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Codes and Graphs
 In STACS 2000 (invited talk), LNCS No. 1770
, 2000
"... . In this paper, I will give a brief introduction to the theory of lowdensity paritycheck codes, and their decoding. I will emphasize the case of correcting erasures as it is still the best understood and most accessible case. At the end of the paper, I will also describe more recent developme ..."
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Cited by 2 (0 self)
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developments. 1 Introduction In this paper, I want to give a brief introduction to the theory of lowdensity paritycheck codes, or LDPC codes, for short. These codes were first introduced in the early 1960's by Gallager in his PhDthesis [6]. They are built using sparse bipartite graphs in a manner
Source Coding and Graph Entropies
 IEEE Trans. Inform. Theory
, 1995
"... A sender wants to accurately convey information to a receiver who has some, possibly related, data. We study the expected number of bits the sender must transmit for one and for multiple instances in two communication scenarios and relate this number to the chromatic and Korner entropies of a natura ..."
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Cited by 57 (0 self)
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naturally defined graph. 1 Introduction We study the expected number of bits a sender must transmit to convey information to a receiver who has some, possibly related, data. We consider single and multipleinstances of two related scenarios. This section describes the two scenarios and the results
Network codes as codes on graphs
 in Conference on Information Sciences and Systems (CISS
, 2004
"... Abstract—This paper points out connections between linear network coding and linear system theory. In particular, a network code is interpreted as a state space realization of a network behavior that implements a desired set of network connections. A reversibility theorem is derived for network co ..."
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Abstract—This paper points out connections between linear network coding and linear system theory. In particular, a network code is interpreted as a state space realization of a network behavior that implements a desired set of network connections. A reversibility theorem is derived for network
Algebraic Graph Theory
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 868 (12 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Iterative quantization using codes on graphs
 in Proc. Allerton Conf. Comm., Control, and Computing
, 2003
"... We study codes on graphs combined with an iterative message passing algorithm for quantization. Specifically, we consider the binary erasure quantization (BEQ) problem which is the dual of the binary erasure channel (BEC) coding problem. We show that duals of capacity achieving codes for the BEC yie ..."
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Cited by 49 (14 self)
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We study codes on graphs combined with an iterative message passing algorithm for quantization. Specifically, we consider the binary erasure quantization (BEQ) problem which is the dual of the binary erasure channel (BEC) coding problem. We show that duals of capacity achieving codes for the BEC
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
On the Number of Errors Correctable with Codes on Graphs
"... Abstract—We estimate the number of errors corrected by two different ensembles of codes on graphs (generalized LDPC codes), namely codes on regular bipartite graphs and their extension to hypergraphs. I. ..."
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Abstract—We estimate the number of errors corrected by two different ensembles of codes on graphs (generalized LDPC codes), namely codes on regular bipartite graphs and their extension to hypergraphs. I.
Interprocedural Slicing Using Dependence Graphs
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1990
"... ... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends previou ..."
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Cited by 822 (85 self)
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... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends
Results 1  10
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565,074