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Algebraic Constructions of Codes on Graphs

English title Algebraic Constructions of Codes on Graphs
Applicant Rosenthal Joachim
Number 113251
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 01.10.2006 - 30.09.2009
Approved amount 206'368.00
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Keywords (5)

LDPC Codes; Codes on Graphs; Turbo Codes; Coding theory; Shannon limit

Lay Summary (English)

Lead
Lay summary
Coding theory has emerged out of the need for better communication and computer data storage 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.

The proposed project is concerned with the analysis and design of a class of error-correcting-codes that are popularly known as ``codes on graphs''. This is a class of codes which became a main focus of current research as these codes can reach Shannon limit in a practical way. The aim of the project is to come up with concrete algebraic constructions of such codes. Such constructions have the potential for future coding implementations in several applications such as writing data onto CD/DVDs, implementing modem-protocols, cellular communication systems, and deep-space communications.
Direct link to Lay Summary Last update: 21.02.2013

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Associated projects

Number Title Start Funding scheme
126948 Algebraic Constructions of Network Codes 01.10.2009 Project funding (Div. I-III)
138080 Algebraic Constructions and Decoding of Network Codes 01.10.2011 Project funding (Div. I-III)

Abstract

Coding theory has emerged out of the need for better communication and computer data storage 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.

The proposed project is concerned with the analysis and design of a class of error-correcting-codes that are popularly known as ``codes on graphs''. This is a class of codes which became a main focus of current research as these codes can reach Shannon limit in a practical way. The aim of the project is to come up with concrete algebraic constructions of such codes. Such constructions have the potential for future coding implementations in several applications such as writing data onto CD/DVDs, implementing modem-protocols, cellular communication systems, and deep-space communications.
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