The Experts below are selected from a list of 93 Experts worldwide ranked by ideXlab platform
Kumar, Vijay P - One of the best experts on this subject based on the ideXlab platform.
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Codes with Locality for Two Erasures
IEEE, 2015Co-Authors: Prakash N., Kumar, Vijay PAbstract:In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, Parity-Check computations. By a local Parity-Check computation, we mean recovery via a single Parity-Check Equation associated with small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan et al, in which recovery from a single erasure is considered. By studying the generalized Hamming weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Turan graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from 2 erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case
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Optimal Linear Codes with a Local-Error-Correction Property
IEEE, 2012Co-Authors: Prakash N., Kamath, Govinda M., Kumar, Vijay PAbstract:Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a Parity-Check Equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' Parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local Parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code
Mohammad Hesam Tadayon - One of the best experts on this subject based on the ideXlab platform.
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effect of one redundant Parity Check Equation on the stopping distance
Journal of Applied Mathematics and Computing, 2019Co-Authors: Zahra Ferdosi, Farhad Rahmati, Mohammad Hesam TadayonAbstract:In this paper, we attempt to correct remaining erasures in the case of an iterative decoding failure. Stopping set plays the most important role in the code’s performance over binary erasure channel (BEC) under iterative decoding. The elimination of the stopping sets is one of the techniques that can be applied on the Parity-Check matrix of the codes for improving their performance in the low BER region. Although the problem is well-studied and many solutions are already known, a new low-complexity algorithm would be an important contribution. We present a modified decoding algorithm for array LDPC codes C(m, q) over BEC with the column weight m and row weight q where $$m
Prakash N. - One of the best experts on this subject based on the ideXlab platform.
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Codes with Locality for Two Erasures
IEEE, 2015Co-Authors: Prakash N., Kumar, Vijay PAbstract:In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, Parity-Check computations. By a local Parity-Check computation, we mean recovery via a single Parity-Check Equation associated with small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan et al, in which recovery from a single erasure is considered. By studying the generalized Hamming weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Turan graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from 2 erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case
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Codes with Locality for Two Erasures
2014Co-Authors: Prakash N., Kumar P. VijayAbstract:In this paper, we study codes with locality that can recover from two erasures via a sequence of two local, Parity-Check computations. By a local Parity-Check computation, we mean recovery via a single Parity-Check Equation associated to small Hamming weight. Earlier approaches considered recovery in parallel; the sequential approach allows us to potentially construct codes with improved minimum distance. These codes, which we refer to as locally 2-reconstructible codes, are a natural generalization along one direction, of codes with all-symbol locality introduced by Gopalan \textit{et al}, in which recovery from a single erasure is considered. By studying the Generalized Hamming Weights of the dual code, we derive upper bounds on the minimum distance of locally 2-reconstructible codes and provide constructions for a family of codes based on Tur\'an graphs, that are optimal with respect to this bound. The minimum distance bound derived here is universal in the sense that no code which permits all-symbol local recovery from $2$ erasures can have larger minimum distance regardless of approach adopted. Our approach also leads to a new bound on the minimum distance of codes with all-symbol locality for the single-erasure case.Comment: 14 pages, 3 figures, Updated for improved readabilit
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Optimal Linear Codes with a Local-Error-Correction Property
2012Co-Authors: Prakash N., Kamath, Govinda M., Kumar P. VijayAbstract:Motivated by applications to distributed storage, Gopalan \textit{et al} recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a Parity-Check Equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such "local" Parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local Parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.Comment: 13 pages, Shorter version submitted to ISIT 201
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Optimal Linear Codes with a Local-Error-Correction Property
IEEE, 2012Co-Authors: Prakash N., Kamath, Govinda M., Kumar, Vijay PAbstract:Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a Parity-Check Equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such ``local'' Parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local Parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code
Bellard Marion - One of the best experts on this subject based on the ideXlab platform.
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Influence du mapping sur la reconnaissance d'un système de communication
2014Co-Authors: Bellard Marion, Sendrier NicolasAbstract:Le contexte de cette thèse est la reconnaissance de systèmes de communication dans un contexte non coopératif. Nous nous intéressons au problème de la reconstruction de codes convolutifs et à la reconstruction du mapping (la bijection utilisée pour associer une séquence binaire à un signal modulé). Nous avons élaboré une nouvelle méthode statistique qui à partir d'une séquence binaire bruitée observée permet de détecter si une séquence binaire est codée par un codeur convolutif. Cette méthode consiste à former des blocs de séquence suffisamment grands pour contenir le support d'une équation de parité et à compter le nombre de blocs identiques. Elle a l'avantage de fournir la longueur du code utilisé lorsque le mapping est inconnu. Cette méthode peut également être utilisée pour reconstruire le dual d'un code convolutif lorsque le mapping est connu. Nous proposons par ailleurs un algorithme de reconnaissance de mapping basé sur le parcours de classes d'équivalences. Deux types de classes sont définies. Nous disposons d'un signal bruité partiellement démodulé (démodulé avec un mapping par défaut) et supposons que les données sont codées par un codeur convolutif. Nous utilisons la reconnaissance d'un tel code comme testeur et parcourons enfin les classes d'équivalences faisant apparaître une structure de codes convolutifs. Cette classification améliore la complexité de la recherche pour les petites constellations (4 et 8-PSK). Dans le cas des constellations 16 à 256-QAM l'algorithme est appliqué aux mappings Gray ou quasi-Gray. L'algorithme ne fournit pas un résultat unique mais il permet de trouver un ensemble de mappings possibles à partir de données bruitées.The context of this thesis is the recognition of communication systems in a non-cooperative context. We are interested in the convolutional code reconstruction problem and in the constellation labeling reconstruction (the mapping used to associate a binary sequence to a modulated signal). We have defined a new statistical method for detecting if a given binary sequence is a noisy convolutional code-word obtained from an unknown convolutional code. It consists in forming blocks of sequence which are big enough to contain the support of a Parity Check Equation and counting the number of blocks which are equal. It gives the length of the convolutional code without knowledge of the constellation labeling. This method can also be used to reconstruct the dual of a convolutional code when the constellation labeling is known. Moreover we propose a constellation labeling recognition algorithm using some equivalence classes. Two types of classes are defined: linear and affine. We observe a noisy signal which is partially demodulated (with a default labeling) and assume that the data are coded by a convolutional encoder. Thus we use the reconstruction of a code as a test and run through the classes which reveal a code structure. This classification improves the complexity of the search for small constellations (4-PSK and 8-PSK). In case of 16-QAM to 256-QAM constellations we apply the algorithm to Gray or quasi-Gray labelings. The algorithm does not give a unique result but it allows to find a small set of possible constellation labelings from noisy data.PARIS-JUSSIEU-Bib.électronique (751059901) / SudocSudocFranceF
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Influence du mapping sur la reconnaissance d'un système de communication
HAL CCSD, 2014Co-Authors: Bellard MarionAbstract:The context of this thesis is the recognition of communication systems in a non-cooperative context. We are interested in the convolutional code reconstruction problem and in the constellation labeling reconstruction (the mapping used to associate a binary sequence to a modulated signal). We have defined a new statistical method for detecting if a given binary sequence is a noisy convolutional code-word obtained from an unknown convolutional code. It consists in forming blocks of sequence which are big enough to contain the support of a Parity Check Equation and counting the number of blocks which are equal. It gives the length of the convolutional code without knowledge of the constellation labeling. This method can also be used to reconstruct the dual of a convolutional code when the constellation labeling is known. Moreover we propose a constellation labeling recognition algorithm using some equivalence classes. Two types of classes are defined: linear and affine. We observe a noisy signal which is partially demodulated (with a default labeling) and assume that the data are coded by a convolutional encoder. Thus we use the reconstruction of a code as a test and run through the classes which reveal a code structure. This classification improves the complexity of the search for small constellations (4-PSK and 8-PSK). In case of 16-QAM to 256-QAM constellations we apply the algorithm to Gray or quasi-Gray labelings. The algorithm does not give a unique result but it allows to find a small set of possible constellation labelings from noisy data.Le contexte de cette thèse est la reconnaissance de systèmes de communication dans un contexte non coopératif. Nous nous intéressons au problème de la reconstruction de codes convolutifs et à la reconstruction du mapping (la bijection utilisée pour associer une séquence binaire à un signal modulé). Nous avons élaboré une nouvelle méthode statistique qui à partir d'une séquence binaire bruitée observée permet de détecter si une séquence binaire est codée par un codeur convolutif. Cette méthode consiste à former des blocs de séquence suffisamment grands pour contenir le support d'une équation de parité et à compter le nombre de blocs identiques. Elle a l'avantage de fournir la longueur du code utilisé lorsque le mapping est inconnu. Cette méthode peut également être utilisée pour reconstruire le dual d'un code convolutif lorsque le mapping est connu. Nous proposons par ailleurs un algorithme de reconnaissance de mapping basé sur le parcours de classes d'équivalences. Deux types de classes sont définies. Nous disposons d'un signal bruité partiellement démodulé (démodulé avec un mapping par défaut) et supposons que les données sont codées par un codeur convolutif. Nous utilisons la reconnaissance d'un tel code comme testeur et parcourons enfin les classes d'équivalences faisant apparaître une structure de codes convolutifs. Cette classification améliore la complexité de la recherche pour les petites constellations (4 et 8-PSK). Dans le cas des constellations 16 à 256-QAM l'algorithme est appliqué aux mappings Gray ou quasi-Gray. L'algorithme ne fournit pas un résultat unique mais il permet de trouver un ensemble de mappings possibles à partir de données bruitées
Zahra Ferdosi - One of the best experts on this subject based on the ideXlab platform.
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effect of one redundant Parity Check Equation on the stopping distance
Journal of Applied Mathematics and Computing, 2019Co-Authors: Zahra Ferdosi, Farhad Rahmati, Mohammad Hesam TadayonAbstract:In this paper, we attempt to correct remaining erasures in the case of an iterative decoding failure. Stopping set plays the most important role in the code’s performance over binary erasure channel (BEC) under iterative decoding. The elimination of the stopping sets is one of the techniques that can be applied on the Parity-Check matrix of the codes for improving their performance in the low BER region. Although the problem is well-studied and many solutions are already known, a new low-complexity algorithm would be an important contribution. We present a modified decoding algorithm for array LDPC codes C(m, q) over BEC with the column weight m and row weight q where $$m