C E Shannon / Lower Bounds to Error Probability for Coding on Discrete 1967

Description: The offprint formLower Bounds to Error Probability for Coding on Discrete Memoryless Channels. [Part] I [offprint] Author: Shannon, C. E. [Claude Elwood] ; Gallager, R. G. [Robert] ; Berlekamp, E. R. [Elwyn] Title: Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. [Part] I [offprint] Publication: [New York, NY]: Academic Press, Inc. February 1967 Description: 65-103, [1-blank] pages. 8 15/16 x 6 inches. Self-wrappers stapled at the spine. Very Good. Wraps. "Information and Control," Vol 10, No 1, February 1967 (pp. 65-103) first published this paper, here offered in offprint form. This offprint does not have separate wrappers that we are aware of - the reprint statement is printed upper left on the first page of the paper."The noisy channel coding theorem (Shannon, 1948) states that for a broad class of communication channels, data can be transmitted over the channel in appropriately coded form at any rate less than channel capacity with arbitrarily small error probability. Naturally, there is a rub in such a delightful sounding theorem, and the rub here is that the error probability can, in general, be made small only by making the coding constraint length large; this, in turn, introduces complexity into the encoder and decoder. Thus, if one wishes to employ coding on a particular channel, it is of interest to know not only the capacity but also how quickly the error probability can be made to approach zero with increasing constraint length..." (pp.65-66)"New lower bounds are presented for the minimum error probability that can be achieved through the use of block coding on noisy discrete memoryless channels. Like previous upper bounds, these lower bounds decrease exponentially with the block length N. The coefficient of N in the exponent is a convex function of the rate. From a certain rate of transmission up to channel capacity, the exponents of the upper and lower bounds coincide. Below this particular rate, the exponents of the upper and lower bounds differ, although they approach the same limit as the rate approaches zero. Examples are given, and various incidental results and techniques relating to coding theory are developed. The paper is presented in two parts: the first, appearing here, summarizes the major results and treats the case of high transmission rates in detail; the second, to appear in the subsequent issue, treats the case of low transmission rate." (abstract)PROVENANCE: The personal files of Claude E. Shannon (unmarked). There were multiple examples of this item in Shannon's files.REFERENCES:Sloane and Wyner, "Claude Elwood Shannon Collected Papers," #122Reprinted in D. Slepian, editor," Key Papers in the Development of Information Theory," IEEE Press, NY, 1974, pp 194-204 Seller ID: 28680 Subject: Mathematics Kuenzig Books Topsfield MA USA Since 1996 Kuenzig Books has bought and sold rare and/or interesting items in many fields with a focus on 19th and 20th century Science, Technology, and Engineering. We are particularly interested in the History of Computing, and the speed with which the technological innovations of the 20th century have impacted the way we live. You'll discover some depth in Physics, Mathematics, Nobel Prize authors, Computing, Scientific Instruments, and Chemistry. We are members of the ABAA (Antiquarian Booksellers' Association of America), ILAB (International League of Antiquarian Booksellers), SNEAB (Southern New England Antiquarian Booksellers), and IOBA (The Independent Online Booksellers Association). We often have material not listed here, please ask if you are looking for something specific. International Buyers Please Note: Import duties, taxes, and charges are not included in the item price or shipping cost. These charges are the buyer's responsibility. Please check with your country's customs office to determine what these additional costs (if any) will be prior to bidding or buying if you are unfamiliar with this. We will not misrepresent the content or value of items on customs forms. We are not responsible for any customs delays, custom fees or any other related custom issues. Once we send shipping confirmation, be sure to check regularly with your local customs or post office to ensure that shipments are not returned "unclaimed". If packages are returned to us "unclaimed" we are happy to resend them but will require separate payment from you for the second shipping charge. Terms and Conditions If you have any questions, please ask before bidding. We package carefully so that your items get to you in the condition they were sent. We ship to PayPal verified addresses only. Any refund fees charged to us by PayPal for payments that don't match the verified addresses will be deducted from your refund. Delivery time frames can only be estimated and will depend on the service used, shipping origin, and destination. Payment All payments in US dollars. Payment must be received within 5 days. Please note that our prices on this venue are increased to reflect the fees charged here. Feedback We leave feedback for buyers once they have posted feedback for us. If you are unhappy with any aspect of a transaction with us, please contact us immediately. We work hard to keep buyers happy and to resolve the rare problem promptly. This listing was created by Bibliopolis.

Price: 403 USD

Location: Topsfield, Massachusetts

End Time: 2024-11-21T21:13:20.000Z

Shipping Cost: 6.13 USD