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Which Codes Have CycleFree Tanner Graphs?
 IEEE TRANS. INFORM. THEORY
, 1999
"... If a linear block code of length has a Tanner graph without cycles, then maximumlikelihood softdecision decoding of can be achieved in time O(n ). However, we show that cyclefree Tanner graphs cannot support good codes. Specifically, let be an (n; k; d) linear code of rate R = k=n that can ..."
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Cited by 44 (2 self)
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If a linear block code of length has a Tanner graph without cycles, then maximumlikelihood softdecision decoding of can be achieved in time O(n ). However, we show that cyclefree Tanner graphs cannot support good codes. Specifically, let be an (n; k; d) linear code of rate R = k=n that can
Which codes have 4cyclefree Tanner graphs
 IEEE Trans. Information Theory
, 2006
"... Abstract — Let C be an [n, k, d] binary linear code with rate R = k/n and dual C ⊥. In this work, it is shown that C can be represented by a 4cyclefree Tanner graph only if: pd ⊥ ≤ $r np(p − 1) + n2 ..."
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Cited by 10 (1 self)
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Abstract — Let C be an [n, k, d] binary linear code with rate R = k/n and dual C ⊥. In this work, it is shown that C can be represented by a 4cyclefree Tanner graph only if: pd ⊥ ≤ $r np(p − 1) + n2
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"... Which codes have 4cyclefree Tanner graphs? (English summary) ..."
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"... Abstract — Let C be an [n, k, d] binary linear code with rate R = k/n and dual C ⊥. In this correspondence, it is shown that C can be represented by a 4cyclefree Tanner graph only if: pd ⊥ ≤ ..."
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Abstract — Let C be an [n, k, d] binary linear code with rate R = k/n and dual C ⊥. In this correspondence, it is shown that C can be represented by a 4cyclefree Tanner graph only if: pd ⊥ ≤
Codes and Decoding on General Graphs
, 1996
"... Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding algorithm ..."
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Cited by 359 (1 self)
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is replaced by an arbitrary graph, the "Tanner graph". With cyclefree Tanner graphs, the resulting decoding algorithms (e.g., Viterbi decoding) are maximumlikelihood but suffer from an exponentially increasing complexity. Iterative decoding occurs when the Tanner graph has cycles (e.g., turbo
Tanner graphs for group block codes and lattices: construction and complexity
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—We develop a Tanner graph (TG) construction for an Abelian group block code with arbitrary alphabets at different coordinates, an important application of which is the representation of the label code of a lattice. The construction is based on the modular linear constraints imposed on the c ..."
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Cited by 3 (0 self)
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lattices, the minimal label codes which achieve the lower bounds cannot be supported by cyclefree Tanner graphs. Index Terms—Dual code, generalized Construction A, group
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 1786 (70 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
Constructing Free Energy Approximations and Generalized Belief Propagation Algorithms
 IEEE Transactions on Information Theory
, 2005
"... Important inference problems in statistical physics, computer vision, errorcorrecting coding theory, and artificial intelligence can all be reformulated as the computation of marginal probabilities on factor graphs. The belief propagation (BP) algorithm is an efficient way to solve these problems t ..."
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Cited by 585 (13 self)
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that is exact when the factor graph is a tree, but only approximate when the factor graph has cycles. We show that BP fixed points correspond to the stationary points of the Bethe approximation of the free energy for a factor graph. We explain how to obtain regionbased free energy approximations that improve
Conditionally CycleFree Generalized Tanner Graphs: Theory and Application to HighRate Serially Concatenated Codes
, 2007
"... ... studied by a number of authors under the rubric of generalized paritycheck matrices. This work considers the conditioning of binary hidden variables in such models in order to break all cycles and thus derive optimal softin softout (SISO) decoding algorithms. Conditionally cyclefree generali ..."
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Cited by 2 (0 self)
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... studied by a number of authors under the rubric of generalized paritycheck matrices. This work considers the conditioning of binary hidden variables in such models in order to break all cycles and thus derive optimal softin softout (SISO) decoding algorithms. Conditionally cyclefree
Conditionally CycleFree Generalized Tanner Graphs: Theory and Application to HighRate Serially Concatenated Codes
, 2006
"... Abstract — Generalized Tanner graphs have been implicitly studied by a number of authors under the rubric of generalized paritycheck matrices. This work considers the conditioning of binary hidden variables in such models in order to break all cycles and thus derive optimal softin softout (SISO) ..."
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) decoding algorithms. Conditionally cyclefree generalized Tanner graphs are shown to imply optimal SISO decoding algorithms for the first order ReedMuller codes and their duals the extended Hamming codes which are substantially less complex than conventional bitlevel trellis decoding. The study of low
Results 1  10
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