# Communication in the Presence of Noise [ Bell Monograph Issue ]

New York, NY: Bell Telephone Laboratories 1949. Later printing. 1-12 pages. 8 1/2 x 11 inches. Publisher's printed grey, blue and black wrappers. 5 hole punched at the spine as issued. Ex-library stamp on front cover dated Aug 11, 1949. Otherwise unmarked. Bell Telephone System Technical Publications, Monograph # B-1644. Near Fine. Wraps. [25294]

*“In 1948, C. E. Shannon … published his classic paper 'A Mathematical Theory of Communication' in the Bell System Technical Journal. [That first] paper founded the discipline of information theory [ appearing in two parts ]... Several months later, he published a second paper 'Communication in the Presence of Noise,” in 'The Proceedings of the Institute of Radio Engineers'. This second paper is ...intimately connected to the earlier classic paper. In fact, since a large part of the material in the second paper is essentially an elaboration of matters discussed in the first...it can be thought of an elaboration and extension of the earlier paper, adopting an 'engineering' rather than [a] strict mathematical point of view. Yet, this [second] paper comprises ideas, notions, and insights that were not reported in the first paper. In retrospect, many of the concepts treated in this [second paper ] proved to be fundamental, and they paved the way for future developments in information theory.
The focus of Shannon's paper is on the transmission of continuous-time (or 'waveform') sources over continuous time channels. Using the sampling theorem, Shannon shows how waveform signals can be represented by vectors in finite-dimensional Euclidean space. He then exploits this representation to establish important facts concerning communication of a waveform source over a waveform channel in the presence of waveform noise. In particular, he gives a geometric proof of the theorem that establishes the famous formula W log (1 + S) for the capacity of a channel with bandwidth W, additive thermal (ie Gaussian) noise, and signal-to-noise ratio S...
One of the most profound ideas is coding waveforms with respect to a reconstruction fidelity criterion. These ideas, which later matured as the rate-distortion theory, provide the theoretical basis to quantization of analog signals (for example, speech coding,vector quantization and the like) which now are ubiquitous in our everyday life (cellular phones for example). Shannon's ideas, described in this paper in a lucid engineering fashion and complementing his celebrated work [Mathematical Theory of Communication] which established the field of information theory, affected in a profound fashion the very thinking on the structure, components, design and analysis of communication systems in general...These ideas of Shannon's had an influence well beyond the technical professional world of electronics engineering and mathematicians” (Wyner2)
The first theorem in this paper is "The Sampling Theorem" : "If a function f(t) contains no frequencies higher than W cps, it is completely determined by giving its ordinates at a series of points spaced 1/2W seconds apart". Shannon immediately notes "This is a fact which is common knowledge in the communication art." Later he adds "Theorem 1 has been given previously in other forms by mathematicians but in spite of its evident importance seems not to have appeared explicitly in the literature of communication theory." He goes on to credit work by Whittaker, Nyquist, and Gabor. It is apparent that after Shannon's publication of this pair of Shannon's papers the eponymous "Shannon's Sampling Theorem" gained traction in the engineering community. This cataloger has heard from multiple modern day engineers that they utilize Shannon's work daily.
A fundamentally important paper.
The original manuscript of this paper was received by the Institute of Radio Engineers July 23, 1940. It was presented at the IRE National Convention in New York on March 24, 1948 and November 12, 1947 (IRE New York Section). It was first published in the Proceedings of the Institute of Radio Engineers, Volume 37, pp 10-21 in January 1949, for which an offprint was issued.
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Literature:
(Wyner1) Sloane and Wyner, "Claude Elwood Shannon Collected Papers", #43 (referring to the IRE first publication).
(Wyner2) Wyner, Aaron D. and Shlomo Shamai (Shitz), "Introduction to 'Communication in the Presence of Noise' by C. E. Shannon", Proceedings of the IEEE, Vol 86, No 2, Feb 1998
Reprinted in D. Slepian, editor, "Key Papers in the Development of Information Theory", IEEE Press, NY, 1974, pp 30-41.
COLLECTORS NOTE: The Monograph series was an organ for publishing the work of Bell System scientists whether first published in another Bell System publication or in another journal. Often (but not always as in this case) the Monographs are the first separate edition of a paper. Not all Bell Lab scientist papers appeared in this series, but the series was subscribed to by major institutions and companies interested in Bell Laboratories advances in an effort to publicize important Bell System work to a wider audience.*

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