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Permutation Decoding and the Stopping Redundancy Hierarchy of Cyclic and Extended Cyclic Codes

Thorsten Hehn, Olgica Milenkovic, Stefan Laendner, Johannes B. Huber
2008 IEEE Transactions on Information Theory  
We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel  ...  We derive lower and upper bounds for the stopping redundancy hierarchy via Lovasz's Local Lemma and Bonferroni-type inequalities, and specialize them for codes with cyclic parity-check matrices.  ...  We extend the scope of the work in [10] by introducing the notion of the stopping redundancy hierarchy of a code.  ... 
doi:10.1109/tit.2008.2006456 fatcat:hv6cnyqt2fbotgscbx462ebfny

Permutation Decoding and the Stopping Redundancy Hierarchy of Linear Block Codes [article]

Thorsten Hehn, Olgica Milenkovic, Stefan Laendner, Johannes B. Huber
2007 arXiv   pre-print
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques.  ...  An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly dependent rows in any parity-check matrix of a code that avoids stopping sets of a given  ...  how the stopping redundancy hierarchy can be studied in the context of permutation decoding, first proposed for decoding of cyclic codes over the binary symmetric channel in [7] .  ... 
arXiv:cs/0702050v2 fatcat:l5zt3aey5rcnlcgfbn23sqe6xi

Permutation Decoding and the Stopping Redundancy Hierarchy of Linear Block Codes

Thorsten Hehn, Olgica Milenkovic, Stefan Laendner, Johannes B. Huber
2007 2007 IEEE International Symposium on Information Theory  
We investigate the stopping redundancy hierarchy of linear block codes and its connection to permutation decoding techniques.  ...  An element in the ordered list of stopping redundancy values represents the smallest number of possibly linearly dependent rows in any parity-check matrix of a code that avoids stopping sets of up to a  ...  how the stopping redundancy hierarchy can be studied in the context of permutation decoding, first proposed for decoding of cyclic codes over the binary symmetric channel in [7] .  ... 
doi:10.1109/isit.2007.4557193 dblp:conf/isit/HehnMLH07 fatcat:btb3c2ecwzhudbwfvworqikpwa

Distance Properties of Short LDPC Codes and Their Impact on the BP, ML and Near-ML Decoding Performance [chapter]

Irina E. Bocharova, Boris D. Kudryashov, Vitaly Skachek, Yauhen Yakimenka
2017 Lecture Notes in Computer Science  
Parameters of LDPC codes, such as minimum distance, stopping distance, stopping redundancy, girth of the Tanner graph, and their influence on the frame error rate performance of the BP, ML and near-ML  ...  In particular, the BP decoding is applied to the code parity-check matrices with an increasing number of redundant rows, and the convergence of the performance to that of the ML decoding is analyzed.  ...  H0             , (2) of an equivalent (in the sense of column permutation) TB code (see [18, Chapter 2] 3 Stopping redundancy and convergence to the ML decoding performance ), where H i ,  ... 
doi:10.1007/978-3-319-66278-7_5 fatcat:adwopy7rzjc7lhkrklauuiwnuq

On the Stopping Redundancy of Reed–Muller Codes

T. Etzion
2006 IEEE Transactions on Information Theory  
The stopping redundancy of the code is an important parameter which arise from analyzing the performance of a linear code under iterative decoding on a binary erasure channel.  ...  We prove that the stopping redundancy of R(m − 2, m), which is also the extended Hamming code of length 2 m , is 2m−1 and thus show that the recursive bound is tight in this case.  ...  ACKNOWLEDGMENT The author would like to thank Alexander Vardy and Moshe Schwartz for presenting the problem to him and many valuable discussions.  ... 
doi:10.1109/tit.2006.883542 fatcat:cryeutu2dzfyhn4myp2sduchru

Genetic Algorithms for Multiple-Choice Problems [article]

Uwe Aickelin
2010 arXiv   pre-print
to the problems and explaining the failure of such approaches due to epistasis.To overcome this, problem-specific information is added in a variety of ways, some of which are designed to increase the  ...  structure exploiting repair schemes and indirect genetic algorithms with self-adjusting decoder functions are identified as promising approaches.The research starts by applying standard genetic algorithms  ...  No doubt without the many of our discussions both this thesis and my research would not have been possible. Additionally, I am very grateful  ... 
arXiv:1004.3147v1 fatcat:gqwp6eizqrb7ve46x7ks65heay

Genetic Algorithms for Multiple-Choice Optimisation Problems

Uwe Aickelin
2009 Social Science Research Network  
Additionally, I am very grateful for the advice and support of Dr Bill Dowsland, the computer support staff and other people of the European Business Management School.  ...  Hence, the main theme of this work is to balance feasibility and cost of solutions.  ...  for area u only (the remainder of the string is redundant).  ... 
doi:10.2139/ssrn.2832542 fatcat:czeuc44vebgxdmsqrtvlm5vffe

Haswell: The Fourth-Generation Intel Core Processor

Per Hammarlund, Alberto J. Martinez, Atiq A. Bajwa, David L. Hill, Erik Hallnor, Hong Jiang, Martin Dixon, Michael Derr, Mikal Hunsaker, Rajesh Kumar, Randy B. Osborne, Ravi Rajwar (+9 others)
2014 IEEE Micro  
team, and Patty Kummrow and the SDG Org for their significant contributions to the success of eDRAM and the Intel Iris Pro Graphics product.  ...  Acknowledgments We thank Kevin Zhang, Fatih Hamzaoglu, Eric Wang, Ruth Brain and the Intel TMG Organization, Dave Dimarco, Manoj Lal, Steve Kulick, the Haswell architecture team, and the entire Intel CCDO  ...  These new instructions benefit many algorithms ranging from fast indexing, to cyclical redundancy checking (CRC), to widespread encryption algorithms. Figure 9 summarizes the performance.  ... 
doi:10.1109/mm.2014.10 fatcat:gc6fvakpm5brln3fdlq7pfjdve

Subject Index Volumes 1–200

2001 Discrete Mathematics  
Erdös and Sós, 4925 Erdös and Szekeres, 4879 Erdös et al., 5529, 5888 Erdös Rubin Taylor, 3815 Erdös Sós Turán, 506 Everett, 2901 Faigle and Sands, 2122 Faudree et al., 4399 Faudree Gould Jacobson  ...  Slater, 5299 Hertz and de Werra, 3748 Hibi, 4839 Hoàng, 3748, 4811 Holton, 1660 Holyer and Cockayne, 1118 Howorka, 2636  ...  , 5326 of a linear code, 864 weight hierarchy, 4386, 4590, 5435 of codes, 5219 of semiprimitive codes, 4590 weight in a code, 67 weight of a code, 67, 75, 76, 78 word, 554 weight of a majority  ... 
doi:10.1016/s0012-365x(00)00471-4 fatcat:znxg54q6ifgutnhzj3urcw455y

Post-Quantum Cryptography [chapter]

Qijun Gu, Pascal Paillier, Tanja Lange, Edlyn Teske, Darrel Hankerson, Alfred Menezes, David Zhang, Feng Yue, Wangmeng Zuo, Jean-Jacques Quisquater, Gildas Avoine, Gerald Brose (+73 others)
2011 Encyclopedia of Cryptography and Security  
Scientists from all over the world gave talks on the state of the art of quantum computers and on cryptographic schemes that may be able to resist attacks by quantum computers.  ...  We hope that it serves as an introduction to the field, as an overview of the state of the art, and as an encouragement for many more scientists to join us in investigating post-quantum cryptography.  ...  Acknowledgements We thank Phong Nguyen and Markus Rückert for helpful discussions on the practical security of lattice-based cryptography.  ... 
doi:10.1007/978-1-4419-5906-5_386 fatcat:ucdkilta7zc3voq7nqctmjkcr4

Parity-Checked Strassen Algorithm [article]

Hsin-Po Wang, Iwan Duursma
2022 arXiv   pre-print
In general, we propose probability-wisely favorable configurations whose numbers of workers are close to, if not less than, the thresholds of other codes (e.g., entangled polynomial code and PolyDot code  ...  Our proposed scheme applies recursively, respects worker locality, incurs moderate pre- and post-processes, and extends over small finite fields.  ...  In LDPC (low-density parity-check) code terminology, a set of unknowns that prohibits the decoding from progressing is called a stopping set.  ... 
arXiv:2011.15082v3 fatcat:bfvzvx6qsnhyzhhj5bfpehbcoi

A Comprehensive Survey of Watermarking Relational Databases Research [article]

Muhammad Kamran, Muddassar Farooq
2018 arXiv   pre-print
A survey of almost all the work done, till date, in these fields has been presented in this paper. The techniques have been classified on the basis of how and where they embed the watermark.  ...  The analysis and comparison of these techniques on different merits has also been provided. In the end, this paper points out the direction of future research in these fields.  ...  This column can have values: -(no error detection mechanism is used by the decoding scheme), Voting (the majority voting scheme is used for error detection), CRC (the cyclic redundancy check is used as  ... 
arXiv:1801.08271v1 fatcat:ensgymv35be67jebrgqasvel7u

Psycholinguistics: a survey of theory and research problems

John W. Gardner, John B. Carroll, Leonard D. Newmark, Susan M. Ervin, Sol Saporta, Joseph H. Greenberg, Donald E. Walker, James J. Jenkins, Kellogg Wilson, Floyd G. Lounsbury, Charles E. Osgood, Thomas A. Sebeok
1954 Journal of Abnormal & Social Psychology  
the t of 'stop  ...  To the extent that a speaker modification (a) makes a difference in the code, (6) is not redundant, and (c) occurs in a position of high information value with respect to appropriate behavior, the hearer  ...  A group of people that has an elaborate and complicated kinship and marriage system should have an equally elaborate and complicated system of kinship and marriage terms.  ... 
doi:10.1037/h0063655 fatcat:hf2c57s3ozetxju46nywrwcdzu

The Relation Between k-Circularity and Circularity of Codes

Elena Fimmel, Christian J. Michel, François Pirot, Jean-Sébastien Sereni, Martin Starman, Lutz Strüngmann
2020 Bulletin of Mathematical Biology  
n is circular, and we determine the least such integer k for all values of n and [Formula: see text].  ...  The k-circular codes may represent an important evolutionary step between the circular codes, such as the comma-free codes, and the genetic code.  ...  From a theoretical point of view, we will show below the existence of a hierarchy of circular codes and k-circular codes allowing a codon decoding without ambiguity, from strong to flexible reading frame  ... 
doi:10.1007/s11538-020-00770-7 pmid:32754878 fatcat:wqr5mdggbrgt5m5knxm2273nzm

Abstracts of Current Computer Literature

1969 IEEE transactions on computers  
Emphasis is on cyclic codes, the most deeply studied and widely used of the many available codes. Operations of typical binary shift registers illustrate the encoding and decoding processes.  ...  6974 Algorithm Classification for Scheduling Time-Sharing Systems 7005 -see also Patterns Codes; Coding; Decoding; Encoding Use of Redundant Codes to Increase the Reliability of Associative Stores  ... 
doi:10.1109/t-c.1969.222790 fatcat:6uoe3hk6ffhxvgnifzisoykq4e
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