# Generalized Kraft Inequality and Arithmetic Coding

@article{Rissanen1976GeneralizedKI, title={Generalized Kraft Inequality and Arithmetic Coding}, author={Jorma Rissanen}, journal={IBM J. Res. Dev.}, year={1976}, volume={20}, pages={198-203} }

Algorithms for encoding and decoding finite strings over a finite alphabet are described. The coding operations are arithmetic involving rational numbers li as parameters such that Σi2-l i≤2-∈. This coding technique requires no blocking, and the per-symbol length of the encoded string approaches the associated entropy within ∈. The coding speed is comparable to that of conventional coding methods.

## 569 Citations

Arithmetic coding into fixed-length codewords

- Computer ScienceIEEE Trans. Inf. Theory
- 1994

The idea here is to apply arithmetic coding piecewise, by cutting the process regularly, and the result consists of fixed-length sequences of bits, representing variable-length substrings of the source.

Fast and Space-Efficient Adaptive Arithmetic Coding

- Computer ScienceIMACC
- 1999

An implementation of the method is suggested whose coding time is less in order of magnitude than that for known methods by using a data structure called “imaginary sliding window”, which allows to significantly reduce the memory size of the encoder and decoder.

A multiplication-free multialphabet arithmetic code

- Computer ScienceIEEE Trans. Commun.
- 1989

A recursion for arithmetic codes used for data compression is described which requires no multiplication or division, even in the case of nonbinary alphabets, and is applicable in conjunction with stationary and nonstationary models alike.

Arithmetic stream coding using fixed precision registers

- Computer ScienceIEEE Trans. Inf. Theory
- 1979

Algorithms are presented for encoding and decoding strings of characters as real binary fractions, using registers of fixed precision, and have storage requirements and computation time O(n \log_{2}N) for string length n and alphabet size N.

Arithmetic Coding

- Computer ScienceIBM J. Res. Dev.
- 1979

The earlier introduced arithmetic coding idea has been generalized to a very broad and flexible coding technique which includes virtually all known variable rate noiseless coding techniques as…

Efficien Decoding of Lexicographical Rank in Binary Combinatorial Coding

- Computer Science2020 5th International Conference on Computer Science and Engineering (UBMK)
- 2020

A method that reduces the decoding complexity of an entropy encoding technique, namely, combinatorial coding, in order to increase compression efficiency without suffering from intolerable decoding latency is presented.

Efficien Decoding of Lexicographical Rank in Binary Combinatorial Coding

- Computer Science
- 2020

A method that reduces the decoding complexity of an entropy encoding technique, namely, combinatorial coding, in order to increase compression efficiency without suffering from intolerable decoding latency is presented.

Introduction to Arithmetic Coding - Theory and Practice

- Computer Science
- 2004

This introduction to arithmetic coding is divided in two parts; the first explains how and why arithmetic coding works, and the second shows some of its basic properties, which are later used in the computational techniques required for a practical implementation.

Analysis of arithmetic coding for data compression

- Computer Science[1991] Proceedings. Data Compression Conference
- 1991

The authors analyze the amount of compression possible when arithmetic coding is used for text compression in conjunction with various input models and finds that adaptive codes are proven to be as good as decrementing semi-adaptive codes.

## References

SHOWING 1-7 OF 7 REFERENCES

A method for the construction of minimum-redundancy codes

- Computer Science, BusinessProceedings of the IRE
- 1952

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

Universal codeword sets and representations of the integers

- Computer ScienceIEEE Trans. Inf. Theory
- 1975

An application is the construction of a uniformly universal sequence of codes for countable memoryless sources, in which the n th code has a ratio of average codeword length to source rate bounded by a function of n for all sources with positive rate.

An algorithm for source coding

- Computer ScienceIEEE Trans. Inf. Theory
- 1972

This work derives a simple algorithm for the ranking of binary sequences of length n and weight w and uses it for source encoding a memoryless binary source that generates O's and l's with probability p = 1 - q.

Enumerative source encoding

- MathematicsIEEE Trans. Inf. Theory
- 1973

This work provides an explicit scheme for calculating the index of any sequence in S according to its position in the lexicographic ordering of S, thus resulting in a data compression of (log\midS\mid)/n.

The author is located ut the IBM Research Laborutory

- The author is located ut the IBM Research Laborutory

Information Theory and Coding, McGrawHill Book Co., Inc

- New York,
- 1963

On the Number of Bits Required to Implement an Associative Memory

- Computer Structures Group
- 1972