Lecture 6: Framing and Error Detection-Data Link Layer Functions

1. Lecture 6: Framing and Error Detection-Data Link Layer Functions

2. Review of Lecture 5 • Level 1: Physical or Hardware Layer • Deals with the transmission of bits • Signal Generation and Modulation • Encoding • Implemented by adapters and device drivers

3. Review of Lecture 5 • Level 2: Data Link Layer • Deals with reliable transmission of data over a single link (does not include routing over a network of links) • Framing • Error Detection

4. 8 16 16 8 Beginning Ending Header Body CRC sequence sequence Review of Lecture 5 • Last time—Bit oriented protocol with sentinel strings (01111110 at beginning and end of frame • Uses bit-stuffing to identify sentinel strings in the payload • Sender inserts zero after string of five 1’s • Receiver deletes stuffed bits

5. Byte oriented framing-Byte counting approach • include payload length in header • e.g., Digital Data Communication Message Protocol (DDCMP) • problem: count field corrupted • solution: catch when CRC fails

6. Byte-oriented framing: Sentinel Approach DLE character precedes ETX within the body

7. Clock-based framing • SONET: Synchronous Optical Network • each frame is 125us long • STS-n (STS-1 = 51.84 Mbps)

8. Error Detection and Correction • Two dimensional Parity • Cyclic Redundency Check • Internet checksum

9. Two Dimensional Parity Detects and corrects single bit errors Detects 2 and 3 bit errors Fails for 4 errors at the corners of box

10. 8 16 16 8 Beginning Ending Header Body CRC sequence sequence Cyclic Redundancy Check • Add k bits of extra data (the CRC field) to an n-bit message to provide error detection function • For efficiency, want k << n • e.g., k = 32 for Ethernet and n = 12,000 (1500 bytes)

11. Polynomials with binary coefficients • Represent n-bit message as n-1 degree polynomial • e.g., MSG=10011010 as M(x) = x7 + x4 + x3 + x1 • Addition (no carry) Subtraction (no borrow) • 10011010 00101110 10110100 10110100 • 00101110 10011010 • A-B=AXORB

12. Polynomials with binary coefficients • Multiplication 1110 The usual 1110 without 11100 carrying 1110 1110 1010100

13. Polynomials with binary coefficients • Division 1110 The usual 1110÷1010100 without the 1110 borrowing 1001 1110 1110 1110 0

14. CRC strategy • Sender and Receiver know the “divisor polynomial” • e.g. C(x)=x3+x2+1=1101 • Send Message÷ CRC with CRC chosen so that the whole thing is evenly divisible by C(x) • Receiver calculates the remainder of Message÷ CRC/C(x) There’s an error if it is not zero

15. CRC example • Message=10011010 C=1101(3 rd order) • Message÷ CRC=10011010XYZ • Choose XYZ so that remainder is zero for Message÷ CRC/C

16. CRC Example cont. • 11111001 1101÷10011010XYZ1101 1001 1101 1000 1101 X=1 1011 Y=0 1101 Z=1 1100 1101 1xyz 1101 • Message÷ CRC=10011010÷ 101

17. CRC Example cont. • 11111001 1101÷10011010000 1101 1001 1101 1000 1101 1011 1101 1100 1101 1000 1101 101 • Message÷ CRC=10011010000 - (xor) 101

18. CRC (cont) • Let k be the degree of some divisor polynomial • e.g., C(x) = x3 + x2 + 1 • Transmit polynomial P(x) that is evenly divisible by C(x) • shift left k bits, i.e., M(x)xk • subtract remainder of M(x)xk / C(x) from M(x)xk • Receiver polynomial P(x) + E(x) • E(x) = 0 implies no errors • Divide (P(x) + E(x)) by C(x); remainder zero if: • E(x) was zero (no error), or • E(x) is exactly divisible by C(x) (unlikely for CRC-32)

19. Selecting C(x) • All single-bit errors, as long as the xk and x0 terms have non-zero coefficients. • All double-bit errors, as long as C(x) contains a factor with at least three terms • Any odd number of errors, as long as C(x) contains the factor (x + 1) • Any ‘burst’ error (i.e., sequence of consecutive error bits) for which the length of the burst is less than k bits. • Most burst errors of larger than k bits can also be detected • See Table 2.6 on page 102 for common C(x)

20. Internet Checksum Algorithm • View message as a sequence of 16-bit integers; sum using 16-bit ones-complement arithmetic; take ones-complement of the result. u_short cksum(u_short *buf, int count) { register u_long sum = 0; while (count--) { sum += *buf++; if (sum & 0xFFFF0000) { /* carry occurred, so wrap around */ sum &= 0xFFFF; sum++; } } return ~(sum & 0xFFFF); }