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Algebraic Constructions of Network Codes

English title Algebraic Constructions of Network Codes
Applicant Rosenthal Joachim
Number 126948
Funding scheme Project funding (Div. I-III)
Research institution Institut für Mathematik Universität Zürich
Institution of higher education University of Zurich - ZH
Main discipline Mathematics
Start/End 01.10.2009 - 30.09.2011
Approved amount 116'264.00
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Keywords (5)

Coding Theory; Network Codes; Finite Projective Geometries; Grassmann variety; finite Grassmann Variety

Lay Summary (English)

Lead
Lay summary
Coding theory has emerged out of the need for better communication and has rapidly developed as a mathematical theory in strong relationship with algebra, combinatorics and algebraic geometry. Nowadays error-correcting-codes are used in everyday practical applications such as digital-storage media, wire-line and wireless networks, and satellite and deep-space communication systems. Example of simple block codes are the international standard book numbers (ISBN), the ASCII code and various encoding schemes used to identify bank accounts.Network coding theory is concerned with the encoding and transmission of information where there may be many information sources and possibly many receivers. R. Koetter and F. Kschischang identified a fundamental mathematical question which lies at the heart of network coding. This formulation seeks the construction of good subsets of the finite Grassmann variety and it is the intended plan of the proposed research to use algebraic techniques to come up with new network codes which have better throughput and efficient decoding.
Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants

Employees

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
ISIT 2011 International Symposium on Information Theory 31.07.2011 St. Petersburg, Russland
6th Workshop on Coding and Systems 13.06.2011 University of Aveiro, Portugal
Seminartalk at the University of Notre Dame, Notre Dame, USA 26.04.2011 University of Notre Dame, Notre Dame, USA
The Seventh International Workshop on Coding and Cryptography 11.04.2011 Institut Henri Poincare, Paris, Frankreich
Seminartalk at the Hong Kong University 21.03.2011 Hong Kong University, China
Colloquiumtalk at the HIT Shenzhen Graduate School, Peking 18.03.2011 University of Peking, China
Seminartalk at the Australian National University 03.02.2011 Australian National University, Canberra, Australia
Seminartalk at the University of Aveiro, Portugal 22.01.2010 University of Aveiro, Portugal


Associated projects

Number Title Start Funding scheme
113251 Algebraic Constructions of Codes on Graphs 01.10.2006 Project funding (Div. I-III)
138080 Algebraic Constructions and Decoding of Network Codes 01.10.2011 Project funding (Div. I-III)
138080 Algebraic Constructions and Decoding of Network Codes 01.10.2011 Project funding (Div. I-III)
150207 Algebraic Aspects of Linear Network Coding 01.01.2014 Project funding (Div. I-III)

Abstract

Coding theory has emerged out of the need for bettercommunication and has rapidly developed as a mathematical theoryin strong relationship with algebra, combinatorics and algebraicgeometry. Nowadays error-correcting-codes are used in everydaypractical applications such as digital-storage media, wire-lineand wireless networks, and satellite and deep-space communicationsystems. Example of simple block codes are the internationalstandard book numbers (ISBN), the ASCII code and various encodingschemes used to identify bank accounts.Network coding theory is concerned with the encoding andtransmission of information where there may be many informationsources and possibly many receivers. R.~K\"otter andF.~Kschischang identified a fundamental mathematicalquestion which lies at the heart of network coding. Thisformulation seeks the construction of good subsets of thefinite Grassmann variety and it is the intended plan of theproposed research to use algebraic techniques to come up with newnetwork codes which have better performance.
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