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. Review of Lecture 5
Last time—Bit oriented protocol with sentinel strings ( 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
Header
Body 8 16
CRC
Beginning
sequence
Ending

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 = 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. 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)
Header
Body 8 16
CRC
Beginning
sequence
Ending

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

12. Polynomials with binary coefficients
Multiplication The usual without carrying

13. Polynomials with binary coefficients
Division The usual ÷ without the borrowing

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= XYZ
Choose XYZ so that remainder is zero for Message÷ CRC/C

16. CRC Example cont.
÷ XYZ X= Y= Z= xyz
Message÷ CRC= ÷ 101

17. CRC Example cont. ÷
Message÷ CRC= (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);