A First Course in Information Theory

This book provides an up-to-date introduction to information theory. In addition to the classical topics discussed, it provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory. ITIP, a software package for proving information inequalities, is also included. With a large number of examples, illustrations, and original problems, this book is excellent as a textbook or reference book for a senior or graduate level course on the subject, as well as a reference for researchers in related fields.

[1]  James Richard Roche Distributed information storage , 1992 .

[2]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[3]  Zhen Zhang,et al.  A class of non-Shannon-type information inequalities and their applications , 2001, Commun. Inf. Syst..

[4]  Richard E. Blahut,et al.  Computation of channel capacity and rate-distortion functions , 1972, IEEE Trans. Inf. Theory.

[5]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[6]  Robert G. Gallager,et al.  A simple derivation of the coding theorem and some applications , 1965, IEEE Trans. Inf. Theory.

[7]  Bruno O. Shubert,et al.  Random variables and stochastic processes , 1979 .

[8]  Amiel Feinstein,et al.  Information and information stability of random variables and processes , 1964 .

[9]  Abraham Lempel,et al.  Compression of individual sequences via variable-rate coding , 1978, IEEE Trans. Inf. Theory.

[10]  Raymond W. Yeung,et al.  A framework for linear information inequalities , 1997, IEEE Trans. Inf. Theory.

[11]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[12]  John B. Anderson,et al.  Source and Channel Coding: An Algorithmic Approach , 1991 .

[13]  Te Sun Han Nonnegative Entropy Measures of Multivariate Symmetric Correlations , 1978, Inf. Control..

[14]  A. Kolmogorov Three approaches to the quantitative definition of information , 1968 .

[15]  James G. Oxley,et al.  Matroid theory , 1992 .

[16]  Brendan J. Frey,et al.  Factor graphs and the sum-product algorithm , 2001, IEEE Trans. Inf. Theory.

[17]  Masud Mansuripur,et al.  Introduction to information theory , 1986 .

[18]  Zhen Zhang,et al.  Distributed Source Coding for Satellite Communications , 1999, IEEE Trans. Inf. Theory.

[19]  Dwijendra K. Ray-Chaudhuri,et al.  Binary mixture flow with free energy lattice Boltzmann methods , 2022, arXiv.org.

[20]  R.W. Yeung,et al.  On factorization of positive functions , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[21]  Yasuichi Horibe An Improved Bound for Weight-Balanced Tree , 1977, Inf. Control..

[22]  En-Hui Yang,et al.  Efficient universal lossless data compression algorithms based on a greedy sequential grammar transform - Part one: Without context models , 2000, IEEE Trans. Inf. Theory.

[23]  Richard D. Gitlin,et al.  Diversity coding for transparent self-healing and fault-tolerant communication networks , 1993, IEEE Trans. Commun..

[24]  Frans M. J. Willems,et al.  The context-tree weighting method: basic properties , 1995, IEEE Trans. Inf. Theory.

[25]  L. P. Hyvarinen,et al.  Information theory for systems engineers , 1968 .

[26]  A. Glavieux,et al.  Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1 , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[27]  Thomas M. Cover,et al.  An algorithm for maximizing expected log investment return , 1984, IEEE Trans. Inf. Theory.

[28]  László Lovász,et al.  On the Shannon capacity of a graph , 1979, IEEE Trans. Inf. Theory.

[29]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[30]  Silviu Guiaşu,et al.  Information theory with applications , 1977 .

[31]  Allen Gersho,et al.  Vector quantization and signal compression , 1991, The Kluwer international series in engineering and computer science.

[32]  Raymond W. Yeung,et al.  Some basic properties of fix-free codes , 2001, IEEE Trans. Inf. Theory.

[33]  Aaron D. Wyner,et al.  The rate-distortion function for source coding with side information at the decoder , 1976, IEEE Trans. Inf. Theory.

[34]  Suguru Arimoto,et al.  An algorithm for computing the capacity of arbitrary discrete memoryless channels , 1972, IEEE Trans. Inf. Theory.

[35]  Michel Mouchart,et al.  Discussion on "Conditional independence in statistitical theory" by A.P. Dawid , 1979 .

[36]  A. Dawid Conditional Independence in Statistical Theory , 1979 .

[37]  Brockway McMillan,et al.  Two inequalities implied by unique decipherability , 1956, IRE Trans. Inf. Theory.

[38]  Edward C. van der Meulen,et al.  Some Reflections On The Interference Channel , 1994 .

[39]  Terence Chan A combinatorial approach to information inequalities , 2001, Commun. Inf. Syst..

[40]  Suguru Arimoto,et al.  On the converse to the coding theorem for discrete memoryless channels (Corresp.) , 1973, IEEE Trans. Inf. Theory.

[41]  Shunsuke Ihara,et al.  Information theory - for continuous systems , 1993 .

[42]  Kenneth Rose,et al.  A mapping approach to rate-distortion computation and analysis , 1994, IEEE Trans. Inf. Theory.

[43]  Jan C. van der Lubbe,et al.  Information theory , 1997 .

[44]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[45]  Zhen Zhang,et al.  On Characterization of Entropy Function via Information Inequalities , 1998, IEEE Trans. Inf. Theory.

[46]  Shun-ichi Amari,et al.  Differential-geometrical methods in statistics , 1985 .

[47]  Solomon W. Golomb,et al.  Basic Concepts in Information Theory and Coding: The Adventures of Secret Agent 00111 , 1994 .

[48]  Philip M. Woodward,et al.  Probability and Information Theory with Applications to Radar , 1954 .

[49]  Amiel Feinstein,et al.  A new basic theorem of information theory , 1954, Trans. IRE Prof. Group Inf. Theory.

[50]  Raymond W. Yeung,et al.  On a relation between information inequalities and group theory , 2002, IEEE Trans. Inf. Theory.

[51]  D. Huffman A Method for the Construction of Minimum-Redundancy Codes , 1952 .

[52]  Shlomo Shamai,et al.  The empirical distribution of good codes , 1997, IEEE Trans. Inf. Theory.

[53]  Vahid Tarokh,et al.  Existence of optimal prefix codes for infinite source alphabets , 1997, IEEE Trans. Inf. Theory.

[54]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[55]  Michael O. Rabin,et al.  Efficient dispersal of information for security, load balancing, and fault tolerance , 1989, JACM.

[56]  Nikolai K. Vereshchagin,et al.  Combinatorial interpretation of Kolmogorov complexity , 2000, Proceedings 15th Annual IEEE Conference on Computational Complexity.

[57]  En-Hui Yang,et al.  Grammar-based codes: A new class of universal lossless source codes , 2000, IEEE Trans. Inf. Theory.

[58]  Norman Abramson,et al.  Information theory and coding , 1963 .

[59]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[60]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[61]  Robert J. McEliece,et al.  The Theory of Information and Coding , 1979 .

[62]  Stephen B. Wicker,et al.  Turbo Coding , 1998 .

[63]  D. J. Wheeler,et al.  A Block-sorting Lossless Data Compression Algorithm , 1994 .

[64]  Raymond W. Yeung,et al.  A simple upper bound on the redundancy of Huffman codes , 2002, IEEE Trans. Inf. Theory.

[65]  Imre Csiszár,et al.  The capacity of the arbitrarily varying channel revisited: Positivity, constraints , 1988, IEEE Trans. Inf. Theory.

[66]  M. Lunelli,et al.  Representation of matroids , 2002, math/0202294.

[67]  Nikolai K. Vereshchagin,et al.  Inequalities for Shannon Entropy and Kolmogorov Complexity , 1997, J. Comput. Syst. Sci..

[68]  Marten van Dijk On the information rate of perfect secret sharing schemes , 1995, Des. Codes Cryptogr..

[69]  Toby Berger,et al.  Information measures for discrete random fields , 1998 .

[70]  Sergio Verdú,et al.  The source-channel separation theorem revisited , 1995, IEEE Trans. Inf. Theory.

[71]  Satoru Fujishige,et al.  Polymatroidal Dependence Structure of a Set of Random Variables , 1978, Inf. Control..

[73]  A. Barron THE STRONG ERGODIC THEOREM FOR DENSITIES: GENERALIZED SHANNON-MCMILLAN-BREIMAN THEOREM' , 1985 .

[74]  P. Shields The Ergodic Theory of Discrete Sample Paths , 1996 .

[75]  Toby Berger,et al.  Multiterminal source encoding with encoder breakdown , 1989, IEEE Trans. Inf. Theory.

[76]  I. Reed,et al.  Polynomial Codes Over Certain Finite Fields , 1960 .

[77]  Thomas M. Cover,et al.  A Proof of the Data Compression Theorem of Slepian and Wolf for Ergodic Sources , 1971 .

[78]  Alon Orlitsky,et al.  Worst-case interactive communication I: Two messages are almost optimal , 1990, IEEE Trans. Inf. Theory.

[79]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[80]  Francesco M. Malvestuto,et al.  Comment on "A unique formal system for binary decompositions of database relations, probability distributions, and graphs" , 1992, Inf. Sci..

[81]  Frantisek Matús,et al.  Conditional Independences among Four Random Variables II , 1995, Combinatorics, Probability and Computing.

[82]  Claude E. Shannon,et al.  Communication theory of secrecy systems , 1949, Bell Syst. Tech. J..

[83]  David J. C. MacKay,et al.  Good Error-Correcting Codes Based on Very Sparse Matrices , 1997, IEEE Trans. Inf. Theory.

[84]  Yasutada Oohama Gaussian multiterminal source coding , 1997, IEEE Trans. Inf. Theory.

[85]  Gustavus J. Simmons,et al.  Contemporary Cryptology: The Science of Information Integrity , 1994 .

[86]  Seth Zimmerman An Optimal Search Procedure , 1959 .

[87]  Shu-Teh Chen Moy,et al.  Generalizations of Shannon-McMillan theorem , 1961 .

[88]  František Matúš,et al.  Conditional Independences among Four Random Variables III: Final Conclusion , 1999, Combinatorics, probability & computing.

[89]  R. Koetter,et al.  An algebraic approach to network coding , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[90]  Douglas R. Stinson,et al.  An explication of secret sharing schemes , 1992, Des. Codes Cryptogr..

[91]  Arak M. Mathai,et al.  Basic Concepts in Information Theory and Statistics: Axiomatic Foundations and Applications , 1975 .

[92]  Jack K. Wolf,et al.  Noiseless coding of correlated information sources , 1973, IEEE Trans. Inf. Theory.

[93]  John C. Kieffer,et al.  A survey of the theory of source coding with a fidelity criterion , 1993, IEEE Trans. Inf. Theory.

[94]  Aaron D. Wyner,et al.  On source coding with side information at the decoder , 1975, IEEE Trans. Inf. Theory.

[95]  Raymond W. Yeung Local redundancy and progressive bounds on the redundancy of a Huffman code , 1991, IEEE Trans. Inf. Theory.

[96]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[97]  T. Cover,et al.  A sandwich proof of the Shannon-McMillan-Breiman theorem , 1988 .

[98]  Fang-Wei Fu,et al.  On the rate-distortion region for multiple descriptions , 2002, IEEE Trans. Inf. Theory.

[99]  Zhen Zhang,et al.  A non-Shannon-type conditional inequality of information quantities , 1997, IEEE Trans. Inf. Theory.

[100]  Stanford Goldman,et al.  Information theory , 1953 .

[101]  Wojciech Szpankowski,et al.  Asymptotic average redundancy of Huffman (and other) block codes , 2000, IEEE Trans. Inf. Theory.

[102]  Robert G. Gallager,et al.  Variations on a theme by Huffman , 1978, IEEE Trans. Inf. Theory.

[103]  Sergio Verdú,et al.  A general formula for channel capacity , 1994, IEEE Trans. Inf. Theory.

[104]  F. Matús PROBABILISTIC CONDITIONAL INDEPENDENCE STRUCTURES AND MATROID THEORY: BACKGROUND1 , 1993 .

[105]  Raymond W. Yeung,et al.  Information-theoretic characterizations of conditional mutual independence and Markov random fields , 2002, IEEE Trans. Inf. Theory.

[106]  Jorma Rissanen,et al.  Universal coding, information, prediction, and estimation , 1984, IEEE Trans. Inf. Theory.

[107]  Gregory. J. Chaitin,et al.  Algorithmic information theory , 1987, Cambridge tracts in theoretical computer science.

[108]  John T. Pinkston An application of rate-distortion theory to a converse to the coding theorem , 1969, IEEE Trans. Inf. Theory.

[109]  Te Sun Han An information-spectrum approach to source coding theorems with a fidelity criterion , 1997, IEEE Trans. Inf. Theory.

[110]  K. Chung A Note on the Ergodic Theorem of Information Theory , 1961 .

[111]  Shlomo Shamai,et al.  Systematic Lossy Source/Channel Coding , 1998, IEEE Trans. Inf. Theory.

[112]  J. Massey CAUSALITY, FEEDBACK AND DIRECTED INFORMATION , 1990 .

[113]  Stephen B. Wicker,et al.  Reed-Solomon Codes and Their Applications , 1999 .

[114]  Katalin Marton,et al.  Error exponent for source coding with a fidelity criterion , 1974, IEEE Trans. Inf. Theory.

[115]  Imre Csiszár,et al.  Arbitrarily varying channels with constrained inputs and states , 1988, IEEE Trans. Inf. Theory.

[116]  Robert G. Gallager,et al.  Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[117]  Lihua Song,et al.  Zero-error network coding for acyclic network , 2003, IEEE Trans. Inf. Theory.

[118]  Alfredo De Santis,et al.  Tight Bounds on the Information Rate of Secret Sharing Schemes , 1997, Des. Codes Cryptogr..

[119]  Jr. G. Forney,et al.  The viterbi algorithm , 1973 .

[120]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[121]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[122]  Steven Roman,et al.  Coding and information theory , 1992 .

[123]  Gunter Dueck,et al.  Reliability function of a discrete memoryless channel at rates above capacity (Corresp.) , 1979, IEEE Trans. Inf. Theory.

[124]  Dake He,et al.  Efficient universal lossless data compression algorithms based on a greedy sequential grammar transform .2. With context models , 2000, IEEE Trans. Inf. Theory.

[125]  Shuo-Yen Robert Li,et al.  Linear network coding , 2003, IEEE Trans. Inf. Theory.

[126]  Gregory J. Chaitin,et al.  Algorithmic Information Theory , 1987, IBM J. Res. Dev..

[127]  Peter Elias,et al.  Universal codeword sets and representations of the integers , 1975, IEEE Trans. Inf. Theory.

[128]  Jacob Wolfowitz Coding Theorems of Information Theory , 1962 .

[129]  Raymond W. Yeung,et al.  A new outlook of Shannon's information measures , 1991, IEEE Trans. Inf. Theory.

[130]  S. Kullback,et al.  Topics in statistical information theory , 1987 .

[131]  Claude E. Shannon,et al.  The zero error capacity of a noisy channel , 1956, IRE Trans. Inf. Theory.

[132]  James L. Massey,et al.  Shift-register synthesis and BCH decoding , 1969, IEEE Trans. Inf. Theory.

[133]  Glen G. Langdon,et al.  An Introduction to Arithmetic Coding , 1984, IBM J. Res. Dev..

[134]  Amiel Feinstein,et al.  Foundations of Information Theory , 1959 .

[135]  G. David Forney,et al.  Convolutional codes I: Algebraic structure , 1970, IEEE Trans. Inf. Theory.

[136]  Claude E. Shannon,et al.  Prediction and Entropy of Printed English , 1951 .

[137]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[138]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[139]  D. Blackwell,et al.  The Capacities of Certain Channel Classes Under Random Coding , 1960 .

[140]  Hu Kuo Ting,et al.  On the Amount of Information , 1962 .

[141]  Elwyn R. Berlekamp,et al.  Key Papers in the Development of Coding Theory , 1974 .

[142]  Douglas R. Stinson,et al.  New General Lower Bounds on the Information Rate of Secret Sharing Schemes , 1992, CRYPTO.

[143]  Jim K. Omura,et al.  A coding theorem for discrete-time sources , 1973, IEEE Trans. Inf. Theory.

[144]  Lee D. Davisson,et al.  Universal noiseless coding , 1973, IEEE Trans. Inf. Theory.

[145]  Alon Orlitsky,et al.  Worst-case interactive communication - II: Two messages are not optimal , 1991, IEEE Trans. Inf. Theory.

[146]  Aleksandr Yakovlevich Khinchin,et al.  Mathematical foundations of information theory , 1959 .

[147]  D. Ornstein Bernoulli shifts with the same entropy are isomorphic , 1970 .

[148]  Toby Berger,et al.  Rate distortion theory : a mathematical basis for data compression , 1971 .

[149]  Rudolf Ahlswede,et al.  Source coding with side information and a converse for degraded broadcast channels , 1975, IEEE Trans. Inf. Theory.

[150]  Solomon Kullback,et al.  Information Theory and Statistics , 1960 .

[151]  Andrei N. Kolmogorov,et al.  On the Shannon theory of information transmission in the case of continuous signals , 1956, IRE Trans. Inf. Theory.

[152]  Raymond W. Yeung,et al.  Multi-way alternating minimization , 1995, Proceedings of 1995 IEEE International Symposium on Information Theory.

[153]  J. Wolfowitz The coding of messages subject to chance errors , 1957 .

[154]  Raymond W. Yeung,et al.  Multilevel diversity coding with distortion , 1995, IEEE Trans. Inf. Theory.

[155]  Leon Gordon Kraft,et al.  A device for quantizing, grouping, and coding amplitude-modulated pulses , 1949 .

[156]  Elwyn R. Berlekamp,et al.  Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. II , 1967, Inf. Control..

[157]  B. McMillan The Basic Theorems of Information Theory , 1953 .

[158]  James M. Ooi Coding for Channels with Feedback , 1998 .

[159]  E. Jaynes On the rationale of maximum-entropy methods , 1982, Proceedings of the IEEE.

[160]  R. Gallager Information Theory and Reliable Communication , 1968 .

[161]  Rodney W. Johnson,et al.  Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy , 1980, IEEE Trans. Inf. Theory.

[162]  Jorma Rissanen,et al.  Generalized Kraft Inequality and Arithmetic Coding , 1976, IBM J. Res. Dev..

[163]  R. Blahut Theory and practice of error control codes , 1983 .

[164]  Y. Kakihara Abstract Methods in Information Theory , 1999 .

[165]  Richard E. Blahut Information bounds of the Fano-Kullback type , 1976, IEEE Trans. Inf. Theory.

[166]  Alfredo De Santis,et al.  On the size of shares for secret sharing schemes , 1991, Journal of Cryptology.

[167]  Te Sun Han,et al.  A unified achievable rate region for a general class of multiterminal source coding systems , 1980, IEEE Trans. Inf. Theory.

[168]  Joven Dj Golic Noiseless Coding for Multiple Channels , 1994 .

[169]  H. Chernoff A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations , 1952 .

[170]  Te Sun Han,et al.  Linear Dependence Structure of the Entropy Space , 1975, Inf. Control..

[171]  Edward C. van der Meulen,et al.  A survey of multi-way channels in information theory: 1961-1976 , 1977, IEEE Trans. Inf. Theory.

[172]  L. Breiman The Individual Ergodic Theorem of Information Theory , 1957 .

[173]  Philippe Jacquet,et al.  Entropy Computations via Analytic Depoissonization , 1999, IEEE Trans. Inf. Theory.

[174]  Raymond W. Yeung,et al.  Symmetrical multilevel diversity coding , 1997, IEEE Trans. Inf. Theory.

[175]  David Slepian,et al.  Key papers in the development of information theory , 1974 .

[176]  Andrei N. Kolmogorov,et al.  Logical basis for information theory and probability theory , 1968, IEEE Trans. Inf. Theory.

[177]  Bruce Hajek,et al.  A Decomposition Theorem for Binary Markov Random Fields , 1987 .

[178]  Aaron D. Wyner,et al.  Claude Elwood Shannon: Collected Papers , 1993 .

[179]  J. Laurie Snell,et al.  Markov Random Fields and Their Applications , 1980 .

[180]  J. Berstel,et al.  Theory of codes , 1985 .

[181]  Rudolf Ahlswede,et al.  Some properties of fix-free codes , 1996 .

[182]  Sergio Verdú,et al.  The role of the asymptotic equipartition property in noiseless source coding , 1997, IEEE Trans. Inf. Theory.

[183]  William J. McGill Multivariate information transmission , 1954, Trans. IRE Prof. Group Inf. Theory.

[184]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[185]  N. Sloane,et al.  Obituary: Claude Shannon (1916–2001) , 2001, Nature.

[186]  R. Gray Entropy and Information Theory , 1990, Springer New York.

[187]  van Me Marten Dijk Secret key sharing and secret key generation , 1997 .

[188]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[189]  G. Jones,et al.  Information and Coding Theory , 2000 .

[190]  Terry A. Welch,et al.  A Technique for High-Performance Data Compression , 1984, Computer.

[191]  D. TER HAAR J. A. Wheeler , 1973, Nature.

[192]  Fazlollah M. Reza,et al.  Introduction to Information Theory , 2004, Lecture Notes in Electrical Engineering.