The Error Probability of Generalized Perfect Codes via the Meta-Converse

作     者：Vazquez-Vilar, Gonzalo Guillen i Fabregas, Albert Verdu, Sergio 

作者机构：Univ Carlos III Madrid Signal Theory & Commun Dept Leganes 28911 Spain Gregorio Maranon Hlth Res Inst Madrid 28007 Spain Univ Pompeu Fabra Dept Informat & Commun Technol Barcelona 08018 Spain Inst Catalana Recerca & Estudis Avancats Barcelona 08010 Spain Univ Cambridge Dept Engn Cambridge CB2 1PZ England Natl Acad Engn Washington DC 20418 USA Natl Acad Sci 2101 Constitut Ave Nw Washington DC 20418 USA Australian Natl Univ Canberra ACT Australia Technion Israel Inst Technol Haifa Israel Univ Tokyo Tokyo Japan Univ Calif Berkeley Berkeley CA 94720 USA Math Sci Res Inst 1000 Centennial Dr Berkeley CA 94720 USA MIT Cambridge MA 02139 USA 

出 版 物：《IEEE TRANSACTIONS ON INFORMATION THEORY》 (IEEE信息论汇刊)

年 卷 期：2019年第65卷第9期

页      面：5705-5717页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：European Research Council (ERC) [714161, 725411] Spanish Ministry of Economy and Competitiveness [TEC2016-78434C3, IJCI-2015-27020] National Science Foundation [CCF-1513915] Center for Science of Information NSF Science and Technology Center [CCF0939370] 

主　　题：Shannon theory perfect codes quasi-perfect codes maximum likelihood decoding finite blocklength analysis meta-converse hypothesis testing channel coding joint source-channel coding rate distortion theory 

摘      要：We introduce a definition of perfect and quasi-perfect codes for discrete symmetric channels based on the packing and covering properties of generalized spheres whose shape is tilted using an auxiliary probability measure. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum distance separable codes. The error probability of these codes, whenever they exist, is shown to coincide with the estimate provided by the meta-converse lower bound. We illustrate how the proposed definition naturally extends to cover almost-lossless source-channel coding and lossy compression.