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Hw2-Sol - check code Answer(a D i L divided by g(D the...

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Homework 2 – Student name: Son Tran (o ) – Student ID: 2007-23576 Class: Data Networks - 2008 2.15 - For a given generator polynomial g(D) of degree L and given data length K, let 0 ) ( 1 1 ) ( 1 ) ( ... ) ( c D c D c D c i L i L i + + + = - - be the CRC resulting from the data string with a single 1 in position i [i.e. s(D) = D i for 0 ≤ i ≤ K-1]. (a) For an arbitrary data polynomial s(D), show that the CRC polynomial is - = = 1 0 ) ( ) ( ) ( K i i i D c s D c (using modulo 2 arithmetic) (b) Let 0 1 1 1 ... ) ( c D c D c D c L L + + + = - - , show that - = = 1 0 ) ( K i i j i j c s c 0 ≤ j < L This shows that each c j is a parity check and that a cyclic redundancy check code is a parity
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Unformatted text preview: check code. Answer: (a) D i+L divided by g(D), the quotient is z (i) (D), c (i) (D) is the remainder, then D i+L = g(D) z (i) (D) + c (i) (D) ∑ ∑-=-= + = 1 ) ( 1 ) ( ) ( ) ( ) ( K i i i K i i i L D c s D z s D D s ∑-= 1 ) ( ) ( K i i i D c s D ∑-= ∴ 1 ) ( ) ( K i i i D c s ∑-= = 1 ) ( ) ( ) ( K i i i D c s D c (b) Two polynomials are equal, and the coefficient is also same, then the above polynomial equality namely contains ∑-= = 1 ) ( K i i j i j c s c...
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