Solve the 4 exercises

Third Year Coding and Data Compression Information and Communications Engineering Department Exercises 1. For the following binary channel, if p(x1)=p(x2)=0.5, find all entropies and average mutual information (1) from/to yl y2 P(y, | xi ) = x1 0.9 0.1 x2 0.1 0.9 2. For the channel model shown, find: (a) source entropy rate if [x1 = 1ms and Tx2 = 2 ms, I(x1)=2 bits. (b) the transinformation. 0.9 X1 Y Y2 X2 0.8 Y3 3. A BSC has p(Y X) = [0.8 0.2] if Lo.2 0.8 , if(Or) = 3 bits , find system and losses entropies 4. Specify the type of the following channels (noiseless or/and symmetric) and then draw the model of each channel: (a) P(yixi) = [8 9 (b) P(v;xi) = Lo.02 0.98] 0.2 1 0 0 (c ) P(y, |xz) = 0 1 0 (d) P(v, |x1 ) = 0 0 OOOH 1 0 0 0 1 0.8 0.2 0 (e) P(yixi ) = 0 0.8 0.2 10.2 0 0.8