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Algebraic Constructions and Decoding of Network Codes

English title Algebraic Constructions and Decoding of Network Codes
Applicant Rosenthal Joachim
Number 138080
Funding scheme Project funding
Research institution Institut für Mathematik Universität Zürich
Institution of higher education University of Zurich - ZH
Main discipline Mathematics
Start/End 01.10.2011 - 30.09.2013
Approved amount 120'000.00
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All Disciplines (3)

Discipline
Mathematics
Electrical Engineering
Information Technology

Keywords (4)

Coding Theory; Network Coding; Constant Dimension Codes; 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.
In the center of the mathematical interest will be the study of orbit
codes, a concept introduced by the PI and his coauthors while supported
by SNF grant Project no. 126948.
Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants

Employees

Publications

Publication
Spread decoding in extension fields
Manganiello Felice, Trautmann Anna-Lena (2014), Spread decoding in extension fields, in Finite Fields and Their Applications , 25(0), 94-105.
A complete characterization of irreducible cyclic orbit codes and their Plucker embedding
Rosenthal Joachim, Trautmann Anna-Lena (2013), A complete characterization of irreducible cyclic orbit codes and their Plucker embedding, in Des. Codes Cryptogr., 66(1-3), 275-289.
A Complete Characterization of Irreducible Cyclic Orbit Codes and their Plücker Embedding
Rosenthal J., Trautmann A.-L. (2013), A Complete Characterization of Irreducible Cyclic Orbit Codes and their Plücker Embedding, in Des. Codes Cryptogr., 66(1--3), 275-289.
Cyclic Orbit Codes
Trautmann A.-L., Manganiello F., Braun M., Rosenthal J. (2013), Cyclic Orbit Codes, in IEEE Transactions of Information Theory, 59(11), 7386-7404.
Decoding of Subspace codes, a Problem of Schubert calculus over Finite Fields
Rosenthal J., Trautmann A.-L. (2013), Decoding of Subspace codes, a Problem of Schubert calculus over Finite Fields, in Hueper K. (ed.), CreateSpace, Seattle, Washington, 353-366.
Decoding of Subspace codes, a Problem of Schubert calculus over Finite Fields
Rosenthal J., Trautmann A.-L. (2013), Decoding of Subspace codes, a Problem of Schubert calculus over Finite Fields, in Hüper K. (ed.), CreateSpace, Part of Amazon group , 353-366.
List Decoding of Lifted Gabidulin Codes via the Plücker Embedding
Trautmann A.-L., Silberstein N., Rosenthal J. (2013), List Decoding of Lifted Gabidulin Codes via the Plücker Embedding, in Proceedings of the Seventh International Workshop on Coding and Cryptography (WCC), Bergen, NorwayWCC 2013, University of Bergen, Norway.
New lower bounds for constant dimension codes
Silberstein N., Trautmann A.-L. (2013), New lower bounds for constant dimension codes, in IEEE International Symposium on Information Theory, IEEE, New Jersey, USA.
An algebraic approach for decoding spread codes
Gorla Elisa, Manganiello Felice, Rosenthal Joachim (2012), An algebraic approach for decoding spread codes, in Adv. Math. Commun., 6(4), 443-466.
Decoding of convolutional codes over the erasure channel
Tomas Virtudes, Rosenthal Joachim, Smarandache Roxana (2012), Decoding of convolutional codes over the erasure channel, in IEEE Trans. Inform. Theory, 58(1), 90-108.
On Burst Error Correction and Storage Security of Noisy Data
Fontein F., Marshall K., Rosenthal J., Schipani D., Trautmann A.-L. (2012), On Burst Error Correction and Storage Security of Noisy Data, in Proceedings of the 20th International Symposium MTNS, MTNS, University of Melbourne.
On conjugacy classes of subgroups of the general linear group and cyclic orbit codes
Manganiello F., Trautmann A., Rosenthal J. (2012), On conjugacy classes of subgroups of the general linear group and cyclic orbit codes, in IEEE International Symposium on Information Theory ISIT 2011, St. Petersburg, RussiaIEEE, New Jersey, USA.
Plücker Embedding of Cyclic Orbit Codes
Trautmann A.-L. (2012), Plücker Embedding of Cyclic Orbit Codes, in Proceedings of the 20th International Symposium MTNS, MTNS, University of Melbourne.
Polynomial evaluation over finite fields: new algorithms and complexity bounds
Elia Michele, Rosenthal Joachim, Schipani Davide (2012), Polynomial evaluation over finite fields: new algorithms and complexity bounds, in Appl. Algebra Engrg. Comm. Comput., 23(3-4), 129-141.

Collaboration

Group / person Country
Types of collaboration
Shannon Institute, University College Dublin Ireland (Europe)
- in-depth/constructive exchanges on approaches, methods or results

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Conference on Random network codes and Designs over GF(q) Talk given at a conference List Decoding of Subspace Codes 18.09.2013 Ghent, Belgien, Belgium Rosenthal Joachim; Marshall Kyle; Trautmann Anna-Lena;
SIAM 2013 - Conference on Applied Algebraic Geometry Talk given at a conference List Decoding of Subspace Codes 01.08.2013 Fort Collins, Colorado, USA, United States of America Rosenthal Joachim; Trautmann Anna-Lena;
European Training School in Network Coding Talk given at a conference Schubert Calculus over Finite Fields 04.02.2013 Barcelona, Spanien, Spain Rosenthal Joachim;
Workshop on Computational Security Talk given at a conference The Difficulty of constructing Oneway Trapdoor Functions 28.11.2012 Bellaterra, Spanien, Spain Rosenthal Joachim;
Colloquium talk: Linear Random Network Codes, a Grassmannian Approach Individual talk Linear Random Network Codes, a Grassmannian Approach 12.10.2012 University of Wisconsin, Madison, USA, United States of America Rosenthal Joachim;
MTNS 2012 Talk given at a conference Decoding of Subspace Codes, a Problem of Schubert Calculus 09.07.2012 Melbourne, Australien, Australia Rosenthal Joachim; Trautmann Anna-Lena;
Codes and Topology Talk given at a conference Convolutional Codes, a Study via Duality 31.05.2012 Castro Urdiales, Spanien, Spain Rosenthal Joachim;


Self-organised

Title Date Place
Trends in Coding Theory 2012 28.10.2012 Ascona, Schweiz, Switzerland
Dagstuhl Seminar in Coding Theory 13.11.2011 Dagstuhl, Germany, Germany

Knowledge transfer events

Active participation

Title Type of contribution Date Place Persons involved
COST Action meeting Workshop 29.04.2012 Initial meeting was in Brussels, Belgium Rosenthal Joachim;


Communication with the public

Communication Title Media Place Year
Talks/events/exhibitions Junior Euler Society Mathematik (U18) - Kryptographie German-speaking Switzerland 2012
Talks/events/exhibitions UZH Kinderuniversität - Wie geheim ist eine Geheimschrift German-speaking Switzerland 2012

Awards

Title Year
Forschungskredit der Universitaet Zuerich 2012

Associated projects

Number Title Start Funding scheme
149716 Algebraic Constructions and Decoding of Subspace Codes 01.10.2013 Project funding
126948 Algebraic Constructions of Network Codes 01.10.2009 Project funding
126948 Algebraic Constructions of Network Codes 01.10.2009 Project funding
149716 Algebraic Constructions and Decoding of Subspace Codes 01.10.2013 Project funding
113251 Algebraic Constructions of Codes on Graphs 01.10.2006 Project funding
144973 Computing equipment 01.05.2013 R'EQUIP
150207 Algebraic Aspects of Linear Network Coding 01.01.2014 Project funding

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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