Geometrically uniform codes in homogeneous spaces

• Grant number: 02/07473-7
• Support type: Research Projects - Thematic Grants
• Duration: July 01, 2003 - October 31, 2007
• Field of knowledge: Engineering - Electrical Engineering
• Principal Investigator: Sueli Irene Rodrigues Costa
• Grantee: Sueli Irene Rodrigues Costa
• Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Co-Principal Investigators: José Plínio de Oliveira Santos ; Reginaldo Palazzo Junior
• Associated grant(s): 04/08990-0 - On Goppa and srivastava codes over finite rings, AR.BR
• Associated scholarship(s): 07/06381-5 - Families of algebraic lattices and ideal lattices, BP.MS; 07/07478-2 - Algebraic and geometric analysis of algebraic and ideal lattices, BP.DD

Abstract

The present research proposal in Geometrically Uniform Codes in Homogeneous Spaces aims at incorporating geometrical structures in addition to the algebraic structures in the characterization of the encoding and decoding processes. It is by means of the incorporation of topological structures that the design of new digital transmission systems, quantization systems and coding & cryptography systems will be undertaken. The research proposal ex-tends research topics of a previous one supported by FAPESP under grant 95/04720-8, whose title is "Algebraic and geometric fundamentaIs of geometrically uniform codes" Sept. 1995 - Aug. 2000) supervised by Prof. Reginaldo Palazzo Júnior. The proponent research group has been working in this interdisciplinary area, for quite some time, in topics such as spherical codes, codes in graphs, labeling of codes in Hamming and Lee spaces, design of signal constellations and probability distributions in hyperbolic spaces, sphere packing and symmetric spaces. The main characteristic of the proposed approach is homogeneity, implying that the signals in consideration have the same distance profile, congruent Voronoi regions, and the same error probability. Labeling of the signals in this context is achieved by the symmetry groups of the corresponding metric spaces such as the Euclidean space, regular graph space, hyperbolic space, and so on. The present research proposal not only follows the guidelines of the aforementioned research proposal as well as extends it by including new research topics based on the error correcting codes approach by use of the associated geometric and algebraic structures. The objectives of this research proposal are twofold: the development of research topics in the interdisciplinary areas such as Information, Coding and Communications Theory and Mathematics; and to provide an effective interaction between the groups working in these two areas. Consequently, joint publications, joint supervised MS and PhD dissertations, offering of new graduate courses and seminars will be met. Besides the inherent theoretical developments, priority will be given to simulation of the proposed mathematical models and also in the generation of new coding/modulation and decoding/demodulation schemes. Consequently, the theoretical and applied results will be available to our scientific and technological community. (AU)

Scientific publications

(7)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

VOLPATO, NILTON; MOURA, ARNALDO. TIGHT QUANTUM BOUNDS FOR COMPUTATIONAL GEOMETRY PROBLEMS. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, v. 7, n. 5, p. 935-947, AUG 2009. Web of Science Citations: 0.

COSTA, S. I. R.; MORAES, S. M.; ROMERO-FUSTER, M. C. Geometric contacts of surfaces immersed in R-n, n >= 5. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 27, n. 3, p. 442-454, JUN 2009. Web of Science Citations: 6.

ALBUQUERQUE, C. D.; PALAZZO, JR., R.; SILVA, E. B. Topological quantum codes on compact surfaces with genus g >= 2. Journal of Mathematical Physics, v. 50, n. 2 FEB 2009. Web of Science Citations: 6.

PANSONATO, CLAUDIA C.; COSTA, SUELI I. R. Total torsion of curves in three-dimensional manifolds. Geometriae Dedicata, v. 136, n. 1, p. 111-121, OCT 2008. Web of Science Citations: 1.

DE ALMEIDA‚ A.C.A.; PALAZZO JR‚ R. Comment on “Quantum convolutional error-correcting codes”. Physical Review A, v. 72, n. 2, p. 026301, 2005.

DE ANDRADE, ANTONIO APARECIDO; PALAZZO, JR., REGINALDO. Goppa and Srivastava codes over finite rings. COMPUTATIONAL & APPLIED MATHEMATICS, v. 24, n. 2, p. 231-244, 2005. Web of Science Citations: 0.

WU‚ S.T.; ALÉSSIO‚ O.; COSTA‚ S.I.R. A complete and non-overlapping tracing algorithm for closed loops. COMPUTER AIDED GEOMETRIC DESIGN, v. 22, n. 6, p. 491-514, 2005.

Filed patent(s) as a result of this research project