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A communication channel is shown in Figure P6.47.
1. Show that, regardless of the contents of the probability transition matrix of the channel, we have
2. Determine one probability transition matrix under which the above upper bound is achieved.
3. Assuming that a Gaussian source with variance σ2 = 1 is to be transmitted via the channel in part 2, what is the minimum achievable distortion? (Mean squared distortion is assumed throughout.)
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Now assume that the transmitter can control the state of the channel and the receiver has access to channel state information. What is the capacity of the resulting channel?
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