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### Arithmetic Coding

J. Rissanen, G. G. Langdon
1979 IBM Journal of Research and Development
The idea of arithmetic coding was suggested by Rissanen  from the theory of enumerative coding by Pasco  Arithmetic Coding Consider an half open interval [low,high).  ...  . • Arithmetic coding achieves this without any codebook -it is a variable-to-fixed coding. • Coding proceeds in two phases -modeling is separated from actual coding.  ...

### Arithmetic Coding [chapter]

Khalid Sayood
2006 Introduction to Data Compression
Another major advantage of arithmetic coding is that it is easy to implement a system with multiple arithmetic codes.  ...  In these cases, the advantage of arithmetic coding over Huffman coding is small, and it might not be worth the extra complexity to use arithmetic coding rather than Huffman coding.  ...

### Distributed Arithmetic Coding

Marco Grangetto, Enrico Magli, Gabriella Olmo
2007 IEEE Communications Letters
We propose a distributed binary arithmetic coder for Slepian-Wolf coding with decoder side information, along with a soft joint decoder.  ...  The proposed scheme provides several advantages over existing schemes, and its performance is equal to or better than that of an equivalent scheme based on turbo codes.  ...  DISTRIBUTED ARITHMETIC CODING A.  ...

### Secure Arithmetic Coding

Hyungjin Kim, Jiangtao Wen, John D. Villasenor
2007 IEEE Transactions on Signal Processing
• Codeword : z 1 z 2 ……z l 011 • 0. z 1 z 2 ……z l 0.011 • The code is prefix-free if and only if the intervals corresponding to codewords are disjoint.  ...

### Distributed Arithmetic Coding [chapter]

2017 Distributed Source Coding: Theory and Practice
We propose a distributed binary arithmetic coder for Slepian-Wolf coding with decoder side information, along with a soft joint decoder.  ...  The proposed scheme provides several advantages over existing schemes, and its performance is equal to or better than that of an equivalent scheme based on turbo codes.  ...  DISTRIBUTED ARITHMETIC CODING A.  ...

### Arithmetic completely regular codes [article]

J. H. Koolen, H. Tanaka
2016 arXiv   pre-print
Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression.  ...  In order to better understand these "arithmetic completely regular codes", we focus on cartesian products of completely regular codes and products of their corresponding coset graphs in the additive case  ...  We call these codes arithmetic completely regular codes and we classify them under some additional conditions.  ...

### Arithmetic completely regular codes

Jacobus Koolen, Woo Sun Lee, William Martin, Hajime Tanaka
2016 Discrete Mathematics & Theoretical Computer Science
Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression.  ...  In order to better understand these "arithmetic completely regular codes", we focus on cartesian products of completely regular codes and products of their corresponding coset graphs in the additive case  ...  In the case of linear arithmetic completely regular codes, more can be said.  ...

### On perfect arithmetic codes

Antoine C. Lobstein
1992 Discrete Mathematics
., On perfect arithmetic codes, Discrete Mathematics 106/107 (1992) 333-336 This short paper treats the perfect codes, in the case of arithmetic codes and Garcia-Rao modular distance.  ...  Introduction Arithmetic codes can detect or correct errors arising in arithmetic operations such as addition, multiplication, modular addition, . . . performed on integers which are represented in a fixed  ...  known perfect codes), have the following parameters Our result is that none of these parameters provides a perfect code (whereas we would have preferred to find one (or more) perfect code(s) among these  ...

### Resynchronization properties of arithmetic coding

P.W. Moo, X. Wu
1999 Proceedings DCC'99 Data Compression Conference (Cat. No. PR00096)
Arithmetic coding is a popular and e cient lossless compression technique that maps a sequence of source symbols to an interval of numbers between zero and one. 1 In arithmetic coding, an entire source  ...  In this paper we consider the problem of resynchronizing simple arithmetic codes. This research l a ys the groundwork for future analysis of arithmetic codes with highorder context models.  ...  Arithmetic coding is a popular and e cient lossless compression technique that maps a sequence of source symbols to an interval of numbers between zero and one. 1 In arithmetic coding, an entire source  ...

### Parallel design of arithmetic coding

J. Jiang, S. Jones
1994 IEE Proceedings - Computers and digital Techniques
The paper presents a parallel algorithm design for real-time implementation of arithmetic coding. The implementation comprises a parallelprocessing array arranged in a tree structure.  ...  This increases the arithmetic coding speed substantially. Details of a fixed-precision algorithm design, its implementation and simulation of its performance are reported.  ...  Introduction Arithmetic coding is a well-established, data-compression algorithm.  ...

### Non-binary distributed arithmetic coding

Ziyang Wang, Yongyi Mao, Iluju Kiringa
2015 2015 IEEE 14th Canadian Workshop on Information Theory (CWIT)
Arithmetic Coding (DAC) due to its simplicity in encoding .  ...  Although many channel code based DSC schemes have been developed (e.g., those based on turbo codes and LDPC codes ), this thesis focuses on the arithmetic coding based approaches, namely, Distributed  ...  Arithmetic coding is a mature optimal entropy coding.  ...

### An Introduction to Arithmetic Coding

G. G. Langdon
1984 IBM Journal of Research and Development
Arithmetic coding differs considerably from the more familiar compression coding techniques, such as prefix (Huffman) codes.  ...  Arithmetic coding is a data compression technique that encodes data (the data string) by creating a code string which represents a fractional value on the number line between 0 and 1.  ...  I thank Gerry Goertzel for his insights in explaining the operation of arithmetic coding.  ...

### Resynchronization properties of arithmetic coding

P.W. Moo, Xiaolin Wu
1999 Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348)
Arithmetic coding is a popular and e cient lossless compression technique that maps a sequence of source symbols to an interval of numbers between zero and one. 1 In arithmetic coding, an entire source  ...  In this paper we consider the problem of resynchronizing simple arithmetic codes. This research l a ys the groundwork for future analysis of arithmetic codes with highorder context models.  ...  Arithmetic coding is a popular and e cient lossless compression technique that maps a sequence of source symbols to an interval of numbers between zero and one. 1 In arithmetic coding, an entire source  ...

### Practical Implementations of Arithmetic Coding [chapter]

Paul G. Howard, Jeffrey Scott Vitter
1992 The Kluwer International Series in Engineering and Computer Science
We indicate the main disadvantage of arithmetic coding, its slowness, and give the basis of a fast, space-e cient, approximate arithmetic coder with only minimal loss of compression e ciency.  ...  We provide a tutorial on arithmetic coding, showing how it provides nearly optimal data compression and how it can be matched with almost any probabilistic model.  ...  We prove analytically that the loss in compression e ciency compared with exact arithmetic coding is negligible.  ...

### Nonlinear recurrences and arithmetic codes

Johannes Mykkeltveit
1977 Information and Control
We show that the binary expansion of the code numbers in an arithmetic BN-code, where B = (2 ~-I)/A and e is the order of 2 modA, may be generated by a unique nonsingular shift register of order h = [log  ...  The results we obtain may also be used for coding and decoding arithmetic codes. i = 1, 2,.... It is linear if and only iff is a linear function. The function f itself we call the feedback function.  ...  The arithmetic BN-code is defined to be the set of integers {B -N; N = 1, 2, 3,..., A --1}, and the integers B -N themselves are called code numbers.  ...
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