(a) Symbols A, B, C, D, E, F, G, H, I, J, and K have probabilities of transmission of 1%, 10%, 3%, 15%, 32%, 5%, 7%, 2%, 2%, 12%, and 11%, respectively. Encode this set of symbols using (i) Binary encoding, (ii) Gray encoding, and (iii) Huffman encoding. Determine also the average number of bits transmitted in each case. (b) 1100001 11 0 1 0 0 1 0 1 A (7, 4) code has a generator matrix given by G- 100 101 10' 00011111 determine the co-set leaders of the standard array. If the receiver has received the word r = [0110111]', find the syndrome and hence calculate the decoded word. (c) Explain the operation of a convolutional encoder and decoder. (a) Symbols A, B, C, D, E, F, G, H, I, J, and K have probabilities of transmission of 1%, 10%, 3%, 15%, 32%, 5%, 7%, 2%, 2%, 12%, and 11%, respectively. Encode this set of symbols using (i) Binary encoding, (ii) Gray encoding, and (iii) Huffman encoding. Determine also the average number of bits transmitted in each case. (b) 1100001 11 0 1 0 0 1 0 1 A (7, 4) code has a generator matrix given by G- 100 101 10' 00011111 determine the co-set leaders of the standard array. If the receiver has received the word r = [0110111]', find the syndrome and hence calculate the decoded word. (c) Explain the operation of a convolutional encoder and decoder