nach oben

Journal of Applied Mathematics and Computing

Erschienen in:

08.02.2018 | Original Research

Effect of one redundant parity-check equation on the stopping distance

verfasst von: Zahra Ferdosi, Farhad Rahmati, Mohammad H. Tadayon

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2019

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, we attempt to correct remaining erasures in the case of an iterative decoding failure. Stopping set plays the most important role in the code’s performance over binary erasure channel (BEC) under iterative decoding. The elimination of the stopping sets is one of the techniques that can be applied on the parity-check matrix of the codes for improving their performance in the low BER region. Although the problem is well-studied and many solutions are already known, a new low-complexity algorithm would be an important contribution. We present a modified decoding algorithm for array LDPC codes C(m, q) over BEC with the column weight m and row weight q where \(m<q\). Our proposed technique provides a step towards improving the decoding results and is compatible with practical implementation constraints. Our results substantiate theoretical analysis for array LDPC codes.

Vorheriger Artikel Local exponential stabilization for a class of uncertain nonlinear impulsive periodic switched systems with norm-bounded input

Nächster Artikel Rough fuzzy digraphs with application

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

The problem of creating a list of possible stopping sets can be related to the coloring problems in graph theory. Vasić et al. [14] proposed the trapping set ontology, which is a hierarchy of trapping sets that exploits the topological relations, and can he utilized for code construction or decoder design. As known in [15], a stopping set is legitimately a trapping set when the underlying channel model is the BEC and the belief propagation decoder is employed.

Every non-zero rows in the sub-matrix corresponding to a stopping set of size t is known as an unsatisfied row if the associated equation is not satisfied during the iterative decoding process.

Without loss of generality we start with the first erasure, however, it is possible to start with any arbitrary erased bit.

Fan, J.L.: Array codes as low-density parity-check codes. In: Proceedings of the 2nd International Symposium on Turbo Codes and Related Topics, Brest, France (2000)

Esmaeili, M., Tadayon, M.H., Gulliver, T.A.: More on the Stopping and Minimum Distances of Array Codes. IEEE Trans. Commun. 59(3), 750–757 (2011)CrossRef

Rosnes, E., Ambroze, M.A., Tomlinson, M.: On the minimum/stopping distance of array low-density parity-check codes. IEEE Trans. Inf. Theory 60(9), 5204–5214 (2014)MathSciNetCrossRefMATH

Rosnes, E., Ytrehus, O.: An efficient algorithm to find all small-size stopping sets of low-density parity-check matrices. IEEE Trans. Inf. Theory 55(9), 4167–4178 (2009)MathSciNetCrossRefMATH

Di, C., Proietti, D., Telatar, I.E., Richardson, T.J., Urbanke, R.L.: Finite-length analysis of low-density parity-check codes on the binary erasure channel. IEEE Trans. Inf. Theory 48(6), 1570–1579 (2002)MathSciNetCrossRefMATH

Jaldn, J., Ottersten, B.: On the complexity of sphere decoding in digital communications. IEEE Trans. Signal Process. 53(4), 1474–1484 (2005)MathSciNetCrossRefMATH

Tasdighi, A., Banihashemi, A.H., Sadeghi, M.R.: Symmetrical constructions for regular girth-8 QC-LDPC codes. IEEE Trans. Commun. 65(1), 14–22 (2017)

Park, H., Hong, S., No, J.S., Shin, D.J.: Construction of high-rate regular quasi-cyclic LDPC codes based on cyclic difference families. IEEE Trans. Commun. 61(8), 3108–3113 (2013)CrossRef

Tasdighi, A., Sadeghi, M.R.: On advisability of designing short length QC-LDPC codes using perfect difference families. arXiv preprint arXiv:1701.06218 (2017)

10.

Baldi, M., Bianchi, M., Cancellieri, G., Chiaraluce, F., Kløve, T.: On the generator matrix of array LDPC codes. In: Proceedings of SoftCOM 2012, Split, Croatia, vol. 5 (2012)

11.

Axler, Sheldon Jay: Linear Algebra Done Right. Springer, New York (2014)MATH

12.

Tian, T., Jones, C., Villasenor, J.D., Wesel, R.D.: Construction of irregular LDPC codes with low error floors. In: IEEE International Conference on Communications, 2003. ICC’03, vol. 5, pp. 3125–3129 (2003)

13.

Pishro-Nik, H., Fekri, F.: On decoding of low-density parity-check codes over the binary erasure channel. IEEE Trans. Inf. Theory 50(3), 439–454 (2004)MathSciNetCrossRefMATH

14.

Vasić, B., Chilappagari, S.K., Nguyen, D.V., Planjery, S.K.: Trapping set ontology, In 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009, pp. 1–7. IEEE (2009)

15.

Wang, Chih-Chun, Kulkarni, Sanjeev R., Vincent Poor, H.: Finding all small error-prone substructures in LDPC codes. IEEE Trans. Inf. Theory 55(5), 1976–1999 (2009)MathSciNetCrossRefMATH

Titel: Effect of one redundant parity-check equation on the stopping distance
verfasst von: Zahra Ferdosi
Farhad Rahmati
Mohammad H. Tadayon
Publikationsdatum: 08.02.2018
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2019
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-018-1170-3

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 1-2/2019

Local convergence analysis for Chebyshev’s method

Monotone iterative technique for a coupled system of nonlinear Hadamard fractional differential equations

Parameter-uniform numerical method for singularly perturbed 2D delay parabolic convection–diffusion problems on Shishkin mesh

Global stability of an age-structured model for pathogen–immune interaction

Rankings and operations for interval type-2 fuzzy numbers: a review and some new methods

Reconstruction of sparse-view tomography via preconditioned Radon sensing matrix