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## Probability Propagation and Iterative Decoding (1996)

Venue: | Proceedings of the 34th Allerton Conference on Communications, Control and Computing |

Citations: | 19 - 9 self |

### Citations

8903 |
Probabilistic reasoning in intelligent systems: networks of plausible inference.
- Pearl
- 1988
(Show Context)
Citation Context ... techniques appears to be \probability propagation in graphical models," a technique developed in the past decade in the expert systems literature, most notably by Pearl and his co-workers (see e=-=.g., [1]-=-). Interestingly, Gallager's algorithm [2] for decoding low-density parity-check codes is an example of an iterative decoding algorithm that also is essentially an instance of \probability propagation... |

1776 | Near Shannon limit error-correcting coding and decoding: turbo codes,” Pruc
- Berrou, Glavieux, et al.
(Show Context)
Citation Context ...sed of constituent codes, each of which can be decoded tractably by probability propagation on a subgraph of the graph that describes the compound code. Examples of compound codes include turbo-codes =-=[5], ser-=-ially concatenated convolutional codes [6], frame-oriented turbo-codes [7], low-density parity-check codes [2], and iteratively decoded product codes [8, 9]. 2 A Simple \Spy Network" We now give ... |

1366 | Low-density parity-check codes,”
- Gallager
- 1962
(Show Context)
Citation Context ...pagation in graphical models," a technique developed in the past decade in the expert systems literature, most notably by Pearl and his co-workers (see e.g., [1]). Interestingly, Gallager's algor=-=ithm [2] for -=-decoding low-density parity-check codes is an example of an iterative decoding algorithm that also is essentially an instance of \probability propagation" published over 30 years ago, but mostly ... |

640 |
A recursive approach to low complexity codes,”
- Tanner
- 1981
(Show Context)
Citation Context ...ariables have even parity and 0 otherwise. The MRF places equal probability on all codewords that satisfy even parity in cliques q 1 , q 2 and q 3 . 3.2 Tanner Graphs Tanner graphs were introduced in =-=[11-=-] for the construction of good long error-correcting codes in terms of shorter codes. Our treatment follows the slightly dierent presentation of Wiberg, et. al. [3]. A Tanner graph is a bipartite grap... |

610 | Iterative Decoding of Binary Block and Convolutional Codes”,
- Hagenauer, Papke
- 1996
(Show Context)
Citation Context ...les of compound codes include turbo-codes [5], serially concatenated convolutional codes [6], frame-oriented turbo-codes [7], low-density parity-check codes [2], and iteratively decoded product codes =-=[8, 9]. 2 A-=- Simple \Spy Network" We now give a simple example of a distributed algorithm that computes a result via local message passing. This example, though simplistic, serves to illustrate many of the i... |

549 |
Statistical inference for probabilistic functions of finite state Markov chains. The annals of mathematical statistics,
- Baum, Petrie
- 1966
(Show Context)
Citation Context ...creasing the complexity of the state variables. The forward-backward algorithm (a.k.a. the \BCJR algorithm") for computing P (u k jy) for such a Markov-type model wassrst developed by Baum and Pe=-=trie [12]-=-. It turns out that this algorithm is identical to the algorithm that results when probability propagation is applied to the corresponding Bayesian network. A simpler, nonsystematic version of the net... |

239 |
Concatenated Codes
- Forney
- 1966
(Show Context)
Citation Context ...in uses a permuted version of the information sequence. A serially concatenated convolutional compound code [6] is shown in Fig. 6b. This system is essentially the same as Forney's concatenated codes =-=[13]-=-, except that a convolutional code is used for both the inner and outer codes, instead of the more popular Reed-Solomon outer code. A frame-oriented turbo-code [7] is shown in Fig. 6c. This code was d... |

197 |
Markov random fields and their applications,
- Kindermann, Snell
- 1980
(Show Context)
Citation Context ... codes, and are the key to \probability propagation" and iterative decoding. 3.1 Markov Random Fields Markov randomselds (MRFs) are graphical models based on undirected graphs (see textbook refer=-=ence [10-=-]). If n(v i ) are the neighbors of vertex v i , then the the distribution P () must satisfy the local Markov property: p(v i jfv j g 8j 6=i ) = p(v i jn(v i )): (1) In a MRF, each variable v i is ind... |

122 |
Codes and iterative decoding on general graphs”,
- Wiberg, Loeliger, et al.
- 1995
(Show Context)
Citation Context ...iterative decoding algorithm that also is essentially an instance of \probability propagation" published over 30 years ago, but mostly forgotten in the interim. Recently, Wiberg, Loeliger and Kot=-=ter [3]-=- have refocussed attention on graphical models for codes. They show that such graphical models provide a natural setting in which to describe and study iterative decoding techniques, much as the code ... |

44 |
Iterative decoding of serially concatenated convolutional codes
- Benedetto, Montorsi
- 1996
(Show Context)
Citation Context ...decoded tractably by probability propagation on a subgraph of the graph that describes the compound code. Examples of compound codes include turbo-codes [5], serially concatenated convolutional codes =-=[6], fra-=-me-oriented turbo-codes [7], low-density parity-check codes [2], and iteratively decoded product codes [8, 9]. 2 A Simple \Spy Network" We now give a simple example of a distributed algorithm tha... |

3 |
Good codes based on very sparse matrices." Submitted to
- MacKay
- 1997
(Show Context)
Citation Context ...ng techniques, much as the code trellis is an appropriate model in which to describe and study \conventional" maximum-likelihood soft-decision decoding using the Viterbi algorithm. MacKay and Nea=-=l in [4] have-=- also observed that iterative decoding is also essentially an instance of probability or \belief" propagation in a graphical model. To motivate the general computational paradigm, wesrst present ... |

2 |
Frame-oriented convolutional turbo-codes
- Berrou, Jezequel
- 1996
(Show Context)
Citation Context ... propagation on a subgraph of the graph that describes the compound code. Examples of compound codes include turbo-codes [5], serially concatenated convolutional codes [6], frame-oriented turbo-codes =-=[7], low-=--density parity-check codes [2], and iteratively decoded product codes [8, 9]. 2 A Simple \Spy Network" We now give a simple example of a distributed algorithm that computes a result via local me... |

1 |
Separable MAP ` for the decoding of product and concatenated codes
- Lodge, Young, et al.
- 1993
(Show Context)
Citation Context ...les of compound codes include turbo-codes [5], serially concatenated convolutional codes [6], frame-oriented turbo-codes [7], low-density parity-check codes [2], and iteratively decoded product codes =-=[8, 9]. 2 A-=- Simple \Spy Network" We now give a simple example of a distributed algorithm that computes a result via local message passing. This example, though simplistic, serves to illustrate many of the i... |