crc - CNT 4104 Intro to Data Comm Cyclic Redundancy Check...

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CNT 4104 Intro to Data Comm Cyclic Redundancy Check Dr. Sam Hsu Computer Science & Engineering Florida Atlantic University
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2 CRC Key concepts Polynomials Modulo 2 arithmetic Algorithm Hardware implementation Shift registers. Exclusive-OR (XOR) gates
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3 Some Math Concepts (1/2) A polynomial of degree n, n 0 in x can be represented as: a n x n + a n-1 x n-1 + … + a 0 (a n 0) Given N(x), a polynomial of degree n , we can show that N(x) = Q(x) * D(x) + R(x) where Q(x), D(x) and R(x) are also polynomials of some degrees n . R(x) = 0 if N(x) is divisible by D(x).
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4 Some Math Concepts (2/2) If B(x) is a polynomial of some degree, then we can show that A(x) = B(x) * x m (m 0) where A(x) is also a polynomial.
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5 Modulo 2 Arithmetic 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 Which are the same as the XOR operations 0 0 = 0 0 1 = 1 1 0 = 1 1 1 = 0 + + + +
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6 Cyclic Redundancy Check Code Is also known as the polynomial code . Is based upon treating bit patterns as representations of polynomials with binary coefficients of 0 and 1 only.
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