**1948 __ « A Mathematical Theory of Communication »**

‣ *Comment* : Claude Shannon at Bell Laboratories publishes a paper on A Mathematical Theory of Communications, which postulates that if all telecommunications messages were in the form of binary digits, which Shannon calls bits, it would be possible to separate the medium and the message, allowing telecom engineers to concentrate on the means of delivery for all types of message, without concern for the content of the message. *(Compiled from various sources)*

‣ *French comment* : Pour décrire la communication entre machines, l'article de 1948 et le livre de 1949 commencent tous deux par un « schéma » qui connut dès lors une postérité étonnante en Sciences de l'information et de la communication, au point que Shannon s'en étonna et s'en dissocia. Le schéma modélise la communication entre machines : Ce schéma est la traduction « civile » d'un schéma préalable, utilisé dans le contexte militaire : source → encodeur → signal → décodeur → destinataire, dans un contexte de brouillage. *(Compiled from various sources)*

‣ *Original excerpt * : « The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one “selected from a set” of possible messages. The system must be designed to operate for each possible selection, not just the one which will actually be chosen since this is unknown at the time of design. If the number of messages in the set is finite then this number or any monotonic function of this number can be regarded as a measure of the information produced when one message is chosen from the set, all choices being equally likely. As was pointed out by Hartley the most natural choice is the logarithmic function. Although this definition must be generalized considerably when we consider the influence of the statistics of the message and when we have a continuous range of messages, we will in all cases use an essentially logarithmic measure. [...] By a communication system we will mean a system of the type indicated schematically in Fig. 1. It consists of essentially five parts: (1) An “information source” which produces a message or sequence of messages to be communicated to the receiving terminal. The message may be of various types: (a) A sequence of letters as in a telegraph of teletype system; (b) A single function of time f t as in radio or telephony; (c) A function of time and other variables as in black and white television. — here the message may be thought of as a function f x y t of two space coordinates and time, the light intensity at point x y and time t on a pickup tube plate; (d) Two or more functions of time, say f t , g t , h t. — this is the case in “three- dimensional” sound transmission or if the system is intended to service several individual channels in multiplex; (e) Several functions of several variables. — in color television the message consists of three functions f x y t , g x y t , h x y t defined in a three-dimensional continuum. — we may also think of these three functions as components of a vector field defined in the region. — similarly, several black and white television sources would produce “messages” consisting of a number of functions of three variables; (f) Various combinations also occur, for example in television with an associated audio channel. (2) A “transmitter” which operates on the message in some way to produce a signal suitable for transmission over the channel. In telephony this operation consists merely of changing sound pressure into a proportional electrical current. In telegraphy we have an encoding operation which produces a sequence of dots, dashes and spaces on the channel corresponding to the message. In a multiplex PCM system the different speech functions must be sampled, compressed, quantized and encoded, and finally interleaved properly to construct the signal. Vocoder systems, television and frequency modulation are other examples of complex operations applied to the message to obtain the signal. (3) The “channel” is merely the medium used to transmit the signal from transmitter to receiver. It may be a pair of wires, a coaxial cable, a band of radio frequencies, a beam of light, etc. (4) The “receiver” ordinarily performs the inverse operation of that done by the transmitter, reconstructing the message from the signal. (5) The “destination” is the person (or thing) for whom the message is intended. We wish to consider certain general problems involving communication systems. To do this it is first necessary to represent the various elements involved as mathematical entities, suitably idealized from their physical counterparts. We may roughly classify communication systems into three main categories: discrete, continuous and mixed. By a discrete system we will mean one in which both the message and the signal are a sequence of discrete symbols. A typical case is telegraphy where the message is a sequence of letters and the signal a sequence of dots, dashes and spaces. A continuous system is one in which the message and signal are both treated as continuous functions, e.g., radio or television. A mixed system is one in which both discrete and continuous variables appear, e.g., PCM transmission of speech. We first consider the discrete case. This case has applications not only in communication theory, but also in the theory of computing machines, the design of telephone exchanges and other fields. — PART I: DISCRETE NOISELESS SYSTEMS. — 1 . THE DISCRETE NOISELESS CHANNEL. — [...] We can think of a discrete source as generating the message, symbol by symbol. It will choose successive symbols according to certain probabilities depending, in general, on preceding choices as well as the particular symbols in question. A physical system, or a mathematical model of a system which produces such a sequence of symbols governed by a set of probabilities, is known as a stochastic process. We may consider a discrete source, therefore, to be represented by a stochastic process. Conversely, any stochastic process which produces a discrete sequence of symbols chosen from a finite set may be considered a discrete source. [...] — PART II: THE DISCRETE CHANNEL WITH NOISE. — 11 . REPRESENTATION OF A NOISY DISCRETE CHANNEL. — We now consider the case where the signal is perturbed by noise during transmission or at one or the other of the terminals. This means that the received signal is not necessarily the same as that sent out by the transmitter. Two cases may be distinguished. If a particular transmitted signal always produces the same received signal, i.e., the received signal is a definite function of the transmitted signal, then the effect may be called distortion. If this function has an inverse. — no two transmitted signals producing the same received signal. — distortion may be corrected, at least in principle, by merely performing the inverse functional operation on the received signal. [...] »

‣ *Source* : *Shannon, Claude E. (1948), “A Mathematical Theory of Communication”, Bell System Technical Journal, vol. 27, p. 379-423 and 623-656, July and October, 1948.*

‣ *Source* : *Shannon, Claude E. (1949), “Communication Theory of Secrecy Systems”, Bell System Technical Journal, Vol 28, p. 656-715, Oct 1949.*

‣ *Urls* : http://pespmc1.vub.ac.be/books/Shannon-TheoryComm.pdf (last visited )

**No comment for this page**