Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
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The broadcast channel was introduced by T. M. Cover in 1972 [7]. In its simplified version, it has one sender (or encoder) E and two users (or decoders) $D_l, \ l=1, \ 2$. The sender E is required to send the messages m1 and m2 uniformly chosen from the message sets ${\cal M}_1$ and ${\cal M}_2$ respectively to D1 and D2 correctly with probability close to one. That is, the sender encodes the message (m1,m2) to an input sequence xn over a finite input alphabet ${\cal X}$ and sends it to the two users via two noisy channels Wn and Vn, respectively. The first (second) user D1 (D2) decodes the output sequence yn over the finite output alphabet ${\cal Y}$ of the channel Wn (the output sequence zn over the finite output alphabet ${\cal Z}$ of the channel Vn) to the first message $\hat{m}_1$ (the second message $\hat{m}_2$ ). In general, the capacity regions for this kind of channels are still unknown. Their determination is probably one of the hardest open problems in Multi-user Shannon Theory.