The Mathematical Theory of Communication
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- Create Date：2021-05-05 11:58:34
- Update Date：2025-09-06
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- Author：Claude Shannon
- ISBN：0252725484
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Summary
Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication， published originally as a paper on communication theory in the Bell System Technical Journal more than fifty years ago。 Republished in book form shortly thereafter， it has since gone through four hardcover and sixteen paperback printings。 It is a revolutionary work， astounding in its foresight and contemporaneity。 The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic。
Reviews
Peter Sahlstrom
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（I actually read the original paper here: http://people。math。harvard。edu/~ctm/h。。。）I feel like I finally understand entropy as a concept in information theory， and also have a better appreciation for entropy as a probabilistic concept in thermodynamics。 I skimmed most of the calculus， and almost all of the "continuous domain" material - I'm not seeking to apply this generally， but just to gain a more intuitive sense of channel capacity， noise， error reduction， etc， as general concepts in informa （I actually read the original paper here: http://people。math。harvard。edu/~ctm/h。。。）I feel like I finally understand entropy as a concept in information theory， and also have a better appreciation for entropy as a probabilistic concept in thermodynamics。 I skimmed most of the calculus， and almost all of the "continuous domain" material - I'm not seeking to apply this generally， but just to gain a more intuitive sense of channel capacity， noise， error reduction， etc， as general concepts in information transfer。 。。。more
Christine Frank
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Read now
Nick Geiser
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Warren Weaver on Shannon's paper: "[the theory] is exceedingly general in its scope， fundamental in the problems it treats， and of classic simplicity and power in the results it reaches。" The book contains Shannon's paper along with a very helpful introductory essay by Warren Weaver that explains its significance in clear， non-technical terms。 On the face of it， Shannon's argument deals 'merely' with what Weaver calls the "technical problem" of communication: the problem of accurately transmitti Warren Weaver on Shannon's paper: "[the theory] is exceedingly general in its scope， fundamental in the problems it treats， and of classic simplicity and power in the results it reaches。" The book contains Shannon's paper along with a very helpful introductory essay by Warren Weaver that explains its significance in clear， non-technical terms。 On the face of it， Shannon's argument deals 'merely' with what Weaver calls the "technical problem" of communication: the problem of accurately transmitting symbols from a sender to a receiver。 However， the other， more "interesting" problems of communication all presuppose a solution to the technical problem， and Shannon showed what the range of possible solutions to the technical problem could be。Regarding the math， Parts I and II of Shannon's essay （where the core theorems for a noiseless/noisy channel are proved） is uses only algebra and precalc。 Part III onward extends the argument to a continuous information source/channel and uses multivariable calculus--having taken my last calculus class over ten years ago I admit I skimmed these parts。 。。。more
Mateo Jaramillo
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Debido a mis limitaciones en cuanto concierne el conocimiento de la matemática， la física， y en general los sistemas eléctricos o de telecomunicaciones， tuve una especial preferencia por la primera parte de este texto， sintetizado de manera digerible y magnífica por Warren Weaver。 Nos ofrece un acercamiento cercano tanto de las premisas básicas de la teoría matemática de la comunicación， como de algunas implicaciones para considerar la comunicación en general。 Es sobre ésta primera parte que emi Debido a mis limitaciones en cuanto concierne el conocimiento de la matemática， la física， y en general los sistemas eléctricos o de telecomunicaciones， tuve una especial preferencia por la primera parte de este texto， sintetizado de manera digerible y magnífica por Warren Weaver。 Nos ofrece un acercamiento cercano tanto de las premisas básicas de la teoría matemática de la comunicación， como de algunas implicaciones para considerar la comunicación en general。 Es sobre ésta primera parte que emito mi juicio， puesto que fue el umbral con tapete de "bienvenida" que permitió la comprensión de la teoría。 Y es por ello que resalto el trabajo de Weaver en esta obra， la cual leí gratamente。 Gracias Shannon， pero sobre todo， gracias Weaver。 。。。more
Richie Cartwright
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too tough for me
Peter
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Rare example where the founder of a field of study also wrote one of the best books on the subject。
Synaps
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This scientific book is a historical artefact in its own right。 The math is lost on the lay reader， but an accessible foreword clues us on concepts central to understanding communication: bits， channel， noise， and entropy， which is another way of saying that information is order。
Koen Crolla
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This is one of those fundamental papers that everyone should read at least once。 It's perhaps not quite as stunningly original as people often claim it is （like everything， it builds on earlier work by other people， and Shannon never pretends otherwise）， but it has been genuinely revolutionary to our ability to reason about information to the point that many of its theorems are now so fundamental that most people have an intuitive understanding of them which， incidentally， also makes the paper m This is one of those fundamental papers that everyone should read at least once。 It's perhaps not quite as stunningly original as people often claim it is （like everything， it builds on earlier work by other people， and Shannon never pretends otherwise）， but it has been genuinely revolutionary to our ability to reason about information to the point that many of its theorems are now so fundamental that most people have an intuitive understanding of them which， incidentally， also makes the paper much more accessible than it would have been at the time it was written—you'll need a little bit of calculus for the continuous stuff， but the discrete portion is intuitive to anyone who's ever used a computer。Is it the best first introduction to the field of information theory？ No， of course—it was written too early， and Shannon doesn't yet fully understand all the ways in which it is important （Weaver's additional introduction， which aims， with moderate success， to provide an overview more accessible to the general public， even less） and there are important pieces still missing。 But it is an easy read and a short one and an extremely important foundational work that is well worth anyone's time。 。。。more
José
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Excelente！ Abre una forma de ver la comunicación desde una perspectiva de la ingeniería de mucho sentido， aunque a veces no es muy fácil seguir toda la matemática de las demostraciones sin detenerse en mucho detalle。
Armin
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This book probably deserves a smarter reader than me。 I picked this up via the recommendation of the CEO of Neuralink in their recent announcements as a ‘very readable’ book， knowing that it might get into maths。 I like math， but in the end for my way too many formulas in the book， so stopped reading。 I read the long first part and foreward by Weaver， which is much more approachable in my mind， and learned some great basic concepts of communication channels and language。
Alexey
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Interesting but requires deep knowledgeInteresting from the point of view of history of ideas and yet too complicated。 Mathematics required to fully appreciate the book
Michael J。 Flynn
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One of the most interesting， straightfoward books i have ever read。 The cornerstone work to telecommunications and far beyond。。。
Juan Carlos Ayala Perdomo
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Posiblemente uno de los papers más influyentes del siglo XX。 Posiblemente la fundación de la ciencia informática como se conoce y vive en el siglo XXI。 Posiblemente uno de los libros más fundamentales， y sin embargo， menos leídos en la Ciencia de la Comunicación y la Información。 Porque， Claude Shannon， genial， ha dejado claro que la información no es el mensaje ni el significado。 Es la medida de la libertad de elección entre bits。 Es la posibilidad。 Es entropía。 Es ruido。 Es posibilidad en los Posiblemente uno de los papers más influyentes del siglo XX。 Posiblemente la fundación de la ciencia informática como se conoce y vive en el siglo XXI。 Posiblemente uno de los libros más fundamentales， y sin embargo， menos leídos en la Ciencia de la Comunicación y la Información。 Porque， Claude Shannon， genial， ha dejado claro que la información no es el mensaje ni el significado。 Es la medida de la libertad de elección entre bits。 Es la posibilidad。 Es entropía。 Es ruido。 Es posibilidad en los confines de la capacidad de transmisión de los canales， tal como Warren Weaver lo acerca a los dominios， siempre apenas posibles， de las Ciencias Sociales。 。。。more
Peter Aronson
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Well， on this re-read I made an effort to read the whole thing。 On my previous read， I think I just read Weaver's introduction， then skimmed Shannon's paper， which isn't the best way to get the most out of this book。 Weaver's introduction is useful， but his three levels of communications is rather besides the point of the main paper， and his prose is rather dry and torturous。 Shannon's paper， is， of course， the meat of this book， and is truly seminal。 I was able to make my way pretty well throug Well， on this re-read I made an effort to read the whole thing。 On my previous read， I think I just read Weaver's introduction， then skimmed Shannon's paper， which isn't the best way to get the most out of this book。 Weaver's introduction is useful， but his three levels of communications is rather besides the point of the main paper， and his prose is rather dry and torturous。 Shannon's paper， is， of course， the meat of this book， and is truly seminal。 I was able to make my way pretty well through the chapters on discrete systems， but the chapters on continuous systems went pretty much over my head， except for an occasional non-mathematical fact。 But I read them anyways， even the equations， and did my best to puzzle them out。 But fortunately I work in a pretty much discrete （digital） world and can leave the continuous stuff to those engineers working on the lowest level of communications systems。 。。。more
VLT
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Way over my head， but sheds light on the basis of cryptographic analysis。 The idea of redundancy in language is fascinating。 Increase redundancy and 3 dimensional crossword puzzles are possible; decrease it and 2D crosswords become impossible。 What are the redundancies of other languages？ Has this been studied？
Mouna boumezbeur
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A MUST READ <3
Kevin
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The Mathematical Theory of Communication is a rigorous explanation of Digital Communication theory， or how a procedure generated and transmitted from one entity to another effects the state of the auxiliary system。Shannon partitions the essential elements of communication into these primary buckets: sources， source encoders， channel encoders， channels， and associated channel and source decoders。 Shannon also covers concept such as noise （or 'entropy'）， which probabilisticaly affects the set of i The Mathematical Theory of Communication is a rigorous explanation of Digital Communication theory， or how a procedure generated and transmitted from one entity to another effects the state of the auxiliary system。Shannon partitions the essential elements of communication into these primary buckets: sources， source encoders， channel encoders， channels， and associated channel and source decoders。 Shannon also covers concept such as noise （or 'entropy'）， which probabilisticaly affects the set of included information during transmission in a channel。As defined by Shannon， the fundamental problem with communication is how to reproduce at one point exactly or approximately a message selected at another point。 As explained by Weaver， Claude Shannon attempts to resolve three primary problems with this essay。 First， how accurately can the symbols of communication be transmitted from one system to another。 Second， how do transmitted symbols carry the desired meaning （transmission or decoding problem）。 And third， how effective is the the transmitted message at altering conduct in the desired way？In the paper， Shannon moves from the simple scenario to the complex， starting with a mathematical formalization of messages transmitted across noiseless， discrete systems - before defining the addition noise and continuous information。Having recently studied Hoffstader's "Godel， Escher， Bach - an Eternal Golden Braid"， I was especially interested as to how the interaction between external/tangent formal information systems （such as the set of real numbers， mu theory， etc。） may be generated and effect each other。I found this paper to be especially valuable in building my understanding of core concepts within mathematical communication theory （specifically concepts like entropy， ergodicity， redundancy of communicatory set， etc。）。After reading the paper， I find it interesting interesting to look for stochastic processes， Markoff threads， and ergodicity within informatic systems。 Ergodic systems have a sort of fractal probability to them where statistical trends of high sample significance may be generalized as an attribute of the entire system itself。I highly recommend this book if you have any interest in the academic understanding of how formal information systems interact and affect each other's state。 This book sets the standard for rigorous analysis of binary communication， with a ruthless focus on the statistical efficiency of information transmission （given channel noise， etc。）。 。。。more
Olmedo Vogue
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Mathematics is very important in the school。But is really difficult。
Alex
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A bit too technical for my abilities
Michal
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This is truly one of the most important and groundbreaking works of modern science。 Shannon dared to introduce the notion of information as a measurable， quantifiable property of signals and has developed a powerful and surprisingly simple framework to describe it。 A must read for anyone seriously interested in science and engineering and likely a compulsory reading for anyone in information engineering field。
Mitchell
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This is the theory that created the foundation for how "information" became associated with the aggregation of data， and how the gleaning of information from the randomness of data was a measure of order。 Critical for information theorists and those interested in understanding the separation between information as a concept of meaning， and information as "probabilities" that delimit the number of arrangements of data into intelligible construction。 This is the theory that created the foundation for how "information" became associated with the aggregation of data， and how the gleaning of information from the randomness of data was a measure of order。 Critical for information theorists and those interested in understanding the separation between information as a concept of meaning， and information as "probabilities" that delimit the number of arrangements of data into intelligible construction。 。。。more
Emre Sevinç
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There isn't much to add: this is one of the classics and if you have any serious interest in the topic， you owe yourself to read this at least twice。 There isn't much to add: this is one of the classics and if you have any serious interest in the topic， you owe yourself to read this at least twice。 。。。more
Alex
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Very informative and relatively understandable， particularly with Weaver's introduction as an aid。 The concepts of ergodicity and information transfer as a probabilistic symbolic state machine come across clearly without needing to understand difficult mathematical proofs。 The notion outlined by Weaver of the extension of some fundamental principles across all three "levels" of communication I also found to be extremely interesting， and reading through Shannon's paper made them all the more conv Very informative and relatively understandable， particularly with Weaver's introduction as an aid。 The concepts of ergodicity and information transfer as a probabilistic symbolic state machine come across clearly without needing to understand difficult mathematical proofs。 The notion outlined by Weaver of the extension of some fundamental principles across all three "levels" of communication I also found to be extremely interesting， and reading through Shannon's paper made them all the more convincing despite Shannon's focus primarily on the mechanics of signal transfer。 。。。more
Jake
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“It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge。” ~Pierre-Simon Laplace Théorie Analytique des Probabilitiés （1812）Human communication is a dichotomy between chaos and statistical dependencies。 Letters in words are， obviously， in some way dependent upon the previous letters in their sequence。 These collections of letters congregate together in different combinations to form words and those word “It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge。” ~Pierre-Simon Laplace Théorie Analytique des Probabilitiés （1812）Human communication is a dichotomy between chaos and statistical dependencies。 Letters in words are， obviously， in some way dependent upon the previous letters in their sequence。 These collections of letters congregate together in different combinations to form words and those words form sentences。 Shannon， quite beautifully and too the point， explores in this dissertation how we might use markov models to imitate such dependencies。 This imitation would lead his conception of entropy in communication or simply put the amount of average disorder in sequences of letters。Here is an excerpt from Emma by Jane Austen， let us explore what I just talked about:Emma Woodh*use， hands*me， clever* and rich，*with a comfortab*e home an* happy di*position，*seemed to*unite som* of the b*st blessings of e*istence;*and had *ived nea*ly twenty-*ne year* in the*world w*th very*little *o distr*ss or vex*her。*he was the you*gest *f the *wo dau*hters *f a most *ffect*onate* indu*gent *ather* and *ad， i* cons*quence*of h*r si*ter'* mar*iage* bee* mis*ress*of h*s ho*se f*om a ver* ea*ly *eri*d。 *er *oth*r h*d d*ed *oo *ong*ago*for*her*to ha*e *or* t*an an in*is*in*t *em*mb*an*e *f *er ca*es*es* a*d h*r p*a*e h*d b*e* *u*p*i*d *y *n e*c*l*e*t w***n a* g*v*****s， w** h** f****n l**t** s***t *f a m****r i* a*******n。You， the reader， like most humans can deal with some deletion because you are doing a probabilistic judgement in your head to fill in that which letters were taken away。 As you make your way down the text， disorder is introduced gradually and the deletion becomes untenable for most。 This is due to the fact that more information is being obscured in the system and with less information to act on your probabilistic judgments become harder and harder to make。 The more uncertainty present in a string of letters， by the previous reasoning， leads us to see that that same string carries more information than strings of less uncertainty。 The infamous unit that Shannon comes to in this paper is of course the bit， which is our quantitative measure of information but in reality is a measure of surprise。 Entropy is maximized when all outcomes are equally likely。 Each time we move away from equally likely outcomes we introduce predictability into the system， allowing us to ask fewer binary questions to convey the same amount of information。‘Your act was unwise，’ I exclaimed ‘as you see by the outcome。’ He solemnly eyed me。‘When choosing the course of my action，’ said he，‘I had not the outcome to guide me。’ ~ Ambrose Bierce 。。。more
Roberto Rigolin F Lopes
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Weaver started strong describing the breakthroughs， pretty exciting intro。 Discrete channels are palatable anywhere， but the continuous ones are tricky。 Okay， perhaps I had a "noisy" channel while reading Shannon's ideas。 Don't try to read it in public places :D Weaver started strong describing the breakthroughs， pretty exciting intro。 Discrete channels are palatable anywhere， but the continuous ones are tricky。 Okay， perhaps I had a "noisy" channel while reading Shannon's ideas。 Don't try to read it in public places :D 。。。more
dead
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It's kind of hard to review this - it's a very good book and more accessible than I expected。 Very short and lucid but kinda profound in its impact？ I guess I can see the reason the title went from "A Mathematical Theory of Communication" to "The Mathematical Theory Of Communication" It's kind of hard to review this - it's a very good book and more accessible than I expected。 Very short and lucid but kinda profound in its impact？ I guess I can see the reason the title went from "A Mathematical Theory of Communication" to "The Mathematical Theory Of Communication" 。。。more
Leonardo
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Entropía de Shannon。
William Schram
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This book contains the landmark paper called "The Mathematical Theory of Communication" written by Claude E。 Shannon back in 1948。 In it are the equations that define channel capacity and other such things。 It is quite interesting， since the first part contains some additional information written by Warren Weaver。 The book itself contains some mathematics， as you might be able to tell from the title of the book。 There are some logarithms in there and some Calculus， so it isn't for those that des This book contains the landmark paper called "The Mathematical Theory of Communication" written by Claude E。 Shannon back in 1948。 In it are the equations that define channel capacity and other such things。 It is quite interesting， since the first part contains some additional information written by Warren Weaver。 The book itself contains some mathematics， as you might be able to tell from the title of the book。 There are some logarithms in there and some Calculus， so it isn't for those that despise math。 However， as I said， the initial part by Weaver does explain some of the implications of Shannon's findings without going into the math part of it。Would definitely read again if given the time。 。。。more
Mengsen Zhang
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Great book！ Satisfied my morbid habit of reading classics off a book-like object。 Weaver's encapsulating article was a wonderful surprise and nice guidance。 And of course Shannon- such a beautiful mind！！ Most impressed with the way he unfolded his logic， also his mastery of the art of using examples and diagrams。 Nonetheless， for someone who's not very familiar with math， some continuous signal sections created lots of hair pulling moments， but I eventually pulled through。。。。 anyways， it clarifi Great book！ Satisfied my morbid habit of reading classics off a book-like object。 Weaver's encapsulating article was a wonderful surprise and nice guidance。 And of course Shannon- such a beautiful mind！！ Most impressed with the way he unfolded his logic， also his mastery of the art of using examples and diagrams。 Nonetheless， for someone who's not very familiar with math， some continuous signal sections created lots of hair pulling moments， but I eventually pulled through。。。。 anyways， it clarified some of my metaperception about communication in terms of perturbation， resonance， and delay。 。。。more
catharine
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