Index coding with side information via penalty method in rank minimisation

Index coding with side information (ICSI) problems can be represented as matrices. These matrices have unique properties with intuitive meaning in its matrix representation. It has been shown by recent studies that minimising the rank of these matrices are equivalent to solving the ICSI problems by...

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Main Author: Goh, You Hui
Other Authors: Chua Chek Beng
Format: Final Year Project
Language:English
Published: 2018
Subjects:
Online Access:http://hdl.handle.net/10356/76210
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-762102023-02-28T23:12:02Z Index coding with side information via penalty method in rank minimisation Goh, You Hui Chua Chek Beng School of Physical and Mathematical Sciences DRNTU::Science::Mathematics Index coding with side information (ICSI) problems can be represented as matrices. These matrices have unique properties with intuitive meaning in its matrix representation. It has been shown by recent studies that minimising the rank of these matrices are equivalent to solving the ICSI problems by finding the minimum index code lengths. This paper investigates the special properties of these matrices associated with the ICSI problems. We will present some theoretical results that will enable us to minimise the rank of these matrices by using a penalty method. The penalty method has been recently shown to have good performance in minimising the rank of positive semidefinite matrices. This paper looks into the implementation of the penalty method to solve ICSI problems. Performance of this implementation will be compared against Alternating Projection (AP) method. AP method has been recently shown to produce promising results in solving ICSI problems by rank minimisation. Key Words: Rank Minimisation, Penalty Method, Proximal Alternating Linearised minimisation, Alternating Projections, Positive Semidefinite Bachelor of Science in Mathematical Sciences 2018-12-03T14:34:45Z 2018-12-03T14:34:45Z 2018 Final Year Project (FYP) http://hdl.handle.net/10356/76210 en 39 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics
spellingShingle DRNTU::Science::Mathematics
Goh, You Hui
Index coding with side information via penalty method in rank minimisation
description Index coding with side information (ICSI) problems can be represented as matrices. These matrices have unique properties with intuitive meaning in its matrix representation. It has been shown by recent studies that minimising the rank of these matrices are equivalent to solving the ICSI problems by finding the minimum index code lengths. This paper investigates the special properties of these matrices associated with the ICSI problems. We will present some theoretical results that will enable us to minimise the rank of these matrices by using a penalty method. The penalty method has been recently shown to have good performance in minimising the rank of positive semidefinite matrices. This paper looks into the implementation of the penalty method to solve ICSI problems. Performance of this implementation will be compared against Alternating Projection (AP) method. AP method has been recently shown to produce promising results in solving ICSI problems by rank minimisation. Key Words: Rank Minimisation, Penalty Method, Proximal Alternating Linearised minimisation, Alternating Projections, Positive Semidefinite
author2 Chua Chek Beng
author_facet Chua Chek Beng
Goh, You Hui
format Final Year Project
author Goh, You Hui
author_sort Goh, You Hui
title Index coding with side information via penalty method in rank minimisation
title_short Index coding with side information via penalty method in rank minimisation
title_full Index coding with side information via penalty method in rank minimisation
title_fullStr Index coding with side information via penalty method in rank minimisation
title_full_unstemmed Index coding with side information via penalty method in rank minimisation
title_sort index coding with side information via penalty method in rank minimisation
publishDate 2018
url http://hdl.handle.net/10356/76210
_version_ 1759853656538087424