Consider the (4,1) repetition code
Consider the (4,1) repetition code. (a) show that HG^T=0 (b) Compute the syndromes for all one error patterns (c) What are the two transmitted codewords for a two-bit message m = 0 1 (d) If the received codewords is 0010 what is the decoded message bit using syndrome decoding
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Exercise 1 Assume that a binary symmetric channel is used in this question as shown in fig. 1 I-p...
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Exercise 1 Assume that a binary symmetric channel is used in this question as shown in fig. 1 I-p 0 0 Alice (encoder) Bob (decoder) 1 1-P Figure 1 The Binary symmetric channel where the probability of a bit being wrongly decoded by Bob is p i) Two codes are proposed: a...
A communication link uses a simple repetition code for error correction, where ain information bit T)"...
A communication link uses a simple repetition code for error correction, where ain information bit T)" is sent by a length-5 sequence of zeros, İ.е., 0 (0,0,0,0,0) Likewise, an information bit "I', is sent by a length-5 sequence of ones, i.e., 1 → (1,1,1,1,1). Assume that information bits "O's" and "1's" are sent with equal prob- ability and each of the 5 corresponding code bits that are transmitted are received in error independently with probability 0.01. The receiver makes a...
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?
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...
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...
The following message is to be transmitted using Huffman coding: ISTHISHISTORYORISTHISHISTESTTHESIS a) Determine a Huffman code...
The following message is to be transmitted using Huffman coding: ISTHISHISTORYORISTHISHISTESTTHESIS a) Determine a Huffman code tree for this message. b) What are the corresponding code words for each character? c) What is the efficiency of this encoding compared to the uncompressed data? [Assume that the uncompressed characters are transmitted using the minimum number of bits needed to code all of the characters of the message.] d)What would be the decoded message if the following bit stream was sent using...
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
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...
Hamming Code: m = 1010 (4-bit message); odd-parity scheme; Compute Hamming Code on the sender’s side....
Hamming Code: m = 1010 (4-bit message); odd-parity scheme; Compute Hamming Code on the sender’s side. On the receiver’s side, detect and verify a 7th bit error-position in the transmitted data.
I need it urgently. Kindly provide me in neat and clean. Thanks
in advance.
This information is complete and if You think info is incomplete
than kindly mention.
Exercise 1 Assume that a binary symmetric channel is used in this question as shown in fig. 1 I-p 0 0 Alice (encoder) Bob (decoder) 1 1-P Figure 1 The Binary symmetric channel where the probability of a bit being wrongly decoded by Bob is p i) Two codes are proposed: a...
A communication link uses a simple repetition code for error correction, where ain information bit T)" is sent by a length-5 sequence of zeros, İ.е., 0 (0,0,0,0,0) Likewise, an information bit "I', is sent by a length-5 sequence of ones, i.e., 1 → (1,1,1,1,1). Assume that information bits "O's" and "1's" are sent with equal prob- ability and each of the 5 corresponding code bits that are transmitted are received in error independently with probability 0.01. The receiver makes a...
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...
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...
The following message is to be transmitted using Huffman coding: ISTHISHISTORYORISTHISHISTESTTHESIS a) Determine a Huffman code tree for this message. b) What are the corresponding code words for each character? c) What is the efficiency of this encoding compared to the uncompressed data? [Assume that the uncompressed characters are transmitted using the minimum number of bits needed to code all of the characters of the message.] d)What would be the decoded message if the following bit stream was sent using...
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...
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