Absrfucr-Given two discrete memoryless channels @MC's) with a common input, it is desired to transmit private messagea to receiver 1 at r&R, andcommon meswgea to both receivers at rate R,, while keeping receiver 2 as ignorant of tbe private messages as possible. Measurhg ignorance by equivocation, a single-letter characterization is given of the. achievable trfplea (RI&R,-,) where 4 is the equivocation rate. Based on this channel ding result, the related source-channel matdng problem is also settled. l%ese results generahe those of Wyner on the wiretap channel and of Kiirner-Marton on tke broahxst channel.

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A broadcast channel with one sender and two receivers is considered. Three independent messages are to be transmitted over this channel: one common message which is meant for both receivers, and one private message for each qf them. The coding theorem and strong converse for this communication situation is proved for the case when one of the private messages has rate zero. I. INTRODUCTION W E CONSIDER a two-receiver broadcast channel defined by T. M. Cover [l] as a pair of discrete memoryless channels (V, W) with common input alphabet Y and respective output alphabets X and 2. (We use the same symbol for discrete memoryless channels and for their transition probability matrices, and we suppose that all alphabets are finite.) The nth memoryless extension of this broadcast channel is defined by the pair (VI", W"), where, e.g., foryn = YIYZ "'Yn E Y",x~=x1x2"'xn E X". An (n,t)-code for this channel is given by codewords yjnkl E Y n (1 _< j 5 M1, 1 _< k 5 M2, 1 5 1 < MO); and corresponding decoding sets 3Qjl c X",,@kl c 2" such that both (&jl{ and (@hll are disjoint families, and Vn(AjllYjnkl) 2 1-t, w"(@)klIy~~~) L 1-e for all j,/z,l. A triple of nonnegative numbers (R~,Rz,Ro) is called an E-achievable rate triple for this channel, if, for any 6 > 0 and large enough n, there exists an (n,t)-code (yj"kl, &jl, @kl;

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