Consider the generator polynomial 100101 and the data 1011100110001. Applying the CRC algorithm we get the transmitted message: 1011100110001 ⏟ D a t a 00011 ⏟ R e m a i n d e r I need to make 3 errors in the transmitted word (that is, bit flips) that the receiver won't notice. Hence, the CRC algorithm will fail to notice the errors and will falsely the data. How can this be arranged?

Question

Consider the generator polynomial   100101 and the data   1011100110001. Applying the CRC algorithm we get the transmitted message:              1011100110001      ⏟              D      a      t      a                      00011      ⏟              R      e      m      a      i      n      d      e      r      I need to make 3 errors in the transmitted word (that is, bit flips) that the receiver won&#039;t notice. Hence, the CRC algorithm will fail to notice the errors and will falsely the data. How can this be arranged?

Dreforganzv · Accepted Answer

In the simplest form of CRC algorithm, the data polynomial   d  (  x  ) is multiplied by       x    5   and then divided by       x    5    +      x    2    +  1, the CRC polynomial, to get a remainder   r  (  x  )  =  x  +  1 in this case.. The transmitted word polynomial is       x    5    d  (  x  )  +  x  +  1 and is a multiple of       x    5    +      x    2    +  1. Can you tell why? That&#039;s what the receiver is checking for: is the word a multiple of       x    5    +      x    2    +  1 or not?? So, it you add       x    5    +      x    2    +  1 to the transmitted word, the result will still pass the test, no?

Alessandra Clarke · Accepted Answer

good answer.

Consider the generator polynomial 100101 and the data 1011100110001 . Applying the CRC algori

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