I am working on a circuit that inputs a 31-bit pseudo-random binary string into a CCIT CRC-16 block which generates a 16-bit CRC output.(adsbygoogle = window.adsbygoogle || []).push({});

I know that M(x)/G(x) = Q(x) + R(x) and the transmitted code will be R(x) appended to M(x).

When I simulated the circuit, I got a CRC of 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0. From the help file of the software (VisSim/Comm), I know that the generating polynomial is G(x) = 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1.

How do I determine the 31-bit input sequence that generated the CRC result?

Since M(x)/G(x) = Q(x) + R(x), we can say that M(x) = [Q(x) + R(x)]G(x). But we don't know Q(x). Assuming the 16-bit CRC is equal to R(x) and the G(x) is given, how do I go about finding M(x) without knowing Q(x)?

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# Find a message given a CRC and generating polynomial

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