Eecs 290s: Network Information Flow Lecture 18 — October 30

First we consider compound channels which have common messages to all the receivers. The best-well known example is TV broadcast. Notice that compound channels are different from broadcast channels with independent messages to different receivers. Fig. 18.1 illustrates the encoding and decoding operations for the compound channel. Since the message is common, we have only one message w. From w, the encoder generates codewords x(w). This passes through different channels (h1, h2, · · · , hK) and we get y 1 , y n 2 , · · · , y K in each receiver, respectively. Since the message is the same, all the receivers also have a common decoder D. Suppose that the channels are non-varying and known to each receiver. Then, the trivial achievable scheme is to generate codewords based on the worst channel. Therefore, we can achieve