Functions of the Data Link Layer

1
Functions of the Data Link Layer

• Provide service interface to the network layer
• Dealing with transmission errors
• Regulating data flow
• Slow receivers not swamped by fast senders

2
Functions of the Data Link Layer (2)

• Relationship between packets and frames.

3
Errors in transmission

• Basics of transmission variation of
  (amplitude/phase/frequency)
• SNR
• 10 log ((peak signal/(RMS Noise)2)
• Regenerative Repeaters
• Bit Error Ratio (BER)
• Optical medium is around 10-14
• Wireless is around 10-3
• Copper in between
• Gaussian Noise/AWGN
• Burst errors

4
Error Detection and Correction

• Error-Correcting, Error-Detecting Codes
• Some Basics
• Msg (m) Redundant(r) Code(n)
• Not all codewords are legal
• Hamming Distance is the number of positions where
  two codewords differ
• If 2 codewords are distance d apart, then it
  takes d errors to convert one to the other gt
• d1 distance for d error detection
• 2d1 distance for d error correction

5
Error Detection and Correction

• Parity as an EDC
• 1 bit parity creates a code with distance 2
• 00 --gt 000, 01 --gt 011
• Suppose we want to correct all single errors in
  an m bit message. How efficient can such a code
  be in terms of length ?
• n bit code gt n single bit errors gt n1
  codes/valid msg
• (n1)2m lt 2n or mr1 lt 2r

6
Hamming Codes

• Hamming codes obtain the theoretical lower bounds
  (perfect parity codes)
• In a codeword, powers of 2 are the check bits,
  and the other bits contain data
• The parity of a data bit is checked by several
  check bits, as directed by the binary
  representation of its position.
• Bit 11s parity is checked by 128
• Reciever adds parity bits in error, and this
  gives the location of the error bit!
• Interleaving to detect burst errors

7
Error-Correcting Codes

• Use of a Hamming code to correct burst errors.

8
Error Detecting Codes

• Useful when BERs are low and overhead of ECC is
  significant compared to Re-Tx.
• Still use the interleaving idea to convert burst
  errors into single bit errors
• Polynomial (CRC) codes
• A k1 bit number is represented as a polynomial
  of degree k in some dummy variable, with leftmost
  bit being most significnt.
• Sender and receiver agree on the generator of
  the code, another polynomial G(x), with 1s in msb
  and lsb
• Polynomial arithmetic is done modulo 2 (no
  carries or borrows, GF(2))

9
CRC Codes

• Append a checksum to the end of the msg
• If G(x) is of degree r, then append r 0s to end
  of the m msg bits. The new number is now xrM(x)
• Divide this by G(x) modulo 2
• Subtract the remainder from XrM(x) modulo 2, and
  let this be T(x). This number is now divisible by
  G(x)
• Transmit T(x), and have receiver check if the
  received data is divisible by G(x)
• Suppose T(x)E(x) arrives.
• (T(x)E(x)/G(x) ) E(x)/G(x)
• Detection whenever E(x)/G(x) ! 0

10
Error detection in CRC

• 1 bit error will be caught as long as G has 2 or
  more terms
• For 2 isolated bit errors if G(x) does not divide
  xk1 where k distance between error bits
• CRC-CCITT 1x5 x12 x16
• IEEE 802 (32,26,23,22,16,12,11,10,8,7,5,4,2,1,0)
• BCH Codes are GF(2m). Reed-Solomon are BCH codes
  with block size 2m
• Convolution codes (Trellis or Viterbi)

11
Error-Detecting Codes
Calculation of the polynomial code checksum.