Problem 4. For the following generating matrix for a (7,3)-code, plot the encoder structure 1 1 0...
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
4. A Manchester encoder maps a bit 1 into 10 and a zero 0 into 01. The signal waveforms corresponding to the Manchester code are shown below. Determine the probability of bit error if the two signals are equally probable and are corrupted by additive zero- mean white Gaussian noise with an auto-correlation function: s2(t) s, (t)
4. A Manchester encoder maps a bit 1 into 10 and a zero 0 into 01. The signal waveforms corresponding to the Manchester...
Request solve following question from coding theory
d)Lethe binary code with generator matrix 01 0 1 0 0 0 1010 0 00 G 1 0011 00 0 0 0 1 1 Give another generator matrix for%" that shows that 'C is the direct sum of two binary codes. Identify the codes of which is a direct sum (Hint: Use row operations.)
d)Lethe binary code with generator matrix 01 0 1 0 0 0 1010 0 00 G 1 0011 00...
coding theory
1. If 100 031 Go 01 0 0 9 0001 27 01 0 054 is a generator matrix for a linear code over Fi encode the message stream m(2, 3,9, 6, 1,4,3, 8) (by breaking it into encodable pieces). 2. If T (1 0 1 2 3 4 be the transpose of a parity-check matrix for a perfect 1-error-correcting code over Fs, with implicit generator matrix 4410 0 0 3 4 0 1 0 0 1400 01
1....
(9) Define a generating matrix G for a group code to be equal to the fol- lowing 3 x 13 binary matrix: 1001010101010 0100101010101 0011100110011 (a) List all the code words (b) What is the maximum number of transmission errors (denote this number by 1) that this code can correct? (c) Suppose a code word β is transmitted and the received word s 0111011100111. If than or equal to (see part (b)), then what is B? the number of transmission...
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...
3 2 0 3. Compute the product 0 01-1 0 013 4. If the matrix A from the previous problem represents a linear transformation T, determine: (a.) Is the mapping onto (b.) Is the mapping one to one (c.) Is the mapping homomorphic (d.) Is the mapping isomorphic (e.) What is the range space? The rank? (f) What is the null space? The nullity? (g.) Does this transformation preserve magnitude? 5. (a.) What is AT, the transpose of the matrix...
Problem 1. For the repetition code (3,1) (namely repeat the information bit three times), find the generating matrix, parity check matrix and the table of error versus syndrome.
Problem 1. For the repetition code (3,1) (namely repeat the information bit three times), find the generating matrix, parity check matrix and the table of error versus syndrome.
DKI=3
Problem 1: Determine the following vector and matrix expressions for the frame structure load system shown below. The vector of unknown displacem ents D; The joint load vector Q; The fixed-end force vector Qo; and The Stiffness matrix K. 1· 2. 3. 4. The vector equation involving the above quantities based on the displacement method is 1-5 K/ft C. 430 24 ft 3 20 ft 20%t 0 0 TiIT
Problem 1: Determine the following vector and matrix expressions for...
Let C be the code generated by the matrix [1 0 0 11 G= 0 1 0 2 over Fz. Lo 0 1 1] (i) How many codewords will have, and why? (ii) Give three distinct codewords of C and find their Hamming weights. (iii) List all the steps required for finding the minimum distance of any code. 7