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5-1 Data Link Layer l Objective: to achieve reliable and efficient communication between 2 adjacent machines l Data link layer design issues n services provided to the network layer –unacknowledged connectionless service –acknowledged connectionless service –acknowledged connection-oriented service l call set-up l transmission l call release

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5-2 Data Link Layer (cont’d) l Framing n character count –use a field in the header to indicate the number of characters in the frame –e.g. 51234 56789 80123456 –unreliable and rarely used n starting & ending characters, with character stuffing –STX and ETX are used for frame synchronization –DLE and DLE insertion are used for data transparency

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5-3 Data Link Layer (cont’d) l Framing n starting & ending characters/flags, with bit stuffing –01111110 as flag byte (flag pattern) for frame and character sync. (for beginning and end) –zero bit insertion (bit stuffing) to achieve data transparency -- to insert a 0 after 5 contiguous 1’s –e.g. original data 011011111111111111110010 data sent 011011111011111011111010010 data stored 011011111111111111110010 n physical layer (bit) encoding violation n hybrid methods (char. count with one of the others)

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5-4 Data Link Layer (cont’d) l Error control n error detection n ACK’s and NACK’s n time-out mechanism n sequence numbers l Flow control n for speed mismatch (sender faster than receiver), finite receiver buffer or occasional unavailability of the receiver n feedback mechanism is typically required

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5-5 Data Link Layer (cont’d) l Error detection and correction n causes of errors n random vs. bursty errors n error-correcting codes vs. error-detecting codes l Error-correcting codes n codeword (m data-bits + r check bits; let n=m+r) n Hamming distance (H.D.) between 2 codewords n Hamming distance of the complete code: the min. Hamming distance between any 2 distinct codewords

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5-6 Data Link Layer (cont’d) l Error-correcting codes (cont’d) n to detect d errors required a distance d+1 code (e.g. d =1 for parity check where H.D.=2) n to correct d errors requires a distance 2d +1 code e.g. 0000000000 0000011111 1111100000 1111111111 n a lower bound on r to correct any single-bit error: Each of the 2 m legal messages has n illegal codewords at a distance of 1 from it. Then 2 m (n+1) 2 n, and 2 m (m+r+1) 2 m+r. Consequently, m+r+1 2 r.

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5-7 Data Link Layer (cont’d) l Error-correcting codes (cont’d) n Hamming code (corrects only single-bit errors) e.g. m = 7. Then 7 + r + 1 2 r, and consequently r 4. Consider an ASCII code 1001000, where even parity is adopted. Then, arrange the data and error-correcting bits as follows. 2 0 2 1 2 2 2 3 X X 1 X 0 0 1 X 0 0 0 r 1 r 2 m 1 r 3 m 2 m 3 m 4 r 4 m 5 m 6 m 7

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5-8 Data Link Layer (cont’d) l Error-correcting codes (cont’d) n Hamming code (cont’d) 2 0 2 1 2 2 2 3 (position) r 1 r 2 r 3 r 4 (check bits) (3) m 1 1 1 (5) m 2 0 0 (6) m 3 0 0 (7) m 4 1 1 1 (9) m 5 0 0 (10) m 6 0 0 (11) m 7 0 0 0 Consequently, r 1 = 0, r 2 = 0, r 3 = 1 and r 4 = 0.

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5-9 Data Link Layer (cont’d) l Error-correcting codes (cont’d) n Hamming code (cont’d) –to correct at most k consecutive bit errors n k order of transmission If each row contains at most 1 bit error, then the error(s) can be corrected.

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5-10 Data Link Layer (cont’d) l Error-detecting codes n parity check n block sum check n cyclic redundancy code (CRC) –using methods based upon polynomial codes which is more efficient to detect error bursts l a set of check digits is generated and appended to the end of each frame to be transmitted l the receiver performs a similar computation on the message and the check bits l if an error is found, then claim error(s); otherwise, claim correctness (true with a high probability)

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5-11 Data Link Layer (cont’d) l Error-detecting codes (cont’d) n cyclic redundancy code (cont’d) –theory behind M(x) = an m-bit number (message) G(x) = an (r+1)-bit number (generator/divisor) R(x) = an r-bit number (remainder based on modulo-2 arithmetic) Q(x) = quotient Property: If M(x)*x r /G(x) = Q(x) + R(x)/G(x), then [M(x)*x r + R(x)]/G(x) = Q(x). Proof: [M(x)*x r + R(x)]/G(x) = Q(x) + R(x)/G(x) + R(x)/G(x) = Q(x)

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5-12 Data Link Layer (cont’d) l Error-detecting codes (cont’d) n cyclic redundancy code (cont’d) –algorithm l sender n append r zeros to M(x) (M(x) is multiplied by x r ) n divide M(x)*x r (using modulo-2 arithmetic/bit-wise XOR) by G(x) to calculate R(x) n append R(x) to M(x) and transmit l receiver n divide the received info. (M(x)*x r +R(x)) by G(x) n if the remainder is 0, OK; otherwise, report error(s)

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5-13 Data Link Layer (cont’d) l Error-detecting codes (cont’d) n cyclic redundancy code (cont’d) –example (Fig. 3-7, p. 189)

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5-14 Data Link Layer (cont’d) l Error-detecting codes (cont’d) n cyclic redundancy code (cont’d) –G(x) of K bits should detect l all single-bit errors l all double-bit errors l all odd number of bit errors l all error bursts with length < K l most error bursts with length K –example CRC l CRC-16 l CRC-CCITT l CRC-32

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Transmission Errors Error Detection and Correction.

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