(a) In Exercise 1, suppose that a single burst of consecutive bit errors occurre
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Question
(a) In Exercise 1, suppose that a single burst of consecutive bit errors occurred in the transmission of C. What is the smallest number of consecutive bit errors that the code would fail to correct?
(b) What is the answer to (a) if instead of F127, the code as above used the field Fp where the prime p = 65537 = 216 + 1?
The example 1 is following :
Example 1. Similar to Example 2, consider the two error correcting Reed-Solomon code with (m, e, n) = (2, 2, 6), with the field F = Fp with p a large prime. Use (a0, a1, a2, a3, a4, a5, a6) = (3, 2, 1, 0, 1, 2, 3). You want to send the plaintext message w = (15, 1, 2) to Bob, and want Bob to be able to correct two errors. You and Bob agree to use the Reed-Solomon code as just described. Find the encoded 7-tuple C for the plaintext message w that you send to Bob
4. (a) In Exercise 1, suppose that a single burst of consecutive bit errors occurred in the transmission of C. What is the smallest number of consecutive bit errors that the code would fail to correct? (b) What is the answer to (a) if instead of F127, the code as above used the field F, where the prime p = 6553-216 + 1?Explanation / Answer
4)
a)
Burst cycle detection will be difficult if l(length of burst error) > r(exponential). It fails only when burst error length is divisible by g(x), here only 2(1-2-r) are divisible by g(x). So finally smallest possible of detection failure is 2-r
---------------------------------------------------------------------------------------------------------------------------------------------------------b)
Given r = 16, So smallest possible of detection failure is 2-16 ===> 1/216 ===> 1/65536 ==> 0.00001525878
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