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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| Other Authors: | |
| Format: | Final Year Project (FYP) |
| Language: | English |
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2018
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| Online Access: | http://hdl.handle.net/10356/76210 |
| _version_ | 1826112404972371968 |
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| author | Goh, You Hui |
| author2 | Chua Chek Beng |
| author_facet | Chua Chek Beng Goh, You Hui |
| author_sort | Goh, You Hui |
| collection | NTU |
| 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 |
| first_indexed | 2024-10-01T03:06:17Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/76210 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:06:17Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-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 |
| spellingShingle | DRNTU::Science::Mathematics Goh, You Hui Index coding with side information via penalty method in rank minimisation |
| title | 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_short | Index coding with side information via penalty method in rank minimisation |
| title_sort | index coding with side information via penalty method in rank minimisation |
| topic | DRNTU::Science::Mathematics |
| url | http://hdl.handle.net/10356/76210 |
| work_keys_str_mv | AT gohyouhui indexcodingwithsideinformationviapenaltymethodinrankminimisation |