Q.19 (3 points) A nonconformist engineer designed a coding scheme. A source outp

Question

Q.19 (3 points)
A nonconformist engineer designed a coding scheme. A source output of 0 is transmitted as 010 and a 1 is transmitted as 101 (while a typical engineer would code 0 as 000 and 1 as 111).
(a) If the source output is 0, identify all of the 3-bit patterns that could be received containing errors that can be corrected.
(b) If the source output is 0, identify all of the 3-bit patterns that could contain errors and the occurance of errors can be detected (this time no correction but just detection).
(c) If the probability of receiving any bit in error is p = 0:01, what is the probability of an undetected error ?
(d) If 010 011 001 101 100 is received, what is the output of the decoder ?

Explanation / Answer

a)011, 110, 000 - And these can be corrected

b) 001, 100 . 101 - These can be detected

c) The error will be undetected if all three bits are reversed

probability of an undetected error 0.01 * 0.01 * 0.01 = 1 * 10-6

d)00110

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