Question

5. In a CRC error-detection scheme, choose P(x)x+x3 x11, a. Encode the bits 10010011011. (5 Marks) b. Introduce an error pattern 010010000000000 (i.e invert the digit in the code word where "" appears in the error pattern sequence.) and see if the error can be detected. (3 Marks) Introduce an error pattern 110110000000000 and see if the error can be detected. What (6 Marks) c. can be deduced?

Answer 1

Given the p (x) = x^4 + x^3 + x� + 1 cyclic redundancy check polynomials of degree 4 a) Encode the bits 100100111011 rightarrow encoding means we need to final transmitted data generator matrix = x^4 x^3 x^2 x^1 x^0 1 1 1 0 1 1 [in given p (x) x^2 term is absent so that it is zero] rightarrow append four zeros at the end of bit stream because degree of polynomial is 4 10010011011 0000 divide bitstream with generator matrix and here substractor is modulo - 2 i.e E x - o R \r\n modular - 2 subtraction 1 1 1 1 1 1 0 0 1 1 1 1 0 0 1 1 11 1 1 1 1 1 1 Therefore transmitted data = 1 1 1 11 1 1 1 1 1 b) error pattern 0100100000000000 divided by generator matrix if reminder is zero then no error otherwise error is there \r\n c) error pattern 1101100000000 Therefore remember zero obtained THEREFORE no error detected.