[Solved]1 Suppose Source Alphabet B C D Following Probability Distribution Pa 05 S 02 Pc01 Po 02 S Q37158923

1. Suppose that the source alphabet [A, B, C, D] has the following probability distribution: PA 0.5, s 0.2, Pc0.1, Po-0.2. For simplicity, let’s also assume that both encoder and decoder know that the length of the message is always 6, so there is no need for a terminating symbol a. Design a Huffman code to code these source symbols. How many bits are needed to encode the message BACADA by Huffman coding? Encode the message BACADA using Arithmetic coding. How many bits are needed this time? b. 2. A source emits symbols Xi, 1 sis 6, in the BCD format with probabilities P(X) as given in Table 1, at a rate Rs 9.6 kbaud (baud-symbol/second). a. State (i) the information rate (R H Rs) and (ii) the data rate (number of bits Rs) of the source Apply Huffman coding to the source signal characterized in Table 1. What is the original symbol sequence of the Huffman coded signal 110011110000110101100? What is the data rate of the signal after Huffman coding? What compression factor has been achieved? Derive the coding efficiency of both the uncoded BCD signal as well as the Huffman coded signal. (CEinformation rate/data rate) b. c. d. e. Table 1 BCD word 0.30 0.10 0.02 0.15 0.40 0.03 001 010 011 100 101 3. Calculate the entropy of a “checkerboard” image in which half of the pixels are BLACK and half of them are WHITE 4. For the given F(u, v) and Q(u, v) matrices below, write the quantization formula and find the quantized F (u,v) matrix 415 -33 -58 35 58-51 -15 -12 一34 49 18 27 -46 14 80-3550 197-1 53 21 34 -20 2 34 36 12 5 -32 -15 45 37 8 15 -16 7 19 -28 -2-26 -2 7 -44-21 18 25 -12-44 35 48-37 -3 16 11 10 16 24 40 51 61 12 12 14 19 2658 60 55 14 13 16 24 40 57 69 56 14 17 22 29 51 87 80 62 18 22 37 56 68 109 103 77 24 35 55 64 81 104 113 92 49 64 78 87 103 121 120 101 72 92 95 98 112 100 103 99 Show transcribed image text 1. Suppose that the source alphabet [A, B, C, D] has the following probability distribution: PA 0.5, s 0.2, Pc0.1, Po-0.2. For simplicity, let’s also assume that both encoder and decoder know that the length of the message is always 6, so there is no need for a terminating symbol a. Design a Huffman code to code these source symbols. How many bits are needed to encode the message BACADA by Huffman coding? Encode the message BACADA using Arithmetic coding. How many bits are needed this time? b. 2. A source emits symbols Xi, 1 sis 6, in the BCD format with probabilities P(X) as given in Table 1, at a rate Rs 9.6 kbaud (baud-symbol/second). a. State (i) the information rate (R H Rs) and (ii) the data rate (number of bits Rs) of the source Apply Huffman coding to the source signal characterized in Table 1. What is the original symbol sequence of the Huffman coded signal 110011110000110101100? What is the data rate of the signal after Huffman coding? What compression factor has been achieved? Derive the coding efficiency of both the uncoded BCD signal as well as the Huffman coded signal. (CEinformation rate/data rate) b. c. d. e. Table 1 BCD word 0.30 0.10 0.02 0.15 0.40 0.03 001 010 011 100 101 3. Calculate the entropy of a “checkerboard” image in which half of the pixels are BLACK and half of them are WHITE
4. For the given F(u, v) and Q(u, v) matrices below, write the quantization formula and find the quantized F (u,v) matrix 415 -33 -58 35 58-51 -15 -12 一34 49 18 27 -46 14 80-3550 197-1 53 21 34 -20 2 34 36 12 5 -32 -15 45 37 8 15 -16 7 19 -28 -2-26 -2 7 -44-21 18 25 -12-44 35 48-37 -3 16 11 10 16 24 40 51 61 12 12 14 19 2658 60 55 14 13 16 24 40 57 69 56 14 17 22 29 51 87 80 62 18 22 37 56 68 109 103 77 24 35 55 64 81 104 113 92 49 64 78 87 103 121 120 101 72 92 95 98 112 100 103 99

Expert Answer

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Answer to 1. Suppose that the source alphabet [A, B, C, D] has the following probability distribution: PA 0.5, s 0.2, Pc0.1, Po-0…. . . .