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decoded message sequence is 1100010
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Consider a convolutional code with G(D) [1D, 1+D2,1+D+D2] When a codeword is transmitted over a BSC and the receive...
Consider a convolutional code with code rate R 1/2,k- 1, and constraint length L-3. The generators a) Find the output f...
Consider a convolutional code with code rate R 1/2,k- 1, and constraint length L-3. The generators a) Find the output for input 10100 based on the trellis diagram of this convolutional code. (6 marks) b) Suppose that the received sequence is 1110110010. Use the Viterbi algorithm to find the most likely transmitted data sequence. (10 marks)
Consider a convolutional code with code rate R 1/2,k- 1, and constraint length L-3. The generators a) Find the output for input 10100 based...
Qu 2: [6 Marks) (a) Information to be transmitted over the internet contains the following characters...
Qu 2: [6 Marks) (a) Information to be transmitted over the internet contains the following characters with their associated frequencies as shown in the following table: Character abenos tu Frequency 11 6 14 12 3 132 Use Huffman Code Algorithm to answer the following questions: (i) Build the Huffman code tree for the message. (ii) Use the tree to find the codeword for each character. (iii)If the data consists of only these characters, what is the total number of bits...
1. (30 points) Consider the systematic binary linear (6,3) code with generator matrix 1 0 01...
1. (30 points) Consider the systematic binary linear (6,3) code with generator matrix 1 0 01 1 0 G- 0 1 0 0 1 1 a) Determine the parity check matrix H of the code. b) What is the minimum distance of the code? How many errors can this code correct and detect? c) Show the results in b) using decoding table d) Find the most likely codeword, given that the noisy received codeword is 010101. e) Now suppose 001101...
6) A convolutional code with constraint length K -3 has generator polynomials g, (D)-1,gz(D)- D +...
6) A convolutional code with constraint length K -3 has generator polynomials g, (D)-1,gz(D)- D +1 and g (D) D +D+1 a) Draw the encoder of this code (2 Marks) b) Is the code systematic? Explain (1 Mark). c) Draw the sate diagram (1 Mark) and trellis of the code (2 Marks). d) Find the output of the encoder if the input is 0010100 (2 Marks)
6) A convolutional code with constraint length K -3 has generator polynomials g, (D)-1,gz(D)-...
Write legibly to receive good rating. Consider a CRC code with a generator polynomial of g(x)...
Write legibly to receive good rating.
Consider a CRC code with a generator polynomial of g(x) -xSx21 a. (15 points) Show step by step (using the longhand division) how to find the codeword that corresponds to information bits of 10011 b. (15 points) Show the shift-register circuit that implements this CRC code. C. Suppose the codeword length is 10. Answer the following questions, with proper justifications i. (10 points) Give an example of undetectable error burst of length 9 ii....
3. Let C be a q-ary code of length n. Assume the minimal distance d(C) is...
3. Let C be a q-ary code of length n. Assume the minimal distance d(C) is an odd number, d(C) = 2r + 1. We showed in class that C can always correct up to r errors. That is, whenever a codeword a from C is sent, and r or fewer errors occur in transmission, the Nearest Neighbour Decoding algorithm will decode the received word b correctly (i.e., will decode b as a). Prove that C cannot always correct r...
1) Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given...
1) Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given as g(x) = 1 + x + x2 + x5 + x + x10. a. Design and draw the circuit of the feedback shift register encoder and decoder (6 Marks) b. Use the encoder obtained in part a to find the code word for the message (10110). (Assume the right most bit is the earliest bit) (5 Marks) C. Repeat the steps of part...
1) Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given...
1) Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given as. g(x) = 1 + x + x2 + x5 + x + x10. a. Design and draw the circuit of the feedback shift register encoder and decoder.(6 Marks) b- Use the encoder obtained in part a to find the code word for the message (11101] (Assume the right most bit is the earliest bit) (5 Marks) c- Repeat the steps of part b...
Consider the (5,2) linear binary code, C, with linear space of codewords spanned by the codewords...
Consider the (5,2) linear binary code, C, with linear space of codewords spanned by the codewords (1, 0, 1,1, 1) and (0, 1, 1, 1, 0). 4. Find all codewords in C, find the systematic generator matrix, G, and a parity check matrix, H, for the code. a. Determine dmin for the code and the code's weight distribution. Determine all codewords in the dual code, Cd . Find a systematic generator matrix, Ga, for the dual code, and corresponding parity...
PARITY CHECK MATRIX DECODING 1. The affine cipher y 21x + 11 (mod 26) was used...
PARITY CHECK MATRIX DECODING 1. The affine cipher y 21x + 11 (mod 26) was used to encode a message. Each resulting letter of the ciphertext was converted to the five-bit string consisting of the base-two equivalent of the value of the letter. The systematic (9,5) linear code with standard generator matrix G given by [1 0 0 0 0 1 0 0 11 To 1000 1100l G= 0 0 1 0 0 1 1 1 1 0 0 0...
Consider a convolutional code with code rate R 1/2,k- 1, and constraint length L-3. The generators a) Find the output for input 10100 based on the trellis diagram of this convolutional code. (6 marks) b) Suppose that the received sequence is 1110110010. Use the Viterbi algorithm to find the most likely transmitted data sequence. (10 marks)
Consider a convolutional code with code rate R 1/2,k- 1, and constraint length L-3. The generators a) Find the output for input 10100 based...
Qu 2: [6 Marks) (a) Information to be transmitted over the internet contains the following characters with their associated frequencies as shown in the following table: Character abenos tu Frequency 11 6 14 12 3 132 Use Huffman Code Algorithm to answer the following questions: (i) Build the Huffman code tree for the message. (ii) Use the tree to find the codeword for each character. (iii)If the data consists of only these characters, what is the total number of bits...
1. (30 points) Consider the systematic binary linear (6,3) code with generator matrix 1 0 01 1 0 G- 0 1 0 0 1 1 a) Determine the parity check matrix H of the code. b) What is the minimum distance of the code? How many errors can this code correct and detect? c) Show the results in b) using decoding table d) Find the most likely codeword, given that the noisy received codeword is 010101. e) Now suppose 001101...
6) A convolutional code with constraint length K -3 has generator polynomials g, (D)-1,gz(D)- D +1 and g (D) D +D+1 a) Draw the encoder of this code (2 Marks) b) Is the code systematic? Explain (1 Mark). c) Draw the sate diagram (1 Mark) and trellis of the code (2 Marks). d) Find the output of the encoder if the input is 0010100 (2 Marks)
6) A convolutional code with constraint length K -3 has generator polynomials g, (D)-1,gz(D)-...
Write legibly to receive good rating.
Consider a CRC code with a generator polynomial of g(x) -xSx21 a. (15 points) Show step by step (using the longhand division) how to find the codeword that corresponds to information bits of 10011 b. (15 points) Show the shift-register circuit that implements this CRC code. C. Suppose the codeword length is 10. Answer the following questions, with proper justifications i. (10 points) Give an example of undetectable error burst of length 9 ii....
1) Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given as g(x) = 1 + x + x2 + x5 + x + x10. a. Design and draw the circuit of the feedback shift register encoder and decoder (6 Marks) b. Use the encoder obtained in part a to find the code word for the message (10110). (Assume the right most bit is the earliest bit) (5 Marks) C. Repeat the steps of part...
1) Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given as. g(x) = 1 + x + x2 + x5 + x + x10. a. Design and draw the circuit of the feedback shift register encoder and decoder.(6 Marks) b- Use the encoder obtained in part a to find the code word for the message (11101] (Assume the right most bit is the earliest bit) (5 Marks) c- Repeat the steps of part b...
Consider the (5,2) linear binary code, C, with linear space of codewords spanned by the codewords (1, 0, 1,1, 1) and (0, 1, 1, 1, 0). 4. Find all codewords in C, find the systematic generator matrix, G, and a parity check matrix, H, for the code. a. Determine dmin for the code and the code's weight distribution. Determine all codewords in the dual code, Cd . Find a systematic generator matrix, Ga, for the dual code, and corresponding parity...
PARITY CHECK MATRIX DECODING 1. The affine cipher y 21x + 11 (mod 26) was used to encode a message. Each resulting letter of the ciphertext was converted to the five-bit string consisting of the base-two equivalent of the value of the letter. The systematic (9,5) linear code with standard generator matrix G given by [1 0 0 0 0 1 0 0 11 To 1000 1100l G= 0 0 1 0 0 1 1 1 1 0 0 0...
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