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On arithmetical first-order theories allowing encoding and decoding of lists

Patrick Cegielski, Denis Richard
1999 Theoretical Computer Science  
In Computer Science, n-tuples and lists are usual tools; we investigate both notions in the framework of first-order logic within the set of nonnegative integers.  ...  The theory of integers equipped with a pairing function can be decidable or not. The theory of decoding of lists (under some natural condition) is always undecidable.  ...  Acknowledgements We thank the referees for pointing out some errors (in particular in Proposition 1.1 ) and suggesting many improvements.  ... 
doi:10.1016/s0304-3975(97)00281-8 fatcat:2sajvd6tfvhfpfbksuf5kflxyy

Rate-compatible distributed arithmetic coding

M. Grangetto, E. Magli, R. Tron, G. Olmo
2008 IEEE Communications Letters  
In this letter, we extend it to rate-compatible coding, which is useful in presence of a feedback channel between encoder and decoder.  ...  Distributed arithmetic coding has been shown to be effective for Slepian-Wolf coding with side information.  ...  Direct ordering 1) Encoder: In direct ordering, the FBs are inserted in a list (called the FB list) following the normal forward ordering of the encoding and decoding procedures.  ... 
doi:10.1109/lcomm.2008.080645 fatcat:vp6bf43ixvcx5kag6b2bbraib4

Universal lossless data compression with side information by using a conditional MPM grammar transform

En-Hui Yang, A. Kaltchenko, J.C. Kieffer
2001 IEEE Transactions on Information Theory  
Consequently, the arithmetic encoding and decoding part of the MPM code has the -space and the -time complexities.  ...  Thus, the sequences , are encoded in the indicated order by a conditional arithmetic encoder.  ... 
doi:10.1109/18.945239 fatcat:pjlujgndwnes7mgvjfzsgq3wsi

Coding with Asymmetric Numeral Systems [chapter]

Jeremy Gibbons
2019 Lecture Notes in Computer Science  
Existing presentations of the ANS encoding and decoding algorithms are somewhat obscured by the lack of suitable presentation techniques; we present here an equational derivation, calculational where it  ...  Asymmetric Numeral Systems (ANS) are an entropy-based encoding method introduced by Jarek Duda, combining the Shannonoptimal compression effectiveness of arithmetic coding with the execution efficiency  ...  and Richard Bird who gave much helpful advice on content and presentation.  ... 
doi:10.1007/978-3-030-33636-3_16 fatcat:ldnmzvasj5dvzke4fn43pm7dwe

Exploring Approximations for Floating-Point Arithmetic Using UppSAT [chapter]

Aleksandar Zeljić, Peter Backeman, Christoph M. Wintersteiger, Philipp Rümmer
2018 Lecture Notes in Computer Science  
We present encodings of floating-point arithmetic into reduced precision floating-point arithmetic, real-arithmetic, and fixed-point arithmetic (encoded into the theory of bit-vectors in practice).  ...  Approximations can be viewed as a composition of an encoding into a target theory, a precision ordering, and a number of strategies for model reconstruction and precision (or approximation) refinement.  ...  Precision regulates the encoding from the input to the output theory, and its domain and ordering are of consequence for encoding, approximation refinement and termination.  ... 
doi:10.1007/978-3-319-94205-6_17 fatcat:trxnsjw4qncglnryvwh4ilhis4

H.264 stream replacement watermarking with CABAC encoding

Dekun Zou, Jeffrey A Bloom
2010 2010 IEEE International Conference on Multimedia and Expo  
In theory, modification of a part of an arithmetically coded stream will cause the rest of the stream to be misinterpreted and thus become undecodable.  ...  This table identifies small segments of data in the encoded stream that can be replaced and identifies one or more replacement values. The embedding process is then very fast.  ...  This represents a number of extensions of typical arithmetic coding schemes. First, CABAC is designed to arithmetically encode binary data.  ... 
doi:10.1109/icme.2010.5583550 dblp:conf/icmcs/ZouB10 fatcat:6vfql4ot2jfizaqcgyaxjlzxhe

Arithmetic Coding with Folds and Unfolds [chapter]

Richard Bird, Jeremy Gibbons
2003 Lecture Notes in Computer Science  
Interval expansion The major problem with encode 2 and decode 2 is that they make use of fractional arithmetic.  ...  Although much of the general theory of folds and unfolds is well-known, see [3, 6] , we will need one or two novel results. One concerns a new pattern of computation, which we call streaming.  ... 
doi:10.1007/978-3-540-44833-4_1 fatcat:swqej6m6svhivdqrgjqbvulyuy

Understanding Entropy Coding With Asymmetric Numeral Systems (ANS): a Statistician's Perspective [article]

Robert Bamler
2022 arXiv   pre-print
We also present and empirically evaluate an open-source library of various entropy coders designed for both research and production use. Related teaching videos and problem sets are available online.  ...  This paper is meant as an educational resource to make ANS more approachable by presenting it from a new perspective of latent variable models and the so-called bits-back trick.  ...  This work was supported by the German Federal Ministry of Education and Research (BMBF): Tübingen AI Center, FKZ: 01IS18039A.  ... 
arXiv:2201.01741v2 fatcat:v2ou4d3dezenvkawt4gkqeeg5i

Adaptable recursive binary entropy coding technique

Aaron B. Kiely, Matthew A. Klimesh, Zia-ur Rahman, Robert A. Schowengerdt, Stephen E. Reichenbach
2002 Visual Information Processing XI  
The encoding process for our technique is adaptable in that ea,& bit to be encoded has an associated probability-of-zero estimate that may depend on previously encoded bits; this adaptability allows more  ...  The encoder compresses a bit sequence by recursively encoding groups of bits that have similar estimated statistics, ordering the output in a way t h t is suited to the decoder.  ...  ACKNOWLEDGMENTS The work described was funded by the IPN-ISD Technology Program and performed at the Jet Propulsion Laboratory, California Institute of Technology under contract with the National Aeronautics  ... 
doi:10.1117/12.477575 dblp:conf/spieVIP/KielyK02 fatcat:mfxln3usdbdjtpp6stifu3qfju

Non-binary distributed arithmetic coding

Ziyang Wang, Yongyi Mao, Iluju Kiringa
2015 2015 IEEE 14th Canadian Workshop on Information Theory (CWIT)  
., those based on turbo codes [11]and LDPC codes [20]), this thesis focuses on the arithmetic coding based approaches, namely, Distributed Arithmetic Coding (DAC) due to its simplicity in encoding [8].  ...  The first algorithm applies a designed overlap structure in DAC process, while the second converts a non-binary sequence into a binary sequence by Huffman Coding and encoding the result in binary DAC.  ...  In [8] ,binary DAC is an extension of binary Arithmetic Coding which allows the overlap of two intervals between zero and one.  ... 
doi:10.1109/cwit.2015.7255140 dblp:conf/cwit/WangMK15 fatcat:k72n6k3lv5bspcibfgi5l5yuc4

Distributed Arithmetic Coding for the Asymmetric Slepian-Wolf problem [article]

M. Grangetto, E. Magli, G. Olmo
2008 arXiv   pre-print
Distributed source coding schemes are typically based on the use of channels codes as source codes.  ...  We have compared the performance of distributed arithmetic coding with turbo codes and low-density parity-check codes, and found that the proposed approach has very competitive performance.  ...  For example, with two sources it is possible to perform "standard" encoding of the first source (called side information) at a rate equal to its entropy, and "conditional" encoding of the second one at  ... 
arXiv:0712.0271v2 fatcat:blrxmdv36rdxbkfbv5iluq74ta

Author index volume 222 (1999)

1999 Theoretical Computer Science  
Richard, On arithmetical first-order theories allowing encoding and decoding of lists (1-2) 55-75 Colson, L., On diagonal fixed points of increasing functions (Note) (1-2) 181-186 Dufourd, C. and A.  ...  ., Design of abstract domains using first-order logic (1-2) 153-179 Nagarajan, R., see S. Abramsky (1-2) 1-53 Ranzato, F., see G. Fil6 (1-2) 77-111 Richard, D., see P.  ... 
doi:10.1016/s0304-3975(99)80007-3 fatcat:dj2y23b3kfgrzdgbevuxmkezea

Embedded image coding using zerotrees of wavelet coefficients

J.M. Shapiro
1993 IEEE Transactions on Signal Processing  
Also, given a bit stream, the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated  ...  Using a n embedded coding algorithm, a n encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly.  ...  , and allows the encoding or decoding to stop at any point, adaptive arithmetic coding, which allows the entropy coder to incorporate learning into the bit stream itself.  ... 
doi:10.1109/78.258085 fatcat:zqylmsbccbf6ppdabqpkrde5ly

Page 2439 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
Dekhtyar (Tver’) 2000d:03147 03F30 03D35 68NO01 68P05 Cegielski, Patrick (F-PARIS12-CL; Fontainebleau); Richard, Denis On arithmetical first-order theories allowing encoding and decoding of lists.  ...  The paper is devoted to the problem of encoding and decoding of lists in first-order theories.  ... 

Lossless and near-lossless source coding for multiple access networks

Qian Zhao, M. Effros
2003 IEEE Transactions on Information Theory  
(i.i.d.) according to joint probability mass function (p.m.f.) ( ); the encoder for each source operates without knowledge of the other source; the decoder jointly decodes the encoded bit streams from  ...  Our central results include generalizations of Huffman and arithmetic codes to the MASC framework for arbitrary ( ), , and ( ) and polynomial-time design algorithms that approximate these optimal solutions  ...  ACKNOWLEDGMENT The authors gratefully acknowledge the detailed critiques and many helpful comments from the anonymous reviewers.  ... 
doi:10.1109/tit.2002.806145 fatcat:gmd3xrik4nctpoi2iwjtq5obki
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