CPET 355

1
CPET 355

• 3. The Data Link Layer
• Framing, Error Detection
• and
• Correction
• Paul I-Hai Lin, Professor
• Electrical and Computer Engineering Technology
• Purdue University, Fort Wayne Campus

2
Topics of Discussion

• Framing
• Error Detection
• Error Correction

3
Framing

• Framing Marking Methods
• Character count
• Flag byte with byte stuffing
• Starting and ending flags, with bit stuffing
• Physical layer coding violations

4
Framing Character Count

• Use a field in the header to specify the number
  of characters in the frame
• Disadvantage the count can be garbled by a
  transmission error the problem of
  resynchronization
• An example

Character Count
5 a A b b 4 6 w w 1 2 y y 8 a b c d e f 1 2
5
Framing Flag Bytes with Byte Stuffing

• Resolve the resynchronization problem
• Use a flag byte as the starting ending
  delimiter
• Potential problems
• When sending objects that containing
  floating-point numbers It can be resolved by
  inserting an ESC byte
• Strong tie to 8-bit character cannot handle
  Unicode (16-bit character coding International
  languages)
• An example Point-to-Point Protocol used by
  Internet Service Provider with modem

6
Framing Flag Bytes with Byte Stuffing
Flag Header Payload field Trailer Flag
Original Characters
After Stuffing
A ESCFLAG B
A FLAG B
A ESCESCB
A ESC B
A ESCFLAG B
A ESCESCESCFLAG B
A ESCESCB
A ESCESCESCESC B
7
Framing Bit Stuffing

• Allow data frames to contain an arbitrary number
  of bits, and character coding
• Starting ending delimiter a special bit
  pattern (flag byte) 01111110
• Sender stuffing a 0 when encounter five
  consecutive 1s in the data
• Receiver destuffing a 0 when it sees five
  consecutive 1s

8
Framing Bit Stuffing
The Original Data
01101111101111110
0110111110011111010
Stuffed 0 bits
9
Checksums

• Checksum Calculation
• ASCII value of a Character x 128
• Divide the number by 255
• The remainder is the checksum
• An Example
• ASCII A 0100 00012 6510
• 65 x 128 8320
• 8320/255 32 remainder 160
• Transmitted checksum character is 160 (010 00002)

10
Hamming Distance

• Error detection and correction
• The number of bit position in which two codeword
  is differ called the hamming distance (1950)
• To detect d errors, we need a distance of d 1
  code
• To correct d errors, we need 2d 1 code

11
Hamming Distance

• Example two code words, 3 bits differ or a
  hamming distance of 3
• Code Word 1 1000 1001
• EXOR --------------
• Code Word 2 1011 0001
• --------------
• 0011 1000
• Count the number of 1-bit 3

12
Parity Bit

• Even parity or odd parity for detect 1-bit error
  with a distance of 2
• Example
• Set 8-bit code
• x101 1010 as even parity code
• 0101 1010
• Set 8-bit code
• x101 1010 as odd parity code
• 1101 1010

13
Hamming Code for Error Correction

• Correct a single error or burst errors
• 7-bit ASCII code, 11-bit code word
• Data are found in bit positions 3, 5, 6, 7, 9,
  10, and 11
• Check bits are found in bit positions 1, 2, 4,
  and 8
• Bit 11 1 2 8 10 2 8 9 1 8 7 1
  2 4 6 2 4 5 1 5 3 12

14
Hamming Code for Error Correction

• An Example
• Bit positions (1 2 3 4 5 6 7 8 9 10 11)
• H 1001000 ? 0011001000

15
Checksums

• Checksum Calculation
• ASCII value of a Character x 128
• Divide the number by 255
• The remainder is the checksum
• An Example
• ASCII A 0100 00012 6510
• 65 x 128 8320
• 8320/255 32 remainder 160
• Transmitted checksum character is 160 (010 00002)

16
Internet Checksums

• RFC 1071 Computing Internet Checksum,
  http//www.faqs.org/rfcs/rfc1071.html
• unsigned short checksum(unsigned short addr, int
  count)
• / Compute Internet checksum for count bytes
  beginning at location addr/
• register long sum 0
• while( count gt 1 )
• / This is the inner loop /
• sum addr
• count - 2

17
Internet Checksums

• / Add left-over byte, if any /
• if( count gt 0 )
• sum addr
• / Fold 32-bit sum to 16 bits /
• while (sumgtgt16)
• sum (sum 0xffff) (sum gtgt 16)
• checksum sum
• / end of checksum() function /

18
Internet Checksums C Program

• Comments
• / / --- C style
• // --- C and Java style
• Function (name, input parameters types, a
  return value type)
• unsigned short checksum(unsigned short addr, int
  count)
• Return value sum

19
Internet Checksums C Program

• Grouping of statements, functions, etc
• ( )
• Data types
• register long sum 0
• unsigned short addr --- Pointer type
• int count

20
Internet Checksums C Program

• Decision making program loop control
• while, for, do while
• if
• Operators
• Add assign
• - Sub assign
• Increment
• -- Decrement

21
Internet Checksums C Program

• Operators (continue)
• Remainder
• / Integer Quotient (or float division)
• Bit-wise AND
• Bit-wise OR
• Exclusive OR
• Bit-wise NOT (1s complement)
• gtgt Shift to the Right
• ltlt Shift to the Left

22
Cyclic Redundancy Checks (CRCs) Frame Check
Sequence

• Generator Polynomial Codes G(x) - for generating
  frame check sequence
• CRC-12 (for 6-bit characters)
• x12 x11 x3 x2 x1 1
• CRC-16 (for 8-bit characters)
• x16 x15 x2 1
• CRC-CCITT x16 x12 x5 1
• CRC-32 (used in IEEE 802)
• x32 x26 x23 x22 x16 x12 x11 x10
  x8 x7 x5 x4 x2 x1 1

23
Cyclic Redundancy Checks (CRCs) Frame Check
Sequence

• An Example
• G(x) x4 x1 1
• M(x) message frame 1101011011
• R(x) remainder is computed from MOD2 operation
  1110
• T(x) transmitted sequence plus append R(x) at the
  end M(x) R(x)

11010110111110
24
Number Systems in C

• Decimal Octal Hex
• 0 00 0x0
• 1 01 0x1
• 2 02 0x2
• 3 03 0x3
• 4 04 0x4
• 5 05 0x5
• 6 06 0x6
• 7 07 0x7

25
Number Systems in C

• Decimal Octal Hex
• 8 010 0x8
• 9 011 0x9
• 10 012 0xa or 0xA
• 11 013 0xb or 0xB
• 12 014 0xc or 0xC
• 13 015 0xd or 0xD
• 14 016 0xe or 0xE
• 15 017 0xf or 0xF

26
Cyclic Redundancy Checks (CRCs) Frame Check
Sequence

• An Implementation Using C Language
• unsigned short Gx 0x0013 /x4 x1 1/
• unsigned short Mx 0x035D /1101011011/
• unsigned short Rx Qx Tx 0x0000
• Rx GxMx / reaminder, 1-bit less than Gx /
• Qx Gx/Mx / quotient /
• Tx Tx Mx / Tx Mx /
• Tx ltlt 5 / Shift Tx to the left for
  5-bit /
• Tx Qx / Append quotient bits /