Problem 9 Consider a C(n,k) CRC. We say a burst error of size L occurs when the received codeword contains L consecutive

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Problem 9 Consider A C N K Crc We Say A Burst Error Of Size L Occurs When The Received Codeword Contains L Consecutive 1 (42.46 KiB) Viewed 18 times

Problem 9 Consider a C(n,k) CRC. We say a burst error of size L occurs when the received codeword contains L consecutive bits all in error; i.e., the codeword has L single-bit errors in bit positions next to one another. See figure below for illustration. Suppose the CRC generator is of the form P(X) = 1+aX+ ... +am-Xm-1 + Xm. Using an analysis similar to the one we used in class, show that all burst errors are guaranteed to be detected by the CRC if L <n-k. Hint: E(X) for this burst error is of the form: E(X) = x +x-11 ... + xi which can also be written as E(X) = X'(XL-1 + ... + x + 1). = Burst errors of size:L=j-i + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x) xi xn-1 xo