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LECTURE
E rror Detection And Correction Methods
s is ganiz in a table (rows and columns) se ing 3 its, we organize them in a table made of 4
bit for each column and create a new row of 8 bits
first
Ex
Longitudinal Red Check( )
r
LRC
o In LRC, a block of bit o ed o For example instead of nd 2 b rows and 8 columns
o We then calculate the Parity which are the parity bits for the whole block o Note that the first parity bit in the 5th row is calculated based on allthe bits o The second parity bit is calculated based on all the second bits and so on
o We then attach the 8 parity bits to the original data and send them to the
receiver
ample 9.
Sup s
______
and some bits are corrupted:
Receiver checks LRC, some of bits do not follow even parity rule and whole block is discarded
po e the following block is sent: 10101001 00111001 11011101
10101010 (LRC)
It is hit by a burst of length 8
10100011 10001001 11011101 11100111
10101010 (LRC)
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o Burst errors can be detected more often o As shown in the last example, an LRC of ‘n; bits can easily detect a burst error of ‘n’ bits o A burst error of more than ‘n’ bits is also detected by LRC with a very high probability o One pattern of errors remain elusive o If two bits in one data unit are changed and two bits in exactly the same place in another data unit are also damaged For Example:
- Original data units 11110000 11000011 Changed data units
of the data unit, so that the resulting data unit becomes exactly ble by a second predetermined binary number unit is divided by the same number step, there is no remainder, the incoming data unit is assumed to be refore accepted der indicates that a data unit has been damaged and therefore must be
To e It m st have exactly one
d of the data must make the resulting bit sequence exactly visib sor
__________
1 0 1 01 0 1 0 (LRC)
Performance of LRC
Cyclic Redundancy Check (CRC) o Most powerful of checking techniques o VRCand LRC are based on Addition o CRC is based on Binary Division o A sequence of redundant bits called CRC or CRC remainder is appended to the end divisi o At its destination, the data o If at this intact and is the o A remain rejected
Qualities of CRC b valid the CRC must have two qualities:
- u less bit than the divisor
- Appending it to the en di le by the divi
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The polynomial format is useful for two reasons:
mathematically
election of a Polynomial
e by ‘x’
at all burst errors affecting an odd number of bits are detected
Polynomials o CRC generator ( the divisor) is most often represented not as a string of 1’s and 0’s but as an algebraic polynomial o
- It is short
- Can be used to prove the concept
S o A polynomial should have the following properties:
- It should not be divisibl
- It should be divisible by ‘x+1’
The first condition guarantees that all burst errors of a length equal to the degree of the polynomial are detected
The 2nd^ guarantees th
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Popular Polynomials for CRC
Performance of CRC o CRC can detect all burst errors that affect an odd number of errors o CRC can detect all burst errors of length less than or equal to the degree of the polynomial o CRC can detect with a very high probability burst errors of length greater than the degree of the polynomial Example 9.
The CRC-12 ( 1
x x x x ) has a degree of 12
rst errors affecting odd no. of bits than 12 of 12 or more
LRC)
It will detect
- All bu
- All burst errors with a length equal to or less
- 99.97 % of the time burst errors with a length
Summary Types of Redundancy Checks Longitudinal Redundancy Check ( Cyclic Redundancy Check (CRC)
Reading Section
Section 9.4, 9. “Data Communications and Networking” 4th Edition by Behrouz A. Forouzan
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