The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Judy L. Walker - One of the best experts on this subject based on the ideXlab platform.
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Coding Theory (Dagstuhl Seminar 13351).
2020Co-Authors: Hans-andrea Loeliger, Emina Soljanin, Judy L. WalkerAbstract:Coding Theory has become an essential ingredient of contemporary information technology, and it remains a fascinating area of research. The seminar brought together 45 high-caliber researchers with backgrounds and interests in various different parts of Coding Theory. The new area of codes for cloud applications received much attention, but other key areas such as network codes, codes on graphs, algebraic Coding, and polar codes, were also well represented and generated lively discussions.
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Coding Theory (Dagstuhl Seminar 11461).
2020Co-Authors: Joachim Rosenthal, Mohammad Amin Shokrollahi, Judy L. WalkerAbstract:This report documents the program and the outcomes of Dagstuhl Seminar 11461 ``Coding Theory''. A (channel) code is typically a set of vectors of the same length n over a finite alphabet \Sigma. By choosing a fixed codebook, binary strings of appropriate length are injectively mapped into the elements of the code. These elements are then transmitted over a communications channel which induces errors on the codeword. Depending on how well the original code is designed, and which algorithms are used, the result of this transmission and attempts to recover the original vector after transmission can be anywhere between disastrous to excellent. Coding Theory is all about the design of excellent codes as a function of the communications channel, and the design of efficient algorithms for choosing the codebook vectors, and more importantly, for recovering the original vector after transmission. As such, successful design of codes requires knowledge and tools in a number of areas such as combinatorics, algorithms design, probability Theory and complexity Theory, to name a few. The purpose of this workshop is to bring together researchers in the field to discuss recent theoretical advances in algebraic Coding, codes on graphs, and network Coding, as well as new and emerging applications of Coding methods to real-world problems.
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Combinatorial Neural Codes from a Mathematical Coding Theory Perspective
Neural Computation, 2013Co-Authors: Carina Curto, Vladimir Itskov, Katherine Morrison, Zachary Roth, Judy L. WalkerAbstract:Shannon's seminal 1948 work gave rise to two distinct areas of research: information Theory and mathematical Coding Theory. While information Theory has had a strong influence on theoretical neuroscience, ideas from mathematical Coding Theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical Coding Theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes). We find, perhaps surprisingly, that the high levels of redundancy present in these codes do not support accurate error correction, although the error-correcting performance of receptive field codes catches up to that of random comparison codes when a small tolerance to error is introduced. However, receptive field codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error-correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.
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combinatorial neural codes from a mathematical Coding Theory perspective
arXiv: Neurons and Cognition, 2012Co-Authors: Carina Curto, Vladimir Itskov, Katherine Morrison, Zachary Roth, Judy L. WalkerAbstract:Shannon's seminal 1948 work gave rise to two distinct areas of research: information Theory and mathematical Coding Theory. While information Theory has had a strong influence on theoretical neuroscience, ideas from mathematical Coding Theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical Coding Theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes). We find, perhaps surprisingly, that the high levels of redundancy present in these codes does not support accurate error correction, although the error-correcting performance of RF codes "catches up" to that of random comparison codes when a small tolerance to error is introduced. On the other hand, RF codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error-correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.
M. Sudan - One of the best experts on this subject based on the ideXlab platform.
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ISSAC - Algebraic algorithms and Coding Theory
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08, 2008Co-Authors: M. SudanAbstract:The associated talk surveys some recent developments in algorithmic Coding Theory that answer some fundamental questions with algebraic techniques.
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FOCS - Coding Theory: Tutorial and Survey
2001Co-Authors: M. SudanAbstract:Coding Theory has played a central role in the theoretical computer science. Computer scientists have long exploited notions, constructions, theorems and techniques of Coding Theory. More recently, theoretical computer science has also been contributing to the Theory of error-correcting codes ? in particular in making progress on some fundamental algorithmic connections. Here we survey some of the central goals of Coding Theory and the progress made via algebraic methods. We stress that this is a very partial view of Coding Theory and a lot of promising combinatorial and probabilistic approaches are not covered by this survey.
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Coding Theory: tutorial & survey
Proceedings 42nd IEEE Symposium on Foundations of Computer Science, 2001Co-Authors: M. SudanAbstract:Coding Theory has played a central role in the theoretical computer science. Computer scientists have long exploited notions, constructions, theorems and techniques of Coding Theory. More recently, theoretical computer science has also been contributing to the Theory of error-correcting codes in particular in making progress on some fundamental algorithmic connections. Here we survey some of the central goals of Coding Theory and the progress made via algebraic methods. We stress that this is a very partial view of Coding Theory and a lot of promising combinatorial and probabilistic approaches are not covered by this survey.
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Coding Theory: Tutorial & survey
Proceedings 42nd IEEE Symposium on Foundations of Computer Science, 2001Co-Authors: M. SudanAbstract:Coding Theory has played a central role in the theoretical computer science. Computer scientists have long exploited notions, constructions, theorems and techniques of Coding Theory. More recently, theoretical computer science has also been contributing to the Theory of error-correcting codes - in particular in making progress on some fundamental algorithmic connections. Here we survey some of the central goals of Coding Theory and the progress made via algebraic methods. We stress that this is a very partial view of Coding Theory and a lot of promising combinatorial and probabilistic approaches are not covered by this survey. In particular some central algorithmic questions of Coding Theory, both in the Shannon sense and in the Hamming sense are open today, and theoretical computer scientists can (and are) contributing. Readers seeking further material are encouraged to check out the website of the author [90]. More stable sources of information include the classical text of MacWilliams and Sloane [1981], the concise text of van Lint on algebraic Coding Theory [1999], the out-of-print, but highly recommended, book by Blahut [1983] which is an excellent source for some of the algorithmic works, and the highly detailed (and not-so-handy) handbook of Coding Theory.
Carina Curto - One of the best experts on this subject based on the ideXlab platform.
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Combinatorial Neural Codes from a Mathematical Coding Theory Perspective
Neural Computation, 2013Co-Authors: Carina Curto, Vladimir Itskov, Katherine Morrison, Zachary Roth, Judy L. WalkerAbstract:Shannon's seminal 1948 work gave rise to two distinct areas of research: information Theory and mathematical Coding Theory. While information Theory has had a strong influence on theoretical neuroscience, ideas from mathematical Coding Theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical Coding Theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes). We find, perhaps surprisingly, that the high levels of redundancy present in these codes do not support accurate error correction, although the error-correcting performance of receptive field codes catches up to that of random comparison codes when a small tolerance to error is introduced. However, receptive field codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error-correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.
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combinatorial neural codes from a mathematical Coding Theory perspective
arXiv: Neurons and Cognition, 2012Co-Authors: Carina Curto, Vladimir Itskov, Katherine Morrison, Zachary Roth, Judy L. WalkerAbstract:Shannon's seminal 1948 work gave rise to two distinct areas of research: information Theory and mathematical Coding Theory. While information Theory has had a strong influence on theoretical neuroscience, ideas from mathematical Coding Theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical Coding Theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes). We find, perhaps surprisingly, that the high levels of redundancy present in these codes does not support accurate error correction, although the error-correcting performance of RF codes "catches up" to that of random comparison codes when a small tolerance to error is introduced. On the other hand, RF codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error-correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.
C. Zemor - One of the best experts on this subject based on the ideXlab platform.
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On greedy algorithms in Coding Theory
IEEE Transactions on Information Theory, 1996Co-Authors: G.d. Cohen, S. Litsyn, C. ZemorAbstract:We study a wide class of problems in Coding Theory for which we consider two different formulations: in terms of incidence matrices and in terms of hypergraphs. These problems are dealt with using a greedy algorithm due to Stein (1974) and Lovasz (1975). Some examples, including constructing covering codes, codes for conflict resolution, separating systems, source enCoding with distortion, etc., are given a unified treatment. Under certain conditions derandomization can be performed, leading to an essential reduction in the complexity of the constructions.
Zhen Zhang - One of the best experts on this subject based on the ideXlab platform.
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Network Coding Theory part II: multiple source
Foundations and Trends in Communications and Information Theory, 2005Co-Authors: Raymond W. Yeung, Shuo-yen Robert Li, Zhen ZhangAbstract:Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network Coding Theory. Network Coding offers a new paradigm for network communications and has generated abundant research interest in information and Coding Theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix Theory.
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network Coding Theory single sources
Foundations and Trends in Communications and Information Theory, 2005Co-Authors: Raymond W. Yeung, Shuo-yen Robert Li, Zhen ZhangAbstract:Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network Coding Theory. Network Coding offers a new paradigm for network communications and has generated abundant research interest in information and Coding Theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix Theory.
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Network Coding Theory
Network Coding Theory, 1Co-Authors: Raymond W. Yeung, Shuo-yen Robert Li, Zhen ZhangAbstract:Network Coding Theory provides a tutorial on the basic of network Coding Theory. It presents the material in a transparent manner without unnecessarily presenting all the results in their full generality. Store-and-forward had been the predominant technique for transmitting information through a network until its optimality was refuted by network Coding Theory. Network Coding offers a new paradigm for network communications and has generated abundant research interest in information and Coding Theory, networking, switching, wireless communications, cryptography, computer science, operations research, and matrix Theory. The tutorial is divided into two parts. Part I is devoted to network Coding for the transmission from a single source node to other nodes in the network. Part II deals with the problem under the more general circumstances when there are multiple source nodes each intending to transmit to a different set of destination nodes. Network Coding Theory presents a unified framework for understanding the basic notions and fundamental results in network Coding. It will be of interest to students, researchers and practitioners working in networking research.