Question

Two binary channels are cascaded as shown in the figure. Transition probabilities for various values of x yi and zk are indicated in the diagram. r1 0.6 0.8 0.4 0.2 0..5 0.1 0.5 0.9 r2 y2 (i) Find the overall channel matrix of the resultant channel and draw the resultant equivalent channel diagram. (i) If Px) 0.7 and P(x) 0.3, find P(z)and Pz)​

Answer 1

Answer:

Transition probabilities for various values of x yi and zk are indicated in the diagram. r1 0.6 0.8 0.4 0.2 0..5 0.1 0.5 0.9 r2 y2 (i) Find the overall channel matrix of the resultant channel and draw the resultant equivalent channel diagram. (i) If Px) 0.7 and P(x) 0.3, find P(z)and Pz) b) The binary symmetric channel (BSC) is a very common channel model used and is given by the channel matrix, Pi P2 p3 P4 (i) Write down three relationships between pı & рг, p3 & p4 and p2 and p3 for a BSC. (ii) Hence find the average mutual information in this BSC for a binary error probability of pe Hence find the capacity of this BSC. (iii)