Analysis of Connections Between Pseudocodewords

Axvig, Nathan; Dreher, Deanna; Morrison, Katherine; Psota, Eric T.; Pérez, Lance C.; Walker, Judy L.

doi:10.1109/tit.2009.2025529

Cited by 19 publications

(20 citation statements)

References 18 publications

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“…Thus, if one can fully understand configurations on the universal cover and devise a decoder on the universal cover that simultaneously extends both graph cover decoding [10] and min-sum decoding, then one can possibly use the theory of graph covers and graph cover pseudocodewords to better understand computation trees and computation tree pseudocodewords, and, ultimately, the behavior of min-sum decoding. This is precisely what is attempted by the authors and their collaborators in [2]- [4].…”

Section: Introductionsupporting

confidence: 67%

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Connections between computation trees and graph covers

Dreher

Walker

2009

2009 Information Theory and Applications Workshop

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Section: Introductionsupporting

confidence: 67%

“…The authors and their collaborators have shown [1] that with a very basic restriction on our Tanner graph, every normalized graph cover pseudocodeword has a connected realization. The restriction on the Tanner graph is given by…”

Section: Definition 14 (Wibergmentioning

confidence: 99%

Connections between computation trees and graph covers

Dreher

Walker

2009

2009 Information Theory and Applications Workshop

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“…The iterative message passing algorithm cannot overcome these weaknesses and gets trapped in error patterns which are easily identifiable as erroneous (in LDPC codes), and are thus not valid codewords, but difficult to overcome or correct [1], [2]. These weaknesses were termed trapping sets by Richardson in [3], a summary definition for the patterns on which the message passing algorithm fails for Gaussian channels.…”

Section: Discussionmentioning

confidence: 99%

“…This code has been extensively analyzed. It has a low error floor that appears at E b /N 0 ≈ 5dB at a BER of 10 −12 , that is too low to be efficiently explored using conventional simulations 1 . ( ( ( ( ( ( ( ( ( 4 4 4 A A A A A A A A A G G G G G G G G G G G G G T T T T T T T T T T T T T T w w w w w w w w w w w w w w w w w w w A A A A A A A A A A A A w w w w w w w w w w w w w w w w w w w w w w w w T T T T T T T T T T T T T T !…”

Section: Ldpc Codes On the Gaussian Channelmentioning

confidence: 99%

On the Dynamics of the Error Floor Behavior in (Regular) LDPC Codes

Schlegel

Zhang

2010

IEEE Trans. Inform. Theory

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Abstract-It is shown that dominant trapping sets of regular LDPC codes, so called absorption sets, undergo a two-phased dynamic behavior in the iterative message-passing decoding algorithm. Using a linear dynamic model for the iteration behavior of these sets, it is shown that they undergo an initial geometric growth phase which stabilizes in a final bit-flipping behavior where the algorithm reaches a fixed point. This analysis is shown to lead to very accurate numerical calculations of the error floor bit error rates down to error rates that are inaccessible by simulation. The topology of the dominant absorption sets of an example code, the IEEE 802.3an (2048, 1723) regular LDPC code, are identified and tabulated using topological relationships in combination with search algorithms.Index Terms-absorption sets, error floor, Low-Density ParityCheck codes. I. SUMMARYT HE error floor in modern graph-based error control codes such as low-density parity-check codes is caused by inherent structural weaknesses in the code's interconnect network. The iterative message passing algorithm cannot overcome these weaknesses and gets trapped in error patterns which are easily identifiable as erroneous (in LDPC codes), and are thus not valid codewords, but difficult to overcome or correct [1], [2]. These weaknesses were termed trapping sets by Richardson in [3], a summary definition for the patterns on which the message passing algorithm fails for Gaussian channels. These trapping sets are dependent on the code, the channel used, and to a lesser degree also on the details of the decoding algorithm. Prior work in identifying the weaknesses of LDPC codes on erasure channels led to the definition of stopping sets in [4]. Stopping sets, being the weaknesses of LDPC codes on erasure channels, also play a role on Gaussian channels, but are not typically the dominant error mechanisms. In [5] the authors define absorption sets, which are the subgraphs of the code graph on which the Gallager bit-flipping decoding algorithms fail for binary symmetric channels. The authors observed that these absorption sets also show up as the dominant trapping sets in certain structured LDPC codes. In [6] they devise post-processing methods to reduce the effects of these absorption sets and lower the error floor of the codes in question.C. Schlegel and S. Zhang are with the High Capacity Digital Communications Laboratory (HCDC), Electrical and Computer Engineering Department, University of Alberta, Edmonton AB, T6G 2V4, CANADA (e-mail: {schlegel, szhang4}@ece.ualberta.ca).In this paper we present a linear algebraic approach to the dynamic behavior of absorption sets. We show that these sets follow a geometric growth phase during early iterations where messages inside the absorption set grow towards a largest eigenvector which characterizes the absorption set. The seemingly erratic behavior of the messages at early iterations is due to the decreasing influence of lesser eigenvectors. We define the gain of an absorption set and show how it affects the inf...

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“…19 To see this, let the active part of a pseudo-codeword be defined as the set of bit nodes corresponding to the support of the pseudo-codeword, along 19 Here and in the following, pseudo-codewords refer to pseudo-codewords as they appear in linear programming (LP) decoding [54], [55] and in the graph-cover-based analysis of message-passing iterative decoding in [22], [23]. For other notions of pseudo-codewords, in particular computation tree pseudo-codewords, we refer to the discussion in [56]. with the adjacent edges and check nodes.…”

Section: A Graph-cycle Analysismentioning

confidence: 99%

Deriving Good LDPC Convolutional Codes from LDPC Block Codes

Pusane

Smarandache

Vontobel

et al. 2011

IEEE Trans. Inform. Theory

120

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Abstract-Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper we discuss several graph-cover-based methods for deriving families of timeinvariant and time-varying LDPC convolutional codes from LDPC block codes and show how earlier proposed LDPC convolutional code constructions can be presented within this framework.Some of the constructed convolutional codes significantly outperform the underlying LDPC block codes. We investigate some possible reasons for this "convolutional gain," and we also discuss the -mostly moderate -decoder cost increase that is incurred by going from LDPC block to LDPC convolutional codes.

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Analysis of Connections Between Pseudocodewords

Cited by 19 publications

References 18 publications

Connections between computation trees and graph covers

Connections between computation trees and graph covers

On the Dynamics of the Error Floor Behavior in (Regular) LDPC Codes

Deriving Good LDPC Convolutional Codes from LDPC Block Codes

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