automatons, and allows redundancy calculations with tens of millions of states that would be otherwise prohibitive.

ANS-based compression and encryption with 128-bit security

The work investigates how to design a compcrypt algorithm using the ANS entropy coding and examines basic properties of ANS and shows that a plain ANS with a hidden encoding table can be broken by statistical attacks.
...

10 References

Twisted GFSR generators

A slightly but essentially modified version of the GFSR, which solves all the above problems without loss of merit and is most suitable for simulation of a large distributive system, which requires a number of mutually independent pseudorandom number generators with compact size.

Low-Density Parity-Check Codes

One of the most important families of LDPC ensembles is introduced, showing that appropriately chosen LDPC ensembles allow to communicate reliably at rates close to Shannon's capacity, and a lower bound on the threshold for reliable communication is derived.

Range Encoding: an Algorithm for Removing Redundancy from a Digitised Message

Range encoding is an algorithm for removing both sorts of redundancy in a message by encoding and decoding a message composed of letters drawn from the alphabet, and forming an encoded string of digits to base ten.

Optimal encoding on discrete lattice with translational invariant constrains using statistical algorithms

It will be shown that the method of encoding information in valuations of discrete lattice with some translational invariant constrains in asymptotically optimal way can reach the optimum for one-dimensional models using maximal entropy random walk.

Generalized Kraft Inequality and Arithmetic Coding

This coding technique requires no blocking, and the per-symbol length of the encoded string approaches the associated entropy within ∈, which is comparable to that of conventional coding methods.

A method for the construction of minimum-redundancy codes

A minimum-redundancy code is one constructed in such a way that the average number of coding digits per message is minimized.

Information Theory, Inference, and Learning Algorithms

Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.