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商品描述
Incepted half a century ago, information theory is a classical yet modern field which is more vibrant than ever before. In particular, there have been a number of major research results on the foundation of the theory during the last ten years. These results enable information theory to be understood and explored in a way which has not been possible before, and they open new dimensions in the theory. In short, the depth of information theory is far beyond what we used to know.
This book is an integration of the most fundamental topics in information theory plus a few selected advanced topics. All concepts and technicalities are explained with clarity. Except for a few classical results, all the results included here are not found elsewhere in book form. These include the theory of I-Measure, Shannon-type and non-Shannon-type information inequalities, and network coding theory. Some important implications of information theory in probability theory and group theory are also explained in this book.
ITIP, the software package that comes with the book, is the only software package of its kind which can prove all Shannon-type information inequalities. It is an essential tool for all information theorists.
This book is suitable for use as a textbook, or as a reference book with any other textbook in a course on information theory. It is also an essential reference for researchers working in areas related to this subject matter.
`No one since Shannon has had a better appreciation for the mathematical structure of information quantities than Prof. Yeung. ... Yeung unveils a smørgasbord of topics in modern information theory that heretofore have been available only in research papers.'
Toby Berger, Cornell University
Contents
1. The Science of Information. 2. Information Measures. 3. Zero-Error Data Compression. 4. Weak Typicality. 5. Strong Typicality. 6. The I-Measure. 7. Markov Structures. 8. Channel Capacity. 9. Rate Distortion Theory. 10. The Blahut-Arimoto Algorithms. 11. Single-Source Network Coding. 12. Information Inequalities. 13. Shannon-Type Inequalities. Appendix 13A: The Basic Inequalities and the Polymatroidal Axioms. 14. Beyond Shannon-Type Inequalities. 15. Multi-Source Network Coding. Appendix 15A: Approximation of Random Variables with Infinite Alphabets. 16. Entropy and Groups. Bibliography. Index.
商品描述(中文翻譯)
信息理論成立於半世紀前,是一個古典卻又現代的領域,現在比以往任何時候都更具活力。特別是在過去十年中,該理論的基礎上出現了許多重要的研究成果。這些成果使得信息理論能以以前無法實現的方式被理解和探索,並為該理論開啟了新的維度。簡而言之,信息理論的深度遠超我們以往的認知。
本書整合了信息理論中最基本的主題以及一些選定的進階主題。所有概念和技術細節都以清晰的方式進行解釋。除了少數幾個經典結果外,這裡包含的所有結果在其他書籍中都找不到。這些包括 I-Measure 理論、Shannon 型和非 Shannon 型信息不等式,以及網絡編碼理論。本書還解釋了信息理論在概率論和群論中的一些重要應用。
ITIP,隨書附贈的軟體包,是唯一能證明所有 Shannon 型信息不等式的軟體包。這是所有信息理論學者必備的工具。
本書適合作為教科書使用,或作為信息理論課程中任何其他教科書的參考書。對於從事與此主題相關領域的研究人員來說,它也是一本必不可少的參考書。
`自 Shannon 以來,沒有任何人能像 Yeung 教授那樣更好地理解信息量的數學結構。... Yeung 揭示了現代信息理論中的一系列主題,這些主題之前僅在研究論文中可見。'
托比·伯傑,康奈爾大學
內容
1. 信息科學。 2. 信息度量。 3. 零錯誤數據壓縮。 4. 弱典型性。 5. 強典型性。 6. I-度量。 7. 馬可夫結構。 8. 通道容量。 9. 速率失真理論。 10. Blahut-Arimoto 算法。 11. 單源網絡編碼。 12. 信息不等式。 13. Shannon 型不等式。 附錄 13A: 基本不等式和多重體公理。 14. 超越 Shannon 型不等式。 15. 多源網絡編碼。 附錄 15A: 具有無限字母表的隨機變量的近似。 16. 熵與群。 參考文獻。 索引。