An upper bound on the rate of transmission of messages
Jacob Wolfowitz · Illinois Journal of Mathematics · 1958
This paper is a sequel to an earlier one entitled The Coding of messages sub- jec o chance errors (Illinois Journal of Mathematics, vol. 1 (1957), pp.591- 606), and should be regarded as the ninth section of the latter.The previous notation, definitions, and list of references remain in force, except that it is convenient to replace p() by p(1 I) and ( 1 p(a)) by p(0 a).The pur- pose of the present paper is to state and prove Theorem 4, which, for any memory m, gives an upper bound on the length of an error correcting code for which the probability of transmitting any word incorrectly is -< k, 0 =< k 1.In Theorem 2 of the earlier paper we gave such an upper bound