{"title":"φ-混合源SWLZ算法中冗余度的逐点分析","authors":"Ayush Jain, R. Bansal","doi":"10.1109/ITW.2015.7133103","DOIUrl":null,"url":null,"abstract":"In this paper, we bound the number of phrases of the sliding window Lempel-Ziv (SWLZ) algorithm using an upper bound on the expected number of phrases in the fixed database Lempel-Ziv (FDLZ) algorithm for a class of φ-mixing sources which includes Markov sources, unifilar sources and finite state sources as special cases, as developed by Yang and Kieffer [1]. We use this bound to obtain a point-wise upper bound on the redundancy rate of SWLZ algorithm to be 2H(log<sub>2</sub>log<sub>2</sub>n<sub>w</sub>/log<sub>2</sub>n<sub>w</sub>) + O(log<sub>2</sub>log<sub>2</sub>log<sub>2</sub>n<sub>w</sub>/log<sub>2</sub>n<sub>w</sub>). Here H is the entropy rate of the source and n<sub>w</sub> is the window size.","PeriodicalId":174797,"journal":{"name":"2015 IEEE Information Theory Workshop (ITW)","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Point-wise analysis of redundancy in SWLZ algorithm for φ-mixing sources\",\"authors\":\"Ayush Jain, R. Bansal\",\"doi\":\"10.1109/ITW.2015.7133103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we bound the number of phrases of the sliding window Lempel-Ziv (SWLZ) algorithm using an upper bound on the expected number of phrases in the fixed database Lempel-Ziv (FDLZ) algorithm for a class of φ-mixing sources which includes Markov sources, unifilar sources and finite state sources as special cases, as developed by Yang and Kieffer [1]. We use this bound to obtain a point-wise upper bound on the redundancy rate of SWLZ algorithm to be 2H(log<sub>2</sub>log<sub>2</sub>n<sub>w</sub>/log<sub>2</sub>n<sub>w</sub>) + O(log<sub>2</sub>log<sub>2</sub>log<sub>2</sub>n<sub>w</sub>/log<sub>2</sub>n<sub>w</sub>). Here H is the entropy rate of the source and n<sub>w</sub> is the window size.\",\"PeriodicalId\":174797,\"journal\":{\"name\":\"2015 IEEE Information Theory Workshop (ITW)\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 IEEE Information Theory Workshop (ITW)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ITW.2015.7133103\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 IEEE Information Theory Workshop (ITW)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ITW.2015.7133103","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Point-wise analysis of redundancy in SWLZ algorithm for φ-mixing sources
In this paper, we bound the number of phrases of the sliding window Lempel-Ziv (SWLZ) algorithm using an upper bound on the expected number of phrases in the fixed database Lempel-Ziv (FDLZ) algorithm for a class of φ-mixing sources which includes Markov sources, unifilar sources and finite state sources as special cases, as developed by Yang and Kieffer [1]. We use this bound to obtain a point-wise upper bound on the redundancy rate of SWLZ algorithm to be 2H(log2log2nw/log2nw) + O(log2log2log2nw/log2nw). Here H is the entropy rate of the source and nw is the window size.
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