Communication in the Presence of Noise [IRE offprint]

[New York]: [The Institute of Radio Engineers, Inc.], 1949. First Separate Edition. Wraps. Good. First Separate Edition. [9]-22 pages. 11 x 8 1/2 inches. Self-wrappers, last page (rear cover) blank. Two staples near spine printed on buff paper. Light soiling and creasing to wrappers. Thumbing crease. Staples rusted. Wraps. Shannon presented this paper at the IRE National Convention, New York, N. Y. on March 24, 1948, and IRE New York Section on November 12, 1947. The Institute of Radio Engineers received the original manuscript of this paper on July 23, 1940 [sic 1948?]. The "Proceedings of the Institute of Radio Engineers" (Volume 37, pp 10-21, January 1949) first published this paper. Here offered in the offprint form. The Bell System Technical Monograph series (#B-1644: 1949) later reprinted this paper.

"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 ... 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 as an elaboration and extension of the earlier paper, adopting an 'engineering' rather than 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 the 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 (i.e., 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 quickly notes, "This is a fact which is common knowledge in the communication art." He later 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." Shannon takes care to credit the previous work of Whittaker, Nyquist, and Gabor. After the publication of this pair of papers, the phrase "Shannon's Sampling Theorem" gained traction in the engineering community.

A fundamentally important paper.

PROVENANCE: The personal files of Claude E. Shannon (unmarked). The last decent copy of five examples found in Shannon's files.

REFERENCES:
(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," in Proceedings of the IEEE, Vol 86, No 2, Feb 1998
D. Slepian, editor, "Key Papers in the Development of Information Theory," IEEE Press, NY, 1974, pp 30-41.