Response to the following problem:
Show that when a binary sequence x of length n is transmitted over a BSC with crossover probability p, the probability of receiving y, which is at Hamming distance d from x, is given by
P( y|x) = (1-p)n(p/1-p)d
From this conclude that if p < ½, P( y|x) is a decreasing function of d and hence ML decoding is equivalent to minimum-Hamming-distance decoding. What happens if p > ½?