The Experts below are selected from a list of 81102 Experts worldwide ranked by ideXlab platform
Gad M Landau - One of the best experts on this subject based on the ideXlab platform.
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construction of aho corasick automaton in linear time for integer Alphabets
Information Processing Letters, 2006Co-Authors: Shiri Dori, Gad M LandauAbstract:We present a new simple algorithm that constructs an Aho Corasick automaton for a set of patterns, P, of total length n, in O(n) time and space for integer Alphabets. Processing a text of size m over an Alphabet @S with the automaton costs O(mlog|@S|+k), where there are k occurrences of patterns in the text. A new, efficient implementation of nodes in the Aho Corasick automaton is introduced, which works for suffix trees as well.
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construction of aho corasick automaton in linear time for integer Alphabets
Combinatorial Pattern Matching, 2005Co-Authors: Shiri Dori, Gad M LandauAbstract:We present a new simple algorithm that constructs an Aho Corasick automaton for a set of patterns, P, of total length n, in O(n) time and space for integer Alphabets. Processing a text of size m over an Alphabet Σ with the automaton costs $O(m \log \left|\Sigma\right| + k)$, where there are k occurrences of patterns in the text.
Elisabeth Gassiat - One of the best experts on this subject based on the ideXlab platform.
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Coding on countably infinite Alphabets
IEEE Transactions on Information Theory, 2009Co-Authors: Stéphane Boucheron, Aurélien Garivier, Elisabeth GassiatAbstract:This paper describes universal lossless coding strategies for compressing sources on countably infinite Alphabets. Classes of memoryless sources defined by an envelope condition on the marginal distribution provide benchmarks for coding techniques originating from the theory of universal coding over finite Alphabets. We prove general upper-bounds on minimax regret and lower-bounds on minimax redundancy for such source classes. The general upper bounds emphasize the role of the Normalized Maximum Likelihood codes with respect to minimax regret in the infinite Alphabet context. Lower bounds are derived by tailoring sharp bounds on the redundancy of Krichevsky-Trofimov coders for sources over finite Alphabets. Up to logarithmic (resp. constant) factors the bounds are matching for source classes defined by algebraically declining (resp. exponentially vanishing) envelopes. Effective and (almost) adaptive coding techniques are described for the collection of source classes defined by algebraically vanishing envelopes. Those results extend ourknowledge concerning universal coding to contexts where the key tools from parametric inference
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coding on countably infinite Alphabets
IEEE Transactions on Information Theory, 2009Co-Authors: Stéphane Boucheron, Aurélien Garivier, Elisabeth GassiatAbstract:This paper describes universal lossless coding strategies for compressing sources on countably infinite Alphabets. Classes of memoryless sources defined by an envelope condition on the marginal distribution provide benchmarks for coding techniques originating from the theory of universal coding over finite Alphabets. We prove general upper bounds on minimax regret and lower bounds on minimax redundancy for such source classes. The general upper bounds emphasize the role of the normalized maximum likelihood (NML) codes with respect to minimax regret in the infinite Alphabet context. Lower bounds are derived by tailoring sharp bounds on the redundancy of Krichevsky-Trofimov coders for sources over finite Alphabets. Up to logarithmic (resp., constant) factors the bounds are matching for source classes defined by algebraically declining (resp., exponentially vanishing) envelopes. Effective and (almost) adaptive coding techniques are described for the collection of source classes defined by algebraically vanishing envelopes. Those results extend our knowledge concerning universal coding to contexts where the key tools from parametric inference are known to fail.
Ido Tal - One of the best experts on this subject based on the ideXlab platform.
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On the Construction of Polar Codes for Channels With Moderate Input Alphabet Sizes
IEEE Transactions on Information Theory, 2017Co-Authors: Ido TalAbstract:Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small input Alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate input Alphabet size, which follows the paradigm of “degrading after each polarization step,” will inherently be impractical with respect to a certain “hard” underlying channel. This result also sheds light on why the construction of low-density parity-check codes using density evolution is impractical for channels with moderate-sized input Alphabets.
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On the Construction of Polar Codes for Channels with Moderate Input Alphabet Sizes
arXiv: Information Theory, 2015Co-Authors: Ido TalAbstract:Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small input Alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate input Alphabet size which follows the paradigm of "degrading after each polarization step" will inherently be impractical with respect to a certain "hard" underlying channel. This result also sheds light on why the construction of LDPC codes using density evolution is impractical for channels with moderate sized input Alphabets.
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on the construction of polar codes for channels with moderate input Alphabet sizes
International Symposium on Information Theory, 2015Co-Authors: Ido TalAbstract:Current deterministic algorithms for the construction of polar codes cannot be argued to be practical for channels with input Alphabets of moderate size. In this paper, we show that any construction algorithm which follows the paradigm of “degrading after each polarization step” will inherently be impractical with respect to a certain “hard” underlying channel having an input Alphabet of moderate size. This result also sheds light on why the construction of LDPC codes using density evolution is impractical for channels with moderate sized input Alphabets.
Shiri Dori - One of the best experts on this subject based on the ideXlab platform.
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construction of aho corasick automaton in linear time for integer Alphabets
Information Processing Letters, 2006Co-Authors: Shiri Dori, Gad M LandauAbstract:We present a new simple algorithm that constructs an Aho Corasick automaton for a set of patterns, P, of total length n, in O(n) time and space for integer Alphabets. Processing a text of size m over an Alphabet @S with the automaton costs O(mlog|@S|+k), where there are k occurrences of patterns in the text. A new, efficient implementation of nodes in the Aho Corasick automaton is introduced, which works for suffix trees as well.
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construction of aho corasick automaton in linear time for integer Alphabets
Combinatorial Pattern Matching, 2005Co-Authors: Shiri Dori, Gad M LandauAbstract:We present a new simple algorithm that constructs an Aho Corasick automaton for a set of patterns, P, of total length n, in O(n) time and space for integer Alphabets. Processing a text of size m over an Alphabet Σ with the automaton costs $O(m \log \left|\Sigma\right| + k)$, where there are k occurrences of patterns in the text.
Hiroshi Fujisaki - One of the best experts on this subject based on the ideXlab platform.
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countably infinite multilevel source polarization for non stationary erasure distributions
International Symposium on Information Theory, 2019Co-Authors: Yuta Sakai, Ken-ichi Iwata, Hiroshi FujisakiAbstract:Polar transforms are central operations in the study of polar codes. This paper examines polar transforms for non-stationary memoryless sources on possibly infinite source Alphabets. This is the first attempt of source polarization analysis over infinite Alphabets. The source Alphabet is defined to be a Polish group, and we handle the Arikan-style two-by-two polar transform based on the group. Defining erasure distributions based on the normal subgroup structure, we give recursive formulas of the polar transform for erasure distributions. We then show concrete examples of multilevel source polarization with countably infinite levels when the group is locally cyclic. We derive this result via elementary techniques in lattice theory.
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Countably Infinite Multilevel Source Polarization for Non-Stationary Erasure Distributions.
arXiv: Information Theory, 2019Co-Authors: Yuta Sakai, Ken-ichi Iwata, Hiroshi FujisakiAbstract:Polar transforms are central operations in the study of polar codes. This paper examines polar transforms for non-stationary memoryless sources on possibly infinite source Alphabets. This is the first attempt of source polarization analysis over infinite Alphabets. The source Alphabet is defined to be a Polish group, and we handle the Ar{\i}kan-style two-by-two polar transform based on the group. Defining erasure distributions based on the normal subgroup structure, we give recursive formulas of the polar transform for our proposed erasure distributions. As a result, the recursive formulas lead to concrete examples of multilevel source polarization with countably infinite levels when the group is locally cyclic. We derive this result via elementary techniques in lattice theory.
