Optimal Index Code With Rate 4 Over F₂
High throughput broadcasting systems requires efficient broadcasting that can broadcast the information source symbols with optimal rate (i.e., maximizing the usage of broadcast channel which exploits the broadcast nature of the wireless medium through index coding). Index coding is the elegant and...
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2025-01-01
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| author | Rajesh Neelakandan Ganesan Kaliyaperumal |
| author_facet | Rajesh Neelakandan Ganesan Kaliyaperumal |
| author_sort | Rajesh Neelakandan |
| collection | DOAJ |
| description | High throughput broadcasting systems requires efficient broadcasting that can broadcast the information source symbols with optimal rate (i.e., maximizing the usage of broadcast channel which exploits the broadcast nature of the wireless medium through index coding). Index coding is the elegant and beautiful idea, which is used to transform the information source symbols for efficient broadcasting. Efficient broadcasting means minimizing the number of transmissions, which facilitate to achieve high throughput in broadcasting systems is the main goal for index coding. In index coding, determining the optimal rate of an index code for the class of index coding problem is the central open problem. In this paper, we present class <inline-formula> <tex-math notation="LaTeX">$\mathbb{I V}$ </tex-math></inline-formula> index coding problems, a new class of index coding problems with the size of maximum acyclic induced subgraph is 4. The main goal of this work is to characterize the optimal rate of class <inline-formula> <tex-math notation="LaTeX">$\mathbb{I V}$ </tex-math></inline-formula> index coding problems over finite field with 2 elements <inline-formula> <tex-math notation="LaTeX">$\left(\mathbb{F}_2\right)$ </tex-math></inline-formula>. We present that optimal linear index code of the class <inline-formula> <tex-math notation="LaTeX">$\mathbb{I V}$ </tex-math></inline-formula> index coding problem over <inline-formula> <tex-math notation="LaTeX">$\mathbb{F}_2$ </tex-math></inline-formula> achieves the rate 4 on the broadcast rate. To present this new result, results of index coding network coding duality are used. We also present that there exists index coding problems with size of maximum acyclic induced subgraph is 4 and optimal broadcast rate greater than 4. We use the technique interference alignment using alignment graph and the conflict hyper graph to present this contrast. |
| format | Article |
| id | doaj-art-c4693f1097754d49a8a70ac1d5af6726 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-c4693f1097754d49a8a70ac1d5af67262025-01-31T23:04:51ZengIEEEIEEE Access2169-35362025-01-0113194841952210.1109/ACCESS.2025.352918610839394Optimal Index Code With Rate 4 Over F₂Rajesh Neelakandan0https://orcid.org/0000-0003-4324-784XGanesan Kaliyaperumal1https://orcid.org/0000-0002-6088-4907Department of Communication Engineering, School of Electronics Engineering, Vellore Institute of Technology, Vellore, IndiaDepartment of Software and System Engineering, School of Computer Science Engineering and Information Systems, Vellore Institute of Technology, Vellore, IndiaHigh throughput broadcasting systems requires efficient broadcasting that can broadcast the information source symbols with optimal rate (i.e., maximizing the usage of broadcast channel which exploits the broadcast nature of the wireless medium through index coding). Index coding is the elegant and beautiful idea, which is used to transform the information source symbols for efficient broadcasting. Efficient broadcasting means minimizing the number of transmissions, which facilitate to achieve high throughput in broadcasting systems is the main goal for index coding. In index coding, determining the optimal rate of an index code for the class of index coding problem is the central open problem. In this paper, we present class <inline-formula> <tex-math notation="LaTeX">$\mathbb{I V}$ </tex-math></inline-formula> index coding problems, a new class of index coding problems with the size of maximum acyclic induced subgraph is 4. The main goal of this work is to characterize the optimal rate of class <inline-formula> <tex-math notation="LaTeX">$\mathbb{I V}$ </tex-math></inline-formula> index coding problems over finite field with 2 elements <inline-formula> <tex-math notation="LaTeX">$\left(\mathbb{F}_2\right)$ </tex-math></inline-formula>. We present that optimal linear index code of the class <inline-formula> <tex-math notation="LaTeX">$\mathbb{I V}$ </tex-math></inline-formula> index coding problem over <inline-formula> <tex-math notation="LaTeX">$\mathbb{F}_2$ </tex-math></inline-formula> achieves the rate 4 on the broadcast rate. To present this new result, results of index coding network coding duality are used. We also present that there exists index coding problems with size of maximum acyclic induced subgraph is 4 and optimal broadcast rate greater than 4. We use the technique interference alignment using alignment graph and the conflict hyper graph to present this contrast.https://ieeexplore.ieee.org/document/10839394/Index codingnetwork codingmultiple unicastdualityoptimal rate |
| spellingShingle | Rajesh Neelakandan Ganesan Kaliyaperumal Optimal Index Code With Rate 4 Over F₂ IEEE Access Index coding network coding multiple unicast duality optimal rate |
| title | Optimal Index Code With Rate 4 Over F₂ |
| title_full | Optimal Index Code With Rate 4 Over F₂ |
| title_fullStr | Optimal Index Code With Rate 4 Over F₂ |
| title_full_unstemmed | Optimal Index Code With Rate 4 Over F₂ |
| title_short | Optimal Index Code With Rate 4 Over F₂ |
| title_sort | optimal index code with rate 4 over f x2082 |
| topic | Index coding network coding multiple unicast duality optimal rate |
| url | https://ieeexplore.ieee.org/document/10839394/ |
| work_keys_str_mv | AT rajeshneelakandan optimalindexcodewithrate4overfx2082 AT ganesankaliyaperumal optimalindexcodewithrate4overfx2082 |