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Kyung Hee University

Prof. Choong Seon HONG

Error Detection and CorrectionError Detection and Correction

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99 장 장 Error Detection and CorrectionError Detection and Correction

9.1 Types of Errors

9.2 Detection

9.3 Error Correction

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Error Detection and CorrectionError 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 Errors9.1 Type of Errors

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Type of Errors(cont’d)Type of Errors(cont’d)

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(cont’d)Type of Errors(cont’d)

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(cont’d)Type of Errors(cont’d)

Burst Error

~ means that two or more consecutive bits in the data

unit have changed

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9.2 Detection9.2 Detection

Error detection uses the concept of redundancy, which

means adding extra bits for detecting errors at the

destination

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Detection(cont’d)Detection(cont’d)

Redundancy

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Detection(cont’d)Detection(cont’d)

Detection methods

VRC(Vertical Redundancy Check)

LRC(Longitudinal Redundancy)

CRC(Cyclical redundancy Check)

Checksum

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Detection(cont’d)Detection(cont’d)

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

VRC can detect all single-bit errors. It can detect multiple-bit or burst errors only the total number of errors is odd.

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Detection(cont’d)Detection(cont’d)

Even parity VRC concept

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Detection(cont’d)Detection(cont’d)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(cont’d)Detection(cont’d)

CRC(Cyclic Redundancy Check)

~ is based on binary division.

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Detection(cont’d)Detection(cont’d)

CRC generator

~ uses modular-2 division.

Binary Divisionin aCRC Generator

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Detection(cont’d)Detection(cont’d)

Binary Divisionin aCRC Checker

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Detection(cont’d)Detection(cont’d)

Polynomials

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

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Detection(cont’d)Detection(cont’d)

A polynomial representing a divisor

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Detection(cont’d)Detection(cont’d)

Standard polynomials

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Detection(cont’d)Detection(cont’d)

Checksum

~ used by the higher layer protocols

~ is based on the concept of redundancy(VRC, LRC, CRC

….)

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Detection(cont’d)Detection(cont’d)

Checksum Generator

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Detection(cont’d)Detection(cont’d)

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 one’s 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(cont’d)Detection(cont’d)

data unit and checksum

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Detection(cont’d)Detection(cont’d)

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9.3 Error Correction9.3 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(cont’d)Error Correction(cont’d)

Single-Bit Error Correction

parity bit

The secret of error correction is to locate the invalid bit or bits

For ASCII code, it needs a three-bit redundancy code(000-111)

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Error Correction(cont’d)Error Correction(cont’d)

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(cont’d)Error Correction(cont’d)

If the total number of bits in a transmittable unit is m+r,

then r must be able to indicate at least m+r+1 different

states

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(cont’d)Error Correction(cont’d)

Relationship between data and redundancy bits

Number of Data Bits(m)

Number of Redundancy Bits(r)

Total Bits(m+r)

1234567

2333444

356791011

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Error Correction(cont’d)Error Correction(cont’d)

Hamming Code

~ developed by R.W.Hamming

positions of redundancy bits in Hamming code

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Error Correction(cont’d)Error Correction(cont’d)

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(cont’d)Error Correction(cont’d)

Redundancy bits calculation(cont’d)

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Error Correction(cont’d)Error Correction(cont’d)

Redundancy bits calculation

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Error Correction(cont’d)Error Correction(cont’d)Calculating the r values

Calculating Even Parity

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Error Correction(cont’d)Error Correction(cont’d)

Error Detection and Correction

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Error Correction(cont’d)Error Correction(cont’d)Error detection using Hamming Code

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Error Correction(cont’d)Error Correction(cont’d)

Multiple-Bit Error Correction

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

Ex) to correct double-bit errors, we must take into consideration that two bits can be a combination of any two bits in the entire sequence