Error Detection
Error Detection and
Correction

Background
– Data can be corrupted during
transmission
– For reliable communication, errors must
be detected and corrected
– Error detection and correction can be
implemented in
Data link layer, or
 Transport layer

Types of Errors
Errors
Single-Bit error
Burst error
Single-Bit Error


Only one bit in the data units has
changed
Example
sent
received
00000100
00001100
Burst Error



Two or more bits in the data unit
have changed
Errors do not occur in consecutive
bits
The length of the burst measured
from the first corrupted bit to the last
corrupted bit
Burst Error

Example
length of burst error
7 bits
sent
received
0000110000110000110
0011110010110000110
Detection : Redundancy


1) Two copies of data unit (packet) are
sent
Receiving device compares them
– Able to detect errors
– Transmission time  double
– Computational time  slow
Detection : Redundancy

2) Only extra information is added
– Shorter group of bits may be added to
each packet
– Used by the receiving device
– Discarded when it is used
Redundancy Check
Redundancy Check

Four types of redundancy checks
– Vertical redundancy check (VRC)
– Longitudinal redundancy check (LRC)
– Cyclical redundancy check (CRC)
– Checksum
Vertical Redundancy
Check (VRC)




Implemented in the physical layer
Most common and least expensive
mechanism for error detection
Also called parity bit check
A redundant bit, called parity bit, is
appended to every data unit
– The number of 1s for each data unit, including
the parity bit, becomes even
– 0 is appended when the data unit consists of
even 1s
VRC
VRC
Original Data
 1110111
1101111 1100100
Parity Bit added
 11101110
11011110 11001001
Received data
11111110
11011110 11001001
Discard this data
VRC

Performance
– Detects all single-bit errors (1, 3, 5, .. Bits
changed)
– Able to detect burst errors if

The total number of bits changed is odd
– Cannot detect errors where the total
number of bits changed is even
Longitudinal Redundancy
Check (LRC)
11100111
11011101
00111001
10101001
11100111
11011101
00111001
10101001
LRC
11100111
11011101

00111001
Original data + LRC
10101001
10101010
10101010
Cyclic Redundancy Check
(CRC)
Based on Binary Division
CRC Generator
Data plus extra
zeros. The
number of zeros is
one less than the
number or bits in
the divisor.
When the
leftmost bit is
zero, we must
use 0000
instead of the
original divisor
CRC Checker


A CRC checker functions exactly like
the generator
Data + CRC is divided by the
predefined divisor
– If the remainder is all 0s, accept
– Otherwise discard the received data
Polynomial
CRC generator (the divisor) is also represented as an algebraic
polynomial
It is short
it can be used to prove the concept mathematically
Polynomial
Polynomial properties :
it should not be divisible by x
it should be divisible by x+1
All burst errors of a
length equal to the
degree of polynomial
are detected
Standard polynomial
Example of CRC
Data = 1010001101
Polynomial = 110101
Calculate:
101000110100000
- 110101
Received Data = 10100011011110
Polynomial = 110101
Calculate:
101000110101110
= 011101110100000
- 110101
Remainder = 1110
= 011101110101110
Send data frame =
10100011011110
Remainder = 0
Checksum



Used by the higher-layer protocols
Based on concept of redundancy
Consists of checksum generator and
checksum checker
Checksum

Checksum generator
– The data unit is divided into k sections,
each of n bits
– All sections are added together using
one’s complement to get the sum
– The sum is complemented and becomes
the checksum
– The checksum is sent with the data
checksum

Checksum checker
– The data unit is divided into k sections,
each of n bits
– All sections are added together using
one’s complement to get the sum
– The sum is complemented
– If the result is zero, the data are
accepted, otherwise, they are rejected
Checksum
Example : Checksum
Generator

(sender) 10101001
00111001
10101001
+
00111001
sum
11100010
checksum
00011101
 Data sent 10101001 00111001 00011101
Example : Checksum
Checker

Received data
10101001 00111001 00011101

sum all sections
Sum
Complement
10101001
00111001
00011101
11111111
00000000  OK
Error Correction

Two methods
– The sender retransmits the entire data
– The receiver corrects errors using errorcorrection code

Error-correction code
– More sophisticated than error-detection
codes
– Require more redundancy bits than errordetection
Error Correction (cont.)

Error-correction code (cont.)
– The number of bits required to correct
multiple-bit or burst error is high
In most case it is inefficient to do
 Most error correction is limited to one-, two-,
or three-bit errors

Error Correction

Self study if you are interested in it.