SHANNON, C.E.

Probability Error for Optimal Codes in a Gaussian Channel.

(New York), American Telephone and Telegraph Compagny, 1959. 8vo. In the original blue printed wrappers. In "The Bell System Technical Journal", Volume 38, Number 3, pp. Light miscolouring to spine, otherwise a very fine, clean and fresh copy. Pp. 611-656. [Entire volume: Pp. 611-907].

First printing of Shannon's important 1959-paper in which he showed that an optimal code is built by uniformly placing codewords on an n-dimensional sphere. An upper and a lower bound for the word error rate performance Pew of such a spherical code have been established by Shannon on an
AWGN channel for finite n.

"A study is made of coding and decoding systems for a continous channel with an additive gaussian noise and subject to an average power limitation at the transmitter. Upper and lower bounds are found for the error probability in decoding with optimal codes and decoding systems. These bounds are close together for signaling rates near channel capacity and also for signaling rates near zero, but diverge in between. Curves exhibiting these bounds are given." (Shannon p. 611).

Hook & Norman: 898.

Order-nr.: 47541