Some observations (a) Case#1: Let, ? ? 0. In this case, ; 11 (;) X Y I a b = ; 22 (;) X Y I a b = 2.

Some observations (a) Case#1: Let, ? ? 0. In this case, ; 11 (;) X Y I a b = ; 22 (;) X Y I a b = 2 log 2(1 ) -? bit = 1.0 bit (approx.) ; 12 (; ) X Y I a b = ; 21 (;) X Y I a b = lo 2 g 2? bit ? a large negative quantity This is an almost noiseless channel. When a1 is transmitted we receive b1 at the output almost certainly. (b) Case#2: Let us put ? = 0.5. In this case, ; 11 (;) X Y I a b = ; 12 (; ) X Y I a b = 0 bit It represents a very noisy channel where no information is received. The input and output are statistically independent, i.e. the received symbols do not help in assessing which symbols were transmitted. (c ) Case#3 : Fortunately, for most practical scenario, 0<?<< 0.5 and usually, ; 11 (;) X Y I a b = ; 22 (;) X Y I a b = 2 log 2(1 ) -? bit = 1.0 bit (approx.) So, reception of the letter y=b1 implies that it is highly likely that a1 was transmitted. Typically, in a practical digital transmission system, ?? 10-3 or less. The following figure, Fig 1.3.1 shows the variation of I(X;Y) vs. ?. I(X;Y) Ç 1.0 0.5 Æ e