CS3502: Data and Computer Networks DATA LINK LAYER - 1

1. CS3502:Data and Computer NetworksDATA LINK LAYER - 1

2. data link layer : objectives • thorough understanding of DL layer -- • where/how it fits into network/other layers • service it provides (to higher layers) • services it uses (from lower layer) • synchronous/asynchronous transmission • error detection and correction • describe flow control protocols: sliding window • specify/verify basic DL protocols • elementary performance analysis of DL protocols

3. data link layer • phys. layer subject to errors; not reliable; and only moves information as bits, which alone are not meaningful. DL layer adds these, and combines bits into frames, or messages. • purpose of DL: transform unreliable physical bit stream into reliable data communications link... • PHY + DL = DATA COMMUNICATIONS • MAC layer (media access control) - takes place of DL layer in LANs (together with LLC)

4. data link layer : functions • framing and frame synchronization • frames marked by sync/async technique • error control • flow control • addressing • control information, data on same link (unlike EIA232) • link management (3 phases)

5. data link layer : framing • bits must be grouped into frames or messages • frames marked by synchronous transmission: frame starts, ends with a special flag pattern • allows bits to be grouped into fields, subgroups; two main types are data and control bits. • several types of control bits; some for • error detection and/or correction • addressing • flow control • other control type information

6. data link layer : error control • 3 basic techniques in this course (more complex techniques exist) • parity checking • very simple and easy error detection • CRC - cyclic redundancy check • more complex, but very effective and efficient • Hamming code • limited error correction; based on complex combinations of parity checks

7. data link layer : parity checking • to a group of data bits add a single extra bit, known as the parity bit. This bit is chosen to make the total number of 1s in the group even (or odd). Called even (odd) parity checking. • example: data bits 0011001; add parity bit 1 --->00110011. • exercise: construct a FSM to (1) output correct parity bit (2) read a string and decide parity

8. data link layer : parity checking • what is the problem with simple parity checking as described? (show how to fool it) X X X P • LRC - double parity checks improve this X X X X P X X X X P X X X X P P P P P P • show how to fool this error check • improves error probability by factor of 102 - 104

9. data link layer : error probabilities let PB = Prob [single bit error]; then (1 - PB ) = Prob [no error] for group of N bits, define P1 : Prob[no errors] P2 : Prob[undetected error] P3 : Prob[detected error] By definition, P1 + P2 + P3 = 1

10. data link layer : error probabilities Case 1: no error detection Then what are these 3 probabilities for Case 1? P1 = Pr [no error] = P2 = Pr [undetected error] = P3 = Pr [detected error] = example

11. data link layer : error probabilities Case 2: error detection using parity bit • for even parity, even # errors goes undetected; so P2 is Pr(even # of errors) P1 = (1 - PB)Nb P2 =  nC2aPb 2a (1-Pb)Nb-2a P3 = 1- P2 - P3 hint: what is Pr(1 error)? Pr(2 errors)? ... k errors? Nb/2 a=1

12. data link layer : error probabilities • examples in a 10 bit word, what is P[only bit 3 wrong]? P[exactly 1 error]? P[exactly 3 errors]? P[at most 3 errors]? P[3 errors or more]? P[3 bit burst error, with other 7 bits correct]?

13. data link layer : error probabilities • frame probabilities, parity checking • given a frame, sent as a sequence of words/bytes, each with a parity check. What are Pf1, Pf2, and Pf3? Pf1 = probability of no error in the whole frame Pf2 = probability of an undetected error and no detected error anywhere else in the frame Pf3 = probability of an detected error

14. data link layer : error probabilities • Nb= no.bits/word; Nc = no.words/frame. Pf1 = P1Nc where: P1 is the probability of no error in a word Pf2 =  NcCiP2 i [ (1-Pb)Nb]Nc -i where: P2 is the probability of undetected error in a word Pb is the probability there is an error in a bit Pf3 = 1 - Pf1 - Pf2 Nc i=0

15. error checking : CRC • stronger error check needed • idea: insert a group of bits in the frame, which serve as as more powerful check. • added bits (frame check sequence, FCS) cause the resulting frame to be exactly divisible by a predetermined number. • modulo-2 arithmetic used; binary addition with no carries • examples

16. error checking : CRC let M denote data message, k bits long to M, add F, the FCS, which is n bits long resulting transmitted frame is T, T = 2nM + F = M| F is evenly divisible by some pattern P, a sequence of (n + 1) bits. Q: how is F calculated from M and P?

17. error checking : CRC • F is n bits, pattern P is (n + 1) bits • 1st, last bits of P must be 1 • FCS F computed from M, P: F = remainder R, when dividing 2nM / P = Q + R note: this“division” is modulo-2, no carries example : let M = 110011; k = 6; n = 3; p = 1001. Find F and T. (answer next page)

18. error checking : CRC • quotient Q = 110101; remainder R = 101; so T = 110011101. • check: divide T by P, R should be 0. • example : M = 1010001101; P = 110101. Find F, T. Then check it.

19. error checking : CRC • CRC summary • all single and double bit errors • all odd numbers of errors • all burst errors smaller than n • most larger burst errors • If error detected, frame is retransmitted; does NOT correct error. • both CRC and parity checking widely used; CRC used in many network protocols, in addition to data link layer, including most LANs. • CRC can be implemented efficiently in hardware... computation done bit by bit

20. error checking : CRC implementation • shift register, XOR gates • 1 XOR gate for each “1” in pattern P, minus 1. • (n-1) 1-bit shift registers • example : show logic circuit for P - 110101.

21. error checking : Hamming code • correct a single bit error • detect multiple errors • extended parity checking; ie, redundant parity bits Idea: parity bits appear in positions corresponding to the nodes of a binary tree; data bits appear in positions corresponding to the leafs. If a bit is in error, the other bits “point” to it by their related positions in the tree.

22. error checking : Hamming code • each parity bit appears in a position corresponding to a power of 2: n = 0,1,2,4,8,16,... • bits checked by parity bit in position n are: 1. itself 2. continue for next n bits (including itself) 3. off (don’t check) next n bits 4. on (check) the next n bits and continue to end of message. Example: for the data 1101100101, show Hamming coded mesage.

23. error checking : Hamming code • How is single error bit detected? example: suppose 01100110011 Xmitted; 01100010011 received. 1st parity bit, position 1: 2nd parity bit, position 2: 3rd parity bit, position 4: 4th parity bit, position 8: 0 parity bit, position 0: result:

24. error checking : Hamming code • example: suppose 0111011 received; is it correct? Q: for a k-bit message, approximately how many bits are needed? Summary, error correction: • more complex codes correct multiple errors • require more redundancy, overhead. Also more time... so not widely used in communications. • do have a place in longer distance communications -- eg, deep space, etc. In fact could be critical to long distance (time) communications