Design (7,3) linear block code with parity check matrix given as
Design (7,3) linear block code with parity check matrix given
as
Homework Answers
In the question given parity check matrix was not given
properly,that is identity matrix was not given properly.just
changed the positio of one column and then calculated.
Design (7,3) linear block code with parity check matrix given as H = 0 1 11 0 0 1 1 0 10 1 0 1 1 1 00 0 1 1 a. Find all...
Design (7,3) linear block code with parity check matrix given as H = 0 1 11 0 0 1 1 0 10 1 0 1 1 1 00 0 1 1 a. Find all the corresponding codewords of the code. b. What is the error the error-correcting and error-detection capabilities of the code? c. Find the syndrome for the received vector R = [1101011]. d. Assuming the receiver Maximum likelihood algorithm construct syndrome table for the correctable error patterns
1. Channel Coding We would like to add linear block code (3,6) using the generator matrix:...
1. Channel Coding We would like to add linear block code (3,6) using the generator matrix: 1 001 01 G-0 1 0 0 1 1 (a) (5 points) Determine the parity check matrix H (b) (20 points) What is the minimum distance of this code? How many error can this code correct? (c) (5 points) What is the code word for the data sequence 011000101111? (d) (20 points) If you receive the codeword 010001000010101010, what is the transmitted sequence?
Consider the 2-error correcting, narrow-sense RS code over GF(16) (α is a primitive element). (a) Write down the generator polynomial and the parity check polynomial. (b) Provide a parity check matrix...
Consider the 2-error correcting, narrow-sense RS code over GF(16) (α is a primitive element). (a) Write down the generator polynomial and the parity check polynomial. (b) Provide a parity check matrix for the code. (c) Decode the received vector V = [α6 α12 α9 α12 0 0 0 α8 0 0 0 α10 α α13 α].
Problem 4. For the following generating matrix for a (7,3)-code, plot the encoder structure 1 1 0...
Problem 4. For the following generating matrix for a (7,3)-code, plot the encoder structure 1 1 01 1 0 0 G- 0 01 01 0 0 01 100 1 0
Problem 4. For the following generating matrix for a (7,3)-code, plot the encoder structure 1 1 01 1 0 0 G- 0 01 01 0 0 01 100 1 0
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...
Let G- be a generator matrix for a block code (not necessarily a "good" code) a) b) c) What is th...
Let G- be a generator matrix for a block code (not necessarily a "good" code) a) b) c) What is the n, k, the rate and the bandwidth expansion for this code? Find the parity check matrix H )Build the standard array for the code. Assume the coset leaders are vectors with one "l", starting from the left side of the vector, i.e., the first coset leader will be (1 0...), the second (01 0 ...) starting again from the...
1. The parity generator matrix for a Hamming (8,4) code is given by Toi 1 il...
1. The parity generator matrix for a Hamming (8,4) code is given by Toi 1 il 1 0 1 1 1 1 0 1 [1 1 1 0 (a) Compute the distance between all pairs of code words and show the distance of the code is 4. You may use MATLAB to do this. (b) Show that the difference between any pair of code words is a code word.
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...
12.32 Use the result of the preceding problem to de- termine the parity-check matrix for the...
12.32 Use the result of the preceding problem to de- termine the parity-check matrix for the coder shown in Figure 12.15. Use the parity-check matrix to decode the received sequences 1101001 and 1101011. Compare your result with that shown in Figure 12.16.
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...
1. Channel Coding We would like to add linear block code (3,6) using the generator matrix: 1 001 01 G-0 1 0 0 1 1 (a) (5 points) Determine the parity check matrix H (b) (20 points) What is the minimum distance of this code? How many error can this code correct? (c) (5 points) What is the code word for the data sequence 011000101111? (d) (20 points) If you receive the codeword 010001000010101010, what is the transmitted sequence?
Problem 4. For the following generating matrix for a (7,3)-code, plot the encoder structure 1 1 01 1 0 0 G- 0 01 01 0 0 01 100 1 0
Problem 4. For the following generating matrix for a (7,3)-code, plot the encoder structure 1 1 01 1 0 0 G- 0 01 01 0 0 01 100 1 0
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...
Let G- be a generator matrix for a block code (not necessarily a "good" code) a) b) c) What is the n, k, the rate and the bandwidth expansion for this code? Find the parity check matrix H )Build the standard array for the code. Assume the coset leaders are vectors with one "l", starting from the left side of the vector, i.e., the first coset leader will be (1 0...), the second (01 0 ...) starting again from the...
1. The parity generator matrix for a Hamming (8,4) code is given by Toi 1 il 1 0 1 1 1 1 0 1 [1 1 1 0 (a) Compute the distance between all pairs of code words and show the distance of the code is 4. You may use MATLAB to do this. (b) Show that the difference between any pair of code words is a code word.
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...
12.32 Use the result of the preceding problem to de- termine the parity-check matrix for the coder shown in Figure 12.15. Use the parity-check matrix to decode the received sequences 1101001 and 1101011. Compare your result with that shown in Figure 12.16.
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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