a) Find the channel capacity of the following discrete memory less channel. 0) W

Question

a) Find the channel capacity of the following discrete memory less channel. 0) Where P(Z = 0) . P(Z = a)--, and a is real number presenting the noise. The alphabet for X is X 10,1. Assume that Z is independent of X. Interpret how its channel capacity depends on the value of a. b) A discrete memoryless channel (DMC) has the graphical representation (12) shown in Figure 3.1: 0.95 0.05 U,05 yi 0.95 Figure 3.1 Assume the source symbols are not equally probable, with Pcox i) Find the expressions for the partial mutual information for each symbol co and c. What is the capacity of this channel? points) 3 points) ili) When- 0.4, find the input and output entropy. Compare them and comment on the comparison result. (5 points) ii) e) iConsider a private-key eryptosystem of Vigenere Cipher ) using the key fun. Use the numcric assignment table in the appendix to decrypt the cipher text "absqorswr". 5 points) ii) Consider a public-key Rivest-Shamir-Adleman (RSA) system. Use the public key (5, 119) to encrypt the value 20. If the encrypted value is 81, use the private key (77, 119) to (6 poinis) decrypt. Tot: 33

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