Codes on graphs: normal realizations

By von Madeleine Leidheiser. 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060), 2000

677 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/74a8959a5971b56dcda05cdde57b724906bf28aa

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Citations in the corpus

A performance comparison of polar codes and Reed-Muller codes (2008, methodology): “Using Forney’s factor graph representation for RM codes, it is easy to see that the encoding and BP-decoding complexities of RM and polar codes are both O ( N log N ) where N is the code block-length.”
Polar codes are optimal for lossy source coding (2009, methodology): “A similar representation was considered for decoding of Reed-Muller codes by Forney in [18].”
The art of error correcting coding (2002, methodology): “Because for most practical codes the Tanner graph has relative short cycles (lengths 4 and 6), convergence of the IBP decoding algorithm is either not guaranteed or is slow (Forney 2001; Kschischang et al. 2001; Richardson et al. 2001).”
Least Squares and Kalman Filtering on Forney Graphs (2002, positive): “In [2], Forney introduced a variation of factor graphs with a number of attractive properties.”
IEEE Signal Processing Magazine (2008, methodology): “The following theorem (due to Kschischang) is a special case of a sweepingly general result on the Fourier transform of an FFG [13].”
Constructing free-energy approximations and generalized belief propagation algorithms (2005, methodology): “We point the interested reader to [22]–[28].”
Channel coding: The road to channel capacity (2006, background): “Subsequently Forney proposed a refinement of factor graphs, namely “normal graphs” [128].”
The Factor Graph Approach to Model-Based Signal Processing (2007, methodology): “We review some key results of Forney [ 43 ] and adapt (and simplify) them to the setting of the present paper.”
An introduction to factor graphs (2004, methodology): “(In the main ideas, we will follow [24] and [13], but we will also adopt some details of notation from [27] and [42].”
Cooperative Localization in Wireless Networks (2009, background): “5 We focus on Forney-style FGs, also known as normal graphs [ 95 ].”
On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit (2001, background): “The message update rule for check nodes can be obtained by observing the duality between variable and check nodes and the resulting Fourier transform relationship [10].”
Low-density parity-check codes based on finite geometries: A rediscovery and new results (2001, background): “These short cycles, especially cycles of length , make successive decoding iterations highly correlated and hence severely limit the decoding performance [3], [10], [11], [20], [33]–[35].”
Factor Graphs for Robot Perception (2017, background): “[199, 198] rediscovered Tanner’s work and extended it to include (hidden) state variables [66].”
Factor graphs and the sum-product algorithm (2001, background): “Indeed, the “cut-set bound” of [31] (see also [8]) strongly motivates the study of graph representations with cycles.”
Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation (2001, methodology): “Figs. 1 and 2 show message flows through a variable node and a check node, respectively, where we use normal realizations [ 22 ] of variable and check nodes, which be-”
Belief Propagation, Dykstra's Algorithm, and Iterated Information Projections (2010, background): “if for any (12) These sets of probability distributions are defined in the same spirit of interpreting variable nodes in a factor graph as equality constraints as introduced in the concept of normal graphs in [45] as depicted in Fig.”