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語(yǔ)義通信的數(shù)學(xué)理論

包郵 語(yǔ)義通信的數(shù)學(xué)理論

出版社:人民郵電出版社出版時(shí)間:2024-12-01
開(kāi)本: 16開(kāi) 頁(yè)數(shù): 112
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語(yǔ)義通信的數(shù)學(xué)理論 版權(quán)信息

語(yǔ)義通信的數(shù)學(xué)理論 本書(shū)特色

長(zhǎng)期以來(lái),由于經(jīng) 典信息論只研究語(yǔ)法信息,限制了通信科學(xué)的進(jìn)一步發(fā)展。近年來(lái),研究語(yǔ)義信息處理與傳輸?shù)耐ㄐ偶夹g(shù)獲得了學(xué)術(shù)界的普遍關(guān)注,語(yǔ)義通信開(kāi)辟了未來(lái)通信技術(shù)發(fā)展的新方向,但還缺乏一般性的數(shù)學(xué)指導(dǎo)理論。為了解決這一難題,本書(shū)構(gòu)建了語(yǔ)義信息論的理論框架,對(duì)語(yǔ)義信息的度量體系與語(yǔ)義通信的理論極限進(jìn)行了系統(tǒng)性闡述。

本書(shū)內(nèi)容為張平院士和牛凱教授團(tuán)隊(duì)在語(yǔ)義信息論方面的理論突破,相關(guān)成果于2024年6月在《通信學(xué)報(bào)》首 發(fā),具有很強(qiáng)的前沿性。

語(yǔ)義通信的數(shù)學(xué)理論 內(nèi)容簡(jiǎn)介

自從1948年經(jīng)典信息論誕生以來(lái),在其指導(dǎo)下,現(xiàn)代通信技術(shù)已經(jīng)逼近了理論性能極限,例如信息熵,信道容量以及率失真函數(shù)。語(yǔ)義通信開(kāi)辟了未來(lái)通信技術(shù)發(fā)展的新方向,但還缺乏數(shù)學(xué)指導(dǎo)理論。為了解決這一難題,本文構(gòu)建了語(yǔ)義信息論的理論框架。通過(guò)研究語(yǔ)義通信的機(jī)制,我們發(fā)現(xiàn)同義性是其基本特征,由此定義了語(yǔ)義信息和語(yǔ)法信息之間的同義映射。基于同義映射這一核心概念,我們引入了語(yǔ)義信息的度量體系,包括語(yǔ)義熵,上/下語(yǔ)義互信息,語(yǔ)義信道容量以及語(yǔ)義率失真函數(shù)。進(jìn)一步,采用隨機(jī)編碼以及(聯(lián)合)同義典型序列編譯碼方法,證明了三個(gè)語(yǔ)義編碼定理,即語(yǔ)義信源編碼定理、語(yǔ)義信道編碼定理以及語(yǔ)義率失真編碼定理。我們發(fā)現(xiàn)同義映射擴(kuò)展了通信系統(tǒng)的極限。進(jìn)一步討論了連續(xù)條件下的語(yǔ)義信息度量。特別地,對(duì)于帶寬受限的高斯信道,我們得到了新的信道容量公式,其中平均同義長(zhǎng)度表征了信息的辨識(shí)能力,這一公式是香農(nóng)信道容量公式的推廣。綜上所述,本文提出的語(yǔ)義信息論,依據(jù)同義映射這一語(yǔ)義信息的本質(zhì)特征,構(gòu)建了語(yǔ)義信息的度量體系,引入新的數(shù)學(xué)工具,證明了語(yǔ)義編碼的基本定理,論證了語(yǔ)義通信系統(tǒng)的性能極限,揭示了未來(lái)語(yǔ)義通信的巨大性能潛力。

語(yǔ)義通信的數(shù)學(xué)理論 目錄

Chapter 1 Introduction 001Chapter 2 Semantic Communication System and Synonymous Mapping 0132.1 Notation Conventions 0132.2 Semantic Communication System 0142.3 Synonymous Mapping 016Chapter 3 Semantic Entropy 0193.1 Semantic Information Measures 019Chapter 1 Introduction 001Chapter 2 Semantic Communication System and Synonymous Mapping 0132.1 Notation Conventions 0132.2 Semantic Communication System 0142.3 Synonymous Mapping 016Chapter 3 Semantic Entropy 0193.1 Semantic Information Measures 0193.2 Semantic Joint Entropy and Semantic Conditional Entropy 022Chapter 4 Semantic Relative Entropy and Mutual Information 0314.1 Semantic Relative Entropy 0314.2 Semantic Mutual Information 036Chapter 5 Semantic Channel Capacity and Semantic Rate-distortion 0415.1 Semantic Channel Capacity 0415.2 Semantic Rate-Distortion 042Chapter 6 Semantic Lossless Source Coding 0456.1 Asymptotic Equipartition Property and Synonymous Typical Set 0456.2 Semantic Source Coding Theorem 0516.3 Semantic Source Coding Method 054Chapter 7 Semantic Channel Coding 0577.1 Jointly Asymptotic Equipartition Property and Jointly Synonymous Typical Set 0577.2 Semantic Channel Coding Theorem 0657.3 Semantic Channel Coding Method 073Chapter 8 Semantic Lossy Source Coding 0818.1 Semantic Distortion and Jointly Typical Set 0818.2 Semantic Rate-Distortion Coding Theorem 085Chapter 9 Semantic Information Measure of Continuous Message 0919.1 Semantic Entropy and Semantic Mutual Information for Continuous Message 0919.2 Semantic Channel Capacity of Gaussian Channel 0989.3 Semantic Channel Capacity of Band-limited Gaussian Channel 1019.4 Semantic Rate-Distortion of Gaussian Source 104Chapter 10 Semantic Joint Source Channel Coding 107Chapter 11 Conclusions 111Appendix 115References 117
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語(yǔ)義通信的數(shù)學(xué)理論 作者簡(jiǎn)介

Kai Niu received the B.S. degree in information engineering and the Ph.D. degree in signal and information processing from Beijing University of Posts and Telecommunications, Beijing, China, in 1998 and 2003, respectively. He is currently a Professor of the School of Artificial Intelligence, Beijing University of Posts and Communications. His research interests include information theory, coding theory, and semantic communication. He has published more than 200 academic papers, and proposed high performance construction algorithm of polar codes applied in 5G standard, and won the first prize of Natural Science of Science and Technology Award of the Chinese Institute of Electronics. Ping Zhang is currently a Professor of the School of Information and Communication Engineering at Beijing University of Posts and Telecommunications, the Director of State Key Laboratory of Networking and Switching Technology, a member of IMT-2020 (5G) Experts Panel, a member of Experts Panel for China’s 6G development. He served as Chief Scientist of National Basic Research Program (973 Program), an expert in Information Technology Division of National High-tech Research and Development program (863 Program), and a member of Consultant Committee on International Cooperation of National Natural Science Foundation of China. His research interests mainly focus on wireless communication. He is an Academician of the Chinese Academy of Engineering (CAE).Kai Niu received the B.S. degree in information engineering and the Ph.D. degree in signal and information processing from Beijing University of Posts and Telecommunications, Beijing, China, in 1998 and 2003, respectively. He is currently a Professor of the School of Artificial Intelligence, Beijing University of Posts and Communications. His research interests include information theory, coding theory, and semantic communication. He has published more than 200 academic papers, and proposed high performance construction algorithm of polar codes applied in 5G standard, and won the first prize of Natural Science of Science and Technology Award of the Chinese Institute of Electronics. Ping Zhang is currently a Professor of the School of Information and Communication Engineering at Beijing University of Posts and Telecommunications, the Director of State Key Laboratory of Networking and Switching Technology, a member of IMT-2020 (5G) Experts Panel, a member of Experts Panel for China’s 6G development. He served as Chief Scientist of National Basic Research Program (973 Program), an expert in Information Technology Division of National High-tech Research and Development program (863 Program), and a member of Consultant Committee on International Cooperation of National Natural Science Foundation of China. His research interests mainly focus on wireless communication. He is an Academician of the Chinese Academy of Engineering (CAE).

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