EE450-Discussion7-Spring09

EE450-Discussion7-Spring09 - Discussion #7 EE450, 2/27/2009...

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Discussion #7 EE450, 2/27/2009 Sample Problems: Flow Control
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Error Detection and Correction Using FCS s Frame Check Sequence (FCS) refers to the redundant information (Extra Checksum Characters) added to a Frame in a communication protocol for error detection and correction. s The sender computes a checksum on the entire frame and sends this along. s The receiver computes the checksum on the frame using the same algorithm, and compares it to the received FCS. s It can then detect whether any data was lost or altered in transit, discard the data, and request retransmission of the corrupted frame. s FCS is used in Ethernet, X.25, HDLC, Frame Relay, and other data link layer protocols. s A cyclic redundancy check (CRC) is often used to compute the FCS. An Ethernet frame including the FCS terminating the frame
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Cyclic Redundancy Check s Add K redundancy bits to N bits of data s K << N s e.g.: Ethernet Frame 12,000 bits – 32 bits Redundancy s Add k bits of redundant data to an n -bit message. s Represent -bit message as an n-1 degree polynomial e.g. MSG=10011010 corresponds to M(x) = x 7 + x 4 3 1 , =8 s Let be the degree of some divisor polynomial G(x) e.g. G(x) = x 3 2 + 1 (corresponds to 1101) K =3
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s Sender wants to transmit MSG=10011010 MSG=10011010 , n =8 corresponds to M(x) = x 7 + x 4 3 1 Divisor=1101 , k =3 corresponds to G(x) = x 3 2 + 1 s Multiply M(x) by x k In this example, we get: M(x).x 3 = 10 7 6 4 =10011010000 s Divide result by G(x) =1101 (Subtraction or addition is XOR in polynomial arithmetic) The remainder is E(x) = x 2 +1 = 101 s Send P(x) = k + E(x) which is exactly divisible by G(x) i.e. Send 10011010000 + 101 = 10011010101, since this is exactly divisible by =1101 Sender: Example
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10011010000 10011010000 = = x 10 10 + x + x 7 + x + x 6 6 + x + x 4 1101 1101 = = x 3 3 + x + x 2 + 1 + 1 11111001 11111001 1101 1101 | 10011010000 10011010000 1101 1101 1001 1001 1101 1101 1000 1000 1101 1101 1011 1011 1101 1101 1100 1100 1101 1101 1000 1000 1101 1101 101 Remainder = x 101 Remainder = x 2 + 1 + 1 Division
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Example of CRC checking s Do the same example in Polynomial 10011010000 = 10011010000 = x 10 10 + x + x 7 + x + x 6 6 + x + x 4 1101 = 1101 = x 3 3 + x + x 3 + 1 + 1 x 7 + x + x 6 + x + x 5 + x + x 4 + x + x 3 3 + 1 + 1 Quotient = 11111001 Quotient = 11111001 x 3 3 + x + x 2 + 1 + 1 | x 10 10 + x + x 7 + x + x 6 6 + x + x 4 x 10 + 10 + x 9 + x + x 7 x 9 + x + x 6 + x + x 4 x 9 + x + x 8 + x + x 6 x 8 + x 4 x 8 + x + x 7 7 + x + x 5 x 7 + x + x 5 5 + x + x 4 4 x 7 + x + x 6 + x + x 4 x 6 6 + x + x 5 x 6 6 + x + x 5 + x + x 3 x 3 x 3 + x + x 2 + 1 + 1 x 2 + 1 Remainder = 101 + 1 Remainder = 101
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s Divides the Received Polynomial by G(X) s If the remainder is not zero – Discard! s
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This note was uploaded on 03/26/2009 for the course EE 450 taught by Professor Zahid during the Spring '06 term at USC.

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EE450-Discussion7-Spring09 - Discussion #7 EE450, 2/27/2009...

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