3. Consider a binary antipodal communication system in which O's and 1's are equally likely to be transmitted. Suppose the input to the decision device at the receiver is modelled as R = -Ven + W, if a 0 was transmitted VEn + W, if a I was transmitted ' where the noise variable, W, is characterized by the probability density function shown below: k + fw (w) K cos (TW ) , |w| = 0/2 fw(w) = 0 , |w> >/2 W -0/2 o/2 (a) Express K in terms of a so that fw (w) is a valid pdf. (b) If a > 2vEt, what rule should the decision device use to minimize the probability of a bit error? Express the rule in the simplest form possible. Show your work