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Probl. Peredachi Inf., 2008, Volume 44, Issue 1, Pages 3–14 (Mi ppi1262)  

This article is cited in 19 scientific papers (total in 19 papers)

Coding Theory

Modeling Hexagonal Constellations with Eisenstein–Jacobi Graphs

C. Martineza, E. Stafforda, R. Beividea, È. M. Gabidulinb

a Universidad de Cantabria, Santander, Spain
b Moscow Institute of Physics and Technology

Abstract: A set of signal points is called a hexagonal constellation if it is possible to define a metric so that each point has exactly six neighbors at distance 1 from it. As sets of signal points, quotient rings of the ring of Eisenstein–Jacobi integers are considered. For each quotient ring, the corresponding graph is defined. In turn, the distance between two points of a quotient ring is defined as the corresponding graph distance. Under certain restrictions, a quotient ring is a hexagonal constellation with respect to this metric. For the considered hexagonal constellations, some classes of perfect codes are known. Using graphs leads to a new way of constructing these codes based on solving a standard graph-theoretic problem of finding a perfect dominating set. Also, a relation between the proposed metric and the well-known Lee metric is considered.

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English version:
Problems of Information Transmission, 2008, 44:1, 1–11

Bibliographic databases:

UDC: 621.391.15
Received: 18.10.2006
Revised: 01.11.2007

Citation: C. Martinez, E. Stafford, R. Beivide, È. M. Gabidulin, “Modeling Hexagonal Constellations with Eisenstein–Jacobi Graphs”, Probl. Peredachi Inf., 44:1 (2008), 3–14; Problems Inform. Transmission, 44:1 (2008), 1–11

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Martinez C., Stafford E., Beivide R., Camarero C., Vallejo F., Gabidulin E., “Graph-based metrics over QAM constellations”, 2008 IEEE International Symposium on Information Theory Proceedings, 2008, 2494–2498  crossref  isi
    2. Zhu Daiyin, Wang Ling, Yu Yusheng, Tao Qingnian, Zhu Zhaoda, “Robust ISAR range alignment via minimizing the entropy of the average range profile”, IEEE Geoscience and Remote Sensing Letters, 6:2 (2009), 204–208  crossref  adsnasa  isi
    3. Acuna U.M., Jancovski N., Kennelly E.J., “Polyisoprenylated benzophenones from clusiaceae: potential drugs and lead compounds”, Current Topics in Medicinal Chemistry, 9:16 (2009), 1560–1580  crossref  isi
    4. Muñoz-Ferreras J.M., Pérez-Martnnez F., “Pitch estimation for non-cooperative maritime targets in ISAR scenarios”, IET Radar Sonar Navig., 3:5 (2009), 521–529  crossref  isi
    5. Martinez C., Beivide R., Gabidulin E.M., “Perfect codes from Cayley graphs over Lipschitz integers”, IEEE Trans. Inform. Theory, 55:8 (2009), 3552–3562  crossref  mathscinet  isi  elib
    6. Yeh Chun-Mao, Xu Jia, Peng Ying-Ning, Wang Xiu-Tan, “Cross-range scaling for ISAR based on image rotation correlation”, IEEE Geoscience and Remote Sensing Letters, 6:3 (2009), 597–601  crossref  adsnasa  isi
    7. Lv Xiaolei, Xing Mengdao, Wan Chunru, Zhang Shouhong, “ISAR imaging of maneuvering targets based on the range centroid doppler technique”, IEEE Trans. Image Process., 19:1 (2010), 141–153  crossref  mathscinet  isi
    8. E. A. Monakhova, “Multiplikativnye tsirkulyantnye seti”, Diskretn. analiz i issled. oper., 17:5 (2010), 56–66  mathnet  mathscinet  zmath
    9. Flahive M., Bose B., “The topology of Gaussian and Eisenstein-Jacobi interconnection networks”, IEEE Transactions on Parallel and Distributed Systems, 21:8 (2010), 1132–1142  crossref  isi
    10. E. A. Monakhova, “Strukturnye i kommunikativnye svoistva tsirkulyantnykh setei”, PDM, 2011, no. 3(13), 92–115  mathnet
    11. Song K.-T., Chen Y.-W., “A Design for integrated face and facial expression recognition”, Iecon 2011: 37th Annual Conference on IEEE Industrial Electronics Society, IEEE Industrial Electronics Society, 2011, 4306–4311  isi
    12. Albader B., Bose B., Flahive M., “Efficient communication algorithms in hexagonal mesh interconnection networks”, IEEE Transactions on Parallel and Distributed Systems, 23:1 (2012), 69–77  crossref  isi
    13. Flahive M., Bose B., “On Resource Placement in Gaussian and Ej Interconnection Networks”, IEEE Trans. Comput., 62:3 (2013), 623–626  crossref  mathscinet  isi  elib
    14. Hussain Z.A., Bose B., Al-Dhelaan A., “Edge Disjoint Hamiltonian Cycles in Eisenstein-Jacobi Networks”, J. Parallel Distrib. Comput., 86 (2015), 62–70  crossref  isi  elib
    15. Touzene A., “All-To-All Broadcast in Hexagonal Torus Networks on-Chip”, IEEE Trans. Parallel Distrib. Syst., 26:9 (2015), 2410–2420  crossref  isi  elib
    16. Touzene A., “on All-To-All Broadcast in Dense Gaussian Network on-Chip”, IEEE Trans. Parallel Distrib. Syst., 26:4 (2015), 1085–1095  crossref  isi  elib
    17. Stafford E., Bosque J.L., Martinez C., Vallejo F., Beivide R., Camarero C., Castillo E., “Assessing the Suitability of King Topologies For Interconnection Networks”, IEEE Trans. Parallel Distrib. Syst., 27:3 (2016), 682–694  crossref  isi  elib
    18. Hussain Z., Shamaei A., “Higher Dimensional Eisenstein-Jacobi Networks”, J. Parallel Distrib. Comput., 102 (2017), 91–102  crossref  isi  scopus
    19. Hussain Z., “An Improved One-to-All Broadcasting in Higher Dimensional Eisenstein-Jacobi Networks”, 2018 26Th Euromicro International Conference on Parallel, Distributed, and Network-Based Processing (Pdp 2018), Euromicro Conference on Parallel Distributed and Network-Based Processing, eds. Merelli I., Lio P., Kotenko I., IEEE, 2018, 34–44  crossref  isi  scopus
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