Abstmct-A coding theorem for the discrete memoryleas broadcast channel is proved for tbe case where no common message is to be transmitted. The theorem is a generalization of the results of Cover and van der Meulen on this problem. Tbe result is tight for broadcast channels having one deterministic component
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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