Error Detection

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Chapter 9
Error Detection And Correction
2
Figure 9-1
Types of Errors

• Data can be corrupted during transmission, and
  errors must be detected or corrected.

3
Figure 9-2
Single-Bit Error
ASCII STXstart of text
ASCII LFline feed

• In a single-bit error, only one bit in the data
  unit has changed.
• In serial transmission system a single-bit error
  rarely occurs, however in parallel transmission
  system can frequently occurs.

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Figure 9-3
Burst Error of Length Five

• A burst error means that two or more bits in the
  data unit have changed.
• A burst error does not necessarily mean that the
  errors occur in consecutive bits.
• Sending data rate is 1 Kbps, a noise of 1/100
  seconds can affect 10 bits.

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Figure 9-4
Redundancy

• Instead of repeating the entire data stream, a
  shorter group of bits may be appended to the end
  of each unit.

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Figure 9-5
Detection Methods

• Use in upper layer

• Use in data link layer

• Vertical redundancy check (VRC) parity check
• Longitudinal redundancy check (LRC)
• Cyclical redundancy check (CRC)
• Checksum

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Figure 9-6
Even Parity VRC Concept

• Can detect all single-bit errors.
• Can detect burst errors only it the total number
  of errors in each data unit is odd.
• Even-parity checking ? Odd-parity checking

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Figure 9-7
LRC

• A block of bits is divided into rows and a
  redundant row of bits is added to the whole
  block.
• LRC increases the likelihood of detecting burst
  errors.

• Do not detect a two-bit error.

• Detect a burst error.

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Figure 9-8
CRC Generator and Checker
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Figure 9-9
Binary Division in a CRC Generator
Modulo-2 division
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Figure 9-10
Binary Division in a CRC Checker
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Figure 9-11
A Polynomial
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Figure 9-12
A Polynomial Representing a Divisor
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Figure 9-13
Standard Polynomials
CRC Performance

• CRC can detect
• - all burst errors that affect an odd number
  of bits.
• - all burst errors of length less than or
  equal to the degree of the polynomial.
• - with a very high probability burst errors of
  length greater than the degree of the polynomial.

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Figure 9-14
Checksum
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Figure 9-15
Data Unit and Checksum

• Performance
• - detects all errors involving an odd number
  of bits.
• - detects most errors involving an even number
  of bits.

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Error Correction

• In theory it is possible to correct any binary
  code errors automatically.
• Error-correction codes are more sophisticated
  than error-detection codes and require more
  redundancy bits.
• Most error correction is limited to one-, two-,
  or three-bit errors.

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Figure 9-16
Single-Bit Error Correction (Data and Redundancy
Bits)

• r bits must be able to indicate at least (mr1)
  different states.
• - No error
• - 1st, 2nd, , and (mr)th bit error

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Figure 9-17
Positions of Redundancy Bits in Hamming Code
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Figure 9-18
Redundancy Bits Calculation

• A seven-bit data sequence
• - 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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Figure 9-19
Example
Even parity
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Figure 9-20
Single-Bit Error
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Figure 9-21
Error Detection Using Hamming Code
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Burst Error Correction

• A Hamming code can be designed to correct burst
  errors of certain lengths.
• The number of redundancy bits required to make
  these corrections is drastically higher than that
  required for single-bit errors.

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Summary

• Single-bit and burst errors
• Error detection methods
• VRC/LRC/CRC
• Data-link layer
• Checksum
• High-layer protocol (TCP/IP)
• Error correction method
• Hamming code