Write a matlab function y = channel(x, p) that takes a vector of transmitted bits x and p as input and returns the vector of received bits y. (b) looking at the received bit y , the receiver estimates the transmitted bit in the form of xˆ. a maximum likelihood (ml) estimator uses the following decision rule to find xˆ: xˆ = ( y if p ≥ (1 − p) y¯ if p < (1 − p) where y¯ is the complementary bit to y , i. e. y¯ = 0 if y = 1, and y¯ = 1 if y = 0. show that the above decision rule is the same as the one that finds b which maximizes p[y = y|x = b] over all values of b. note both b and y can be 0 or 1. p[y = y|x = b] is called the likelihood of y given x. (c) write a matlab function xhat = mlreceiver(y, p) that takes a vector of received bits y and p as input and returns the vector of estimated bits xhat.