### Citations

8886 |
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
- Pearl
- 1988
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Citation Context ...of its performance are widely open and of great curiosity and research importance. Similar to the well-known Belief Propagation (BP) algorithm used in iterative decoding [6] and statistical inference =-=[7]-=-, SP operates by iteratively passing “messages” in a factor graph representation [8] of the problem instance, where each variable vertex corresponds to a variable whose value is to be decided and each... |

1787 | Factor graphs and the sum-product algorithm
- Kschischang, Frey, et al.
- 2001
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Citation Context ...imilar to the well-known Belief Propagation (BP) algorithm used in iterative decoding [6] and statistical inference [7], SP operates by iteratively passing “messages” in a factor graph representation =-=[8]-=- of the problem instance, where each variable vertex corresponds to a variable whose value is to be decided and each function vertex corresponds to a local constraint imposed on the variables. This ob... |

1773 | Near Shannon Limit Error-Correcting Coding and Decoding
- Berrou, Glavieux, et al.
- 1993
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Citation Context ...itnessed repeatedly in the history of communication research, for example, in understanding the Viterbi algorithm as a dynamic programming algorithm [9], in understanding the turbo decoding algorithm =-=[10]-=- as an instance of Belief Propagation [11], and in unifying the BCJR algorithm [12] and the Viterbi algorithm under the umbrella of the generalized distributive law [13], etc. These unified frameworks... |

1046 | The complexity of theorem-proving procedures - Cook - 1971 |

990 | The Viterbi algorithm
- Forney
- 1973
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Citation Context ...significance of questions of such a kind has been witnessed repeatedly in the history of communication research, for example, in understanding the Viterbi algorithm as a dynamic programming algorithm =-=[9]-=-, in understanding the turbo decoding algorithm [10] as an instance of Belief Propagation [11], and in unifying the BCJR algorithm [12] and the Viterbi algorithm under the umbrella of the generalized ... |

582 | Constructing free energy approximations and generalized belief propagation algorithms
- Yedidia, Freeman, et al.
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Citation Context ...ances of CSPs, whether or not SP or BP is considered as the choice of algorithms. 8 Further we note that the BP algorithm has been understood as a special case of Generalized Belief Propagation (GBP) =-=[20]-=-. In that perspective, BP may be derived from iterative minimization of the Bethe-approximation of the notion of free energy [20]. The framework of GBP allows a variety of ways (unified under the noti... |

572 | The capacity of low-density parity-check codes under message-passing decoding,” Information Theory
- Richardson, Urbanke
- 2001
(Show Context)
Citation Context ...and rigorous characterization of its performance are widely open and of great curiosity and research importance. Similar to the well-known Belief Propagation (BP) algorithm used in iterative decoding =-=[6]-=- and statistical inference [7], SP operates by iteratively passing “messages” in a factor graph representation [8] of the problem instance, where each variable vertex corresponds to a variable whose v... |

404 | Turbo decoding as an instance of pearl’s belief propagation algorithm
- McEliece, Mackay, et al.
- 1998
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Citation Context ...unication research, for example, in understanding the Viterbi algorithm as a dynamic programming algorithm [9], in understanding the turbo decoding algorithm [10] as an instance of Belief Propagation =-=[11]-=-, and in unifying the BCJR algorithm [12] and the Viterbi algorithm under the umbrella of the generalized distributive law [13], etc. These unified frameworks have on one hand provided additional insi... |

359 | The Generalized Distributive Law,”
- Aji, McEliece
- 2000
(Show Context)
Citation Context ...g the turbo decoding algorithm [10] as an instance of Belief Propagation [11], and in unifying the BCJR algorithm [12] and the Viterbi algorithm under the umbrella of the generalized distributive law =-=[13]-=-, etc. These unified frameworks have on one hand provided additional insights into the nature of the algorithms, and on the other hand allowed an easier access of the algorithm by much wider research ... |

195 | Analytic and algorithmic solution of random satisfiability problems, Science 297
- Mézard, Parisi, et al.
- 2002
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Citation Context ...sing. Index Terms Survey Propagation, Belief Propagation, constraint satisfaction, Markov random field, factor graph, message-passing algorithm, k-SAT, q-COL2 I. INTRODUCTION Survey Propagation (SP) =-=[1]-=- is a recent algorithmic breakthrough in solving certain hard families of constraint satisfaction problems (CSPs). Derived from statistical physics, SP first demonstrated its power in solving classic ... |

178 |
Codes on graphs: Normal realizations
- Forney
- 2001
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Citation Context ... now call weighted PTP. In [17], similar results are shown using a different MRF formalism, where (generalized) states are introduced and the MRF is represented by a Forney graph or normal realization=-=[18]-=-. Although in some sense, the normally realized MRF formalism of [17] is equivalent to the MRF of [15], the Forney-graph formalism in [17] makes the development cleaner and more transparent, and the e... |

66 | A new look at survey propagation and its generalizations
- Maneva, Mossel, et al.
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Citation Context ...ongs or to discover the unique algorithmic nature of SP. The first result reporting that SP is an instance of BP is the work of [14] in the context of k-3 SAT problems. This result is generalized in =-=[15]-=- to an extended version of SP for solving k-SAT problems. Briefly, the authors of [15] present a Markov Random Field (MRF) [16] formalism for k-SAT problems; a parameter, denoted by γ in this paper, i... |

50 |
Survey propagation as local equilibrium equations
- Braunstein, Zecchina
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Citation Context ...then motivated to seek a different algorithmic framework to which SP belongs or to discover the unique algorithmic nature of SP. The first result reporting that SP is an instance of BP is the work of =-=[14]-=- in the context of k-3 SAT problems. This result is generalized in [15] to an extended version of SP for solving k-SAT problems. Briefly, the authors of [15] present a Markov Random Field (MRF) [16] ... |

29 | Lossy source encoding via message-passing and decimation over generalized codewords of LDGM codes
- Wainwright, Maneva
- 2005
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Citation Context ...ph coloring (or q-COL) problems [3], as well as problems arising in communications and data compressions, some examples being coding for Blackwell channels [4] and quantization of Bernoulli sequences =-=[5]-=-. In all these cases, great successes have been demonstrated. Powerful as it appears, SP however largely remains as a heuristic algorithm to date, where analytic understanding of its algorithmic natur... |

25 |
Polynomial iterative algorithms for coloring and analyzing random graphs,
- Braunstein, Mulet, et al.
- 2003
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Citation Context ...hard regime, SP is shown to be the first efficient solver [1]. Recently, SP has also been applied to other CSPs, including other NPcomplete problem families such as graph coloring (or q-COL) problems =-=[3]-=-, as well as problems arising in communications and data compressions, some examples being coding for Blackwell channels [4] and quantization of Bernoulli sequences [5]. In all these cases, great succ... |

21 |
Constraint satisfaction by survey propagation
- Braunstein, Mezard, et al.
- 2003
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Citation Context ... is blurred in the binary special cases. Second, for non-weighted SP, we note that its formulation in the context of general CSPs primarily exists in the literature of statistical physics (see, e.g., =-=[19]-=-). Although its design recipe has been laid out for arbitrary CSPs, its exposition in statistical physics language has made it rather difficult for readers with primarily engineering or computer scien... |

8 | Coding for the blackwell channel: A survey propagation approach - Yu, Aleksic - 2005 |

4 |
On generalized survey propagation: normal realization and sum-product interpretation
- Tu, Mao, et al.
- 2006
(Show Context)
Citation Context ...another significance of this result is a conclusive answer to the titular question in that context, namely that SP is BP for the k-SAT problem family. This result was re-developed in our earlier work =-=[17]-=- where a simpler MRF formalism using Forney graphs [18] is presented and a more transparent reduction of BP messages to weighted SP messages is given. The objective of this paper is to answer the ques... |