Find the generator polynomial of the length-1023, primitive binary BCH code with designed error-correcting capability (a) t = 1. (b) t = 2. (c) t = 3. (d) t = 4.
Find the generator polynomial of the length-1023, primitive binary BCH code with designed error-correcting capability (a) t = 1. (b) t = 2. (c) t = 3. (d) t = 4.
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Find the generator polynomial of the length-1023, primitive binary BCH code with designed error-correcting capability (a) t = 1. (b) t = 2. (c) t = 3. (d) t = 4.
Find the generator polynomial of the length-1023, primitive binary BCH code with designed error-correcting capability (a)...
Find the generator polynomial of the length-1023, primitive binary BCH code with designed error-correcting capability (a) t = 1. (b) t = 2. (c) t = 3. (d) t = 4.
Problem 2 Find the generator polynomial of the primitive binary BCH code of length 1023 and...
Problem 2 Find the generator polynomial of the primitive binary BCH code of length 1023 and designed error correcting capability of t-1 t=2 and t=3. Problem3 Determine all the binary cyclic codes of length 21
Consider the 2-error correcting RS code over GF(8). Let α be a primitive element of GF(8). (a) List the parameters of the code. Find the generator polynomial of the code. Encode the message [1 α α2 ]...
Consider the 2-error correcting RS code over GF(8). Let α be a primitive element of GF(8). (a) List the parameters of the code. Find the generator polynomial of the code. Encode the message [1 α α2 ] systematically. (b) List the parameters of the binary expanded code. Provide binary equivalents of the encoding above. (c) Decode the received word [0 1 α α2 α3 1 0].
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].
Consider a (7, 4) code whose generator matrix is
Consider a (7, 4) code whose generator matrix isa) Find all the codewords of the code b) Find H, the parity check matrix of the code. c) Compute the syndrome for the received vector 1 101 1 0 1. Is this a valid code vector? d) What is the error-correcting capability of the code? e) What is the error-detecting capability of the code?
Consider a message D 110100111011001110111. Calculate the CRC code R for that message using a generator-polynomial...
Consider a message D 110100111011001110111. Calculate the CRC code R for that message using a generator-polynomial x4+x+1 (CRC-4-ITU) . Represent in binary code the message to be sent (D and R). Generate 2-bit burst error (erasure error) and show the checking procedure.
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...
(c) Consider the (7, 4) Hamming Code defined by the generator polynomial g(x)-1 +x+x'. The code...
(c) Consider the (7, 4) Hamming Code defined by the generator polynomial g(x)-1 +x+x'. The code word 1000101 is sent over a noisy channel, producing the received word 0000101 that has a single error. Determine the syndrome polynomial s(x) for this received word. Find its corresponding message vector m and express m in polynomial m(x). 0
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)-...
Let C' be a binary code of length n and distance d 2t +1. Prove that 2"
Let C' be a binary code of length n and distance d 2t +1. Prove that 2"
Let C' be a binary code of length n and distance d 2t +1. Prove that 2"
Problem 2 Find the generator polynomial of the primitive binary BCH code of length 1023 and designed error correcting capability of t-1 t=2 and t=3. Problem3 Determine all the binary cyclic codes of length 21
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...
(c) Consider the (7, 4) Hamming Code defined by the generator polynomial g(x)-1 +x+x'. The code word 1000101 is sent over a noisy channel, producing the received word 0000101 that has a single error. Determine the syndrome polynomial s(x) for this received word. Find its corresponding message vector m and express m in polynomial m(x). 0
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)-...
Let C' be a binary code of length n and distance d 2t +1. Prove that 2"
Let C' be a binary code of length n and distance d 2t +1. Prove that 2"
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