The offprint issue - one of only two copies from Shannon's files

Shannon, C. E. [Claude Elwood]; Gallager, R. G.; Berlekamp, E. R.

Lower Bounds to Error Probability for Coding on Discrete Memoryless Channels. [Part] II [offprint]

[New York, NY]: Academic Press, Inc. May 1967. [1-blank], 522-552 pages. 8 15/16 x 6 inches. Self-wrappers stapled at the spine. Very Good. Wraps. [28681]


"Information and Control," Vol 10, No 5, May 1967 (pp. 522-552) first published this paper, here offered in offprint form. Not issued with separate wrappers that we are aware of - the reprint statement is at the top of the first page.

"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 in the January issue, summarizes the major results and treats the case of high transmission rates in detail; the second, appearing here, treats the case of low transmission rates." (abstract)

This paper is the follow-up to Part I, this time dealing with low transmission rates.

PROVENANCE: The personal files of Claude E. Shannon (unmarked). One of two examples found in Shannon's files.

REFERENCES:
Sloane and Wyner, "Claude Elwood Shannon Collected Papers," #123
D. Slepian, editor, "Key Papers in the Development of Information Theory," IEEE Press, NY, 1974, pp 205-213.

Price: $500.00