a) A channel with alphabet (0, 1, 2, 3, 4) has transition probabilities of the (10)...

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a) A channel with alphabet (0, 1, 2, 3, 4) has transition probabilities of the (10) form P(y|x) = $₁ Compute the capacity of this channel in bits. b) A discrete memoryless channel (DMC) has the graphical representation (12) shown in Figure 3.1: 0.8 0.2 if y=x ±1 mod 5 0, otherwise 0.2 0.8 Figure 3.1 Assume the source symbols are not equally probable, with pe, X. 1) Find the expressions for the partial mutual information for each symbol co and c1. (4 points) ii) What is the capacity of this channel? (3 points) iii) When x=0.3, find the input and output entropy. Compare them and comment on the comparison result. (5 points) 1) Consider a private-key cryptosystem of Vigenere Cipher using (11) the key "fun". Use the numeric assignment table in the appendix to decrypt the cipher text "ahfucefavuh". (5 points) ii) Consider a public-key Rivest-Shamir-Adleman (RSA) system. Use the public key (7, 187) to encrypt the value 88. If one wishes to the decrypt without knowing the private key but knowing the two primes (p, q)=(17, 11), derive the private key. (6 points) Tot: 33 a) A channel with alphabet (0, 1, 2, 3, 4) has transition probabilities of the (10) form P(y|x) = $₁ Compute the capacity of this channel in bits. b) A discrete memoryless channel (DMC) has the graphical representation (12) shown in Figure 3.1: 0.8 0.2 if y=x ±1 mod 5 0, otherwise 0.2 0.8 Figure 3.1 Assume the source symbols are not equally probable, with pe, X. 1) Find the expressions for the partial mutual information for each symbol co and c1. (4 points) ii) What is the capacity of this channel? (3 points) iii) When x=0.3, find the input and output entropy. Compare them and comment on the comparison result. (5 points) 1) Consider a private-key cryptosystem of Vigenere Cipher using (11) the key "fun". Use the numeric assignment table in the appendix to decrypt the cipher text "ahfucefavuh". (5 points) ii) Consider a public-key Rivest-Shamir-Adleman (RSA) system. Use the public key (7, 187) to encrypt the value 88. If one wishes to the decrypt without knowing the private key but knowing the two primes (p, q)=(17, 11), derive the private key. (6 points) Tot: 33

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a To compute the capacity of the given channel we need to determine the channels transition probabilities and calculate the mutual information The tra... View the full answer