Suppose that we are given the following communication system described in Fig. 1 with the channel corrupted by an additive white Gaussian noise z with zero mean and variance 1 where the channel input r is used for signal transmission to produce the channel output y, i.e., Tx+z. Then the channel is further passed through a hard limiter, i.e., sign detector described by Q2() in Fig. 2. decisions Qa(r) Figure 1. A channel with the input x and output r corrupted by a Gaussian noise z where -1 Figure 2. Sign detector (a) (. ) Assume that two signals So =-1 and s| = 1 will be used for transmission with probabilities 1/4 and 3/4. Let the decision costs be defined by 10 Cy is the cost of claiming signal s, when s, is actually transmitted. Construct a binary channel resulting from the sign detector in Fig. 2 for (y) in Fig. 1. | coo col 0 21