{"title":"On the code length of TCAM coding schemes","authors":"Ori Rottenstreich, I. Keslassy","doi":"10.1109/ISIT.2010.5513403","DOIUrl":null,"url":null,"abstract":"All high-speed Internet devices need to implement classification, i.e. they must determine whether incoming packet headers belong to a given subset of a search space. To do it, they encode the subset using ternary arrays in special high-speed devices called TCAMs (ternary content-addressable memories). However, the optimal coding for arbitrary subsets is unknown. In particular, to encode an arbitrary range subset of the space of all W-bit values, previous works have successively reduced the upper-bound on the code length from 2W–2 to 2W–4, then 2W–5, and finally W TCAM entries. In this paper, we prove that this final result is optimal for typical prefix coding and cannot be further improved, i.e. the bound of W is tight. To do so, we introduce new analytical tools based on independent sets and alternating paths.","PeriodicalId":147055,"journal":{"name":"2010 IEEE International Symposium on Information Theory","volume":"65 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 IEEE International Symposium on Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2010.5513403","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 18
Abstract
All high-speed Internet devices need to implement classification, i.e. they must determine whether incoming packet headers belong to a given subset of a search space. To do it, they encode the subset using ternary arrays in special high-speed devices called TCAMs (ternary content-addressable memories). However, the optimal coding for arbitrary subsets is unknown. In particular, to encode an arbitrary range subset of the space of all W-bit values, previous works have successively reduced the upper-bound on the code length from 2W–2 to 2W–4, then 2W–5, and finally W TCAM entries. In this paper, we prove that this final result is optimal for typical prefix coding and cannot be further improved, i.e. the bound of W is tight. To do so, we introduce new analytical tools based on independent sets and alternating paths.