9 Error Detection and Correction

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9? Error Detection and Correction

• 9.1 Types of Errors
• 9.2 Detection
• 9.3 Error Correction
• 9.4 ??

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Error Detection and Correction

• Data can be corrupted during transmission. For
  reliable communication, error must be detected
  and corrected
• are implemented either at the data link layer
  or the transport layer of the OSI model

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9.1 Type of Errors
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Type of Errors(contd)

• Single-Bit Error
• is when only one bit in the data unit has
  changed (ex ASCII STX - ASCII LF)

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Type of Errors(contd)

• Multiple-Bit Error
• is when two or more nonconsecutive bits in the
  data unit have changed(ex ASCII B - ASCII LF)

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Type of Errors(contd)

• Burst Error
• means that two or more consecutive bits in the
  data unit have changed

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9.2 Detection

• error detection uses the concept of
  redundancy, which means adding extra bits for
  detecting errors at the destination

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Detection(contd)

• Redundancy

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Detection(contd)

• Detection methods
• VRC(Vertical Redundancy Check)
• LRC(Longitudinal Redundancy)
• CRL(Cyclical redundancy Check)
• Checksum

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Detection(contd)

• VRC(Vertical Redundancy Check)
• a parity bit is added to every data unit so
  that the total number of 1s(including the parity
  bit) becomes even for even-parity check or odd
  for odd-parity check

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Detection(contd)

• Even parity VRC concept

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Detection(contd)

• LRC(Longitudinal Redundancy Check)
• parity bits of all the positions are assembled
  into a new data unit, which is added to the end
  of the data block

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Detection(contd)

• LRC calculation

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Detection(contd)

• CRC(Cyclic Redundancy Check)
• is based on binary division.

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Detection(contd)

• CRC generator
• uses modular-2 division.
• Binary division

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Detection(contd)

• Polynomials
• CRC generator(divisor) is most often
  represented not as a string of 1s and 0s, but as
  an algebraic.

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Detection(contd)

• A polynomial representing a divisor

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Detection(contd)

• Standard polynomials

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Detection(contd)

• Checksum
• used by the higher layer protocols
• is based on the concept of redundancy(VRC,
  LRC, CRC .)

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Detection(contd)

• Checksum Generator

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Detection(contd)

• To create the checksum the sender does the
  following
• The unit is divided into K sections, each of n
  bits.
• Section 1 and 2 are added together using ones
  complement.
• Section 3 is added to the result of the previous
  step.
• Section 4 is added to the result of the previous
  step.
• The process repeats until section k is added to
  the result of the previous step.
• The final result is complemented to make the
  checksum.

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Detection(contd)

• data unit and checksum

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9.3 Error Correction

• can be handled in two ways
• ? when an error is discovered, the receiver can
  have the sender retransmit the entire data unit.
• ? a receiver can use an error-correcting code,
  which automatically corrects certain errors.

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Error Correction(contd)

• Single-Bit Error Correction
• parity bit
• The secret of error correction is to locate the
  invalid bit or bits
• For ASCII code, it need a three-bit redundancy
  code(000-111)

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Error Correction(contd)

• Redundancy Bits
• to calculate the number of redundancy bits (R)
  required to correct a given number of data bit (M)

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Error Correction(contd)

• If the total number of bits in a transmittable
  unit is mr, then r must be able to indicate at
  least mr1 different
• 2r ? m r 1
• ex) For value of m is 7(ASCII) , the smallest r
  value that can satisfy this equation is 4
• 24 ? 7 4 1

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Error Correction(contd)

• Relationship between data and redundancy bits

Number of Redundancy Bits (r)
Number of Data Bits (m)
Total Bits (mr)
1 2 3 4 5 6 7
2 3 3 3 4 4 4
3 5 6 7 9 10 11
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Error Correction(contd)

• Hamming Code
• developed by R.W.Hamming
• positions of redundancy bits in Hamming code

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Error Correction(contd)

• each r bit is the VRC bit for one combination of
  data bits
• r1 bits 1, 3, 5, 7, 9, 11
• r2 bits 2, 3, 6, 7, 10, 11
• r4 bits 4, 5, 6, 7
• r8 bits 8, 9, 10, 11

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Error Correction(contd)

• Redundancy bits calculation(contd)

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Error Correction(contd)

• Redundancy bits calculation

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Error Correction(contd)

• Calculating the r values

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Error Correction(contd)

• Error Detection and Correction

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Error Correction(contd)

• Error detection using Hamming Code

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Error Correction(contd)

• Multiple-Bit Error Correction
• redundancy bits calculated on overlapping sets
  of data units can also be used to correct
  multiple-bit errors.

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9.4 ??