Kota Srinivas Reddy, Nujoom Sageer Karat, N. Karamchandani
{"title":"On the Optimal Transmission Rate for Symmetric Index Coding Problems","authors":"Kota Srinivas Reddy, Nujoom Sageer Karat, N. Karamchandani","doi":"10.1109/ISIT45174.2021.9517865","DOIUrl":null,"url":null,"abstract":"An Index Coding Problem (ICP) has a central server that possesses files and is connected to multiple users through a shared link. Each user demands a subset of files and possesses another subset of files as side-information. The files which are neither demanded nor possessed as side-information by a user are called its interference files. In a symmetric ICP, the relative positions of side-information and interference files are the same for all the users. In this paper, a general representation for symmetric ICPs is proposed, and using this representation, we give bounds on the optimal transmission rate for a general symmetric ICP. We identify two broad categories of symmetric ICPs: Neighboring Interference ICP (NI-ICP) and Neighboring Side-information ICP (NS-ICP). For a particular class of NI-ICP, we find the optimal transmission rate, and for another class, an order-optimal transmission rate is derived. An upper bound on the optimal transmission rate is established for NS-ICP. Furthermore, for a particular class of NS-ICP, a lower bound for the optimal transmission rate is also derived.","PeriodicalId":299118,"journal":{"name":"2021 IEEE International Symposium on Information Theory (ISIT)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 IEEE International Symposium on Information Theory (ISIT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT45174.2021.9517865","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
An Index Coding Problem (ICP) has a central server that possesses files and is connected to multiple users through a shared link. Each user demands a subset of files and possesses another subset of files as side-information. The files which are neither demanded nor possessed as side-information by a user are called its interference files. In a symmetric ICP, the relative positions of side-information and interference files are the same for all the users. In this paper, a general representation for symmetric ICPs is proposed, and using this representation, we give bounds on the optimal transmission rate for a general symmetric ICP. We identify two broad categories of symmetric ICPs: Neighboring Interference ICP (NI-ICP) and Neighboring Side-information ICP (NS-ICP). For a particular class of NI-ICP, we find the optimal transmission rate, and for another class, an order-optimal transmission rate is derived. An upper bound on the optimal transmission rate is established for NS-ICP. Furthermore, for a particular class of NS-ICP, a lower bound for the optimal transmission rate is also derived.