Mathematics, 16.03.2020 21:35 citlalli30
Berlekamp-Welch Algorithm with Fewer Errors In class we derived how the Berlekamp-Welch algorithm can be used to correct k general errors, given n + 2k points transmitted. In real life, it is usually difficult to determine the number of errors that will occur. What if we have less than k errors? This is a follow up to the exercise posed in the notes. Suppose Alice wants to send 1 message to Bob and wants to guard against 1 general error. She decides to encode the message with Px) 4 (on GF(7)) such that P(0) 4 is the message she want to send. She then sends P(0),P(1),P(2) = (4,4,4) to Bob.
(a) Suppose Bob receives the message (4,5,4). Without performing Gaussian elimination explic- itly, find E(x) and Q(x).
(b) Now, suppose there were no general errors and Bob receives the original message (4,4,4) Show that the Q(x),E(x) that you found in part (a) still satisfies Q(i) E(i) for all i 0,1,2.
(c) Verify that E(x) =x, Q(x) = 4x is another possible set of polynomials that satisfies Q(i) = rE(i) for al 0, 1,2.
q(d) Suppose you're actually trying to decode the received message (4,4,4). Based on what you showed in the previous two parts, what will happen during row reduction when you try to solve for the unknowns?
(e) Prove that no matter what the solution of Cx) and E(x) are though, the recovered P(x) will always be the same.
Answers: 1
Mathematics, 21.06.2019 14:10, SMURFETTE86
Can u guys do this ratio question. this is extremely urgent a tap is leaking water at a rage of 1l every 8 hours. how long will it take for the tap to leak a total of 300ml?
Answers: 1
Mathematics, 21.06.2019 16:00, destinyaus14
Mr and mrs smith buy tickets for themselves and their four children. the cost of an adult ticket is ? 6 more than the adult ticket. the total cost of the six tickets is ? 40.50 work out the cost of an adult ticket. in your working let c be the cost of the child ticket and a be the cost of the adult ticket.
Answers: 1
Berlekamp-Welch Algorithm with Fewer Errors In class we derived how the Berlekamp-Welch algorithm ca...