Algebraic and geometric fundamentals of geometrically uniform codes

• Grant number: 95/04720-8
• Support Opportunities: Research Projects - Thematic Grants
• Start date: September 01, 1996
• End date: August 31, 2000
• Field of knowledge: Engineering - Electrical Engineering - Telecommunications
• Principal Investigator: Reginaldo Palazzo Junior
• Grantee: Reginaldo Palazzo Junior
• Host Institution: Faculdade de Engenharia Elétrica e de Computação (FEEC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant(s): 99/02987-8 - Gerardus Rudolf Pellikaan | Eindhoven University Technology - Holanda, AV.EXT; 98/10679-9 - On alternant codes over ommutative rings., AR.EXT; 98/03070-8 - Improving the performance os asymmetric m-pam signal constellation in euclidean space by embedding them in hyperbolic space., AR.EXT; 97/01788-6 - Lattice constellations matched to gf(p)., AR.EXT; 97/02107-2 - 1) the symmetry group of znq in the lee space and the znq - linear codes. 2) lattice constellations matched to gf (p)., AR.EXT

Abstract

The research in algebraic and geometric fundamentals of geometrically uniform codes aims at introducing topological structures in the encoding and decoding processes not only in the traditional algebraic structure of fields as well as in the algebraic structures of rings and groups. Hence, the design of new signal constellations and of new classes of codes by studying the topological spaces, metric spaces, and the corresponding surfaces where they are embedded bring new light to the current approach. As an example, certain source and channel coding problems can be viewed as one through the existence of a homeomorphism between the corresponding metric spaces. Associated with this approach, it is our aim to propose coding techniques for linear q-ary codes, G-linear codes, where G is a group, convolutional codes over groups, characterize the surfaces of linear trellis codes, to propose new signal constellations and corresponding demodulations in hyperbolic geometry, codes over algebraic integers, etc. Since the computational complexity of the problems involved in this research is high we also intend to develop the corresponding software. (AU)