Computer Networks - Error Control (Parity Check, Checksum, CRC, Hamming Code)

2. Types of Error
• Whenever bits flow from one point to another, they
are subject to unpredictable changes because of
interference and thermal noise.
Error Control

3. Single Bit Error
• single-bit error means that only 1 bit of a given data unit (such as
a byte, character, or packet) is changed from 1 to 0 or from 0 to1.
Burst Error
• The term burst error means that 2 or more bits in the data unit
have changed from 1 to 0 or from 0 to 1.
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4. Error Control
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Error Control
Error Detection Error Correction
Two Dimensional Parity
Internet Checksum
Cyclic Redundant Check (CRC)
Hamming Code

5. Error Detection Techniques
 Two approaches when the recipient detects an error
 Notify the sender that the message was corrupted, so the sender can
send again, if the error is rare, then the retransmitted message will
be error-free
 Using some error correct detection and correction algorithm, the
receiver reconstructs the message.
 Common technique for detecting transmission error
 CRC (Cyclic Redundancy Check)
 Used in HDLC, DDCMP, CSMA/CD
 Other approaches
 Two Dimensional Parity (used in BISYNC)
 Checksum (used in IP)
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6. Basic Idea of Error Detection
– To add redundant information to a frame that can be used
to determine if errors have been introduced
– Imagine (Extreme Case)
• Transmitting two complete copies of data
– Identical  No error
– Differ  Error
– Poor Scheme ???
» n bit message, n bit redundant information
» Error can go undetected
• In general, we can provide strong error detection technique
– k redundant bits, n bits message, k << n
– In Ethernet, a frame carrying up to 12,000 bits of data requires only 32-
bit CRC.
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7. TWO-DIMENSIONAL PARITY
 It is based on “simple” (one-dimensional) parity, which usually
involves adding one extra bit to a 7-bit code to balance the
number of 1s in the byte. For example,
 Odd parity sets the eighth bit to 1 if needed to give an odd number of
1s in the byte.
 Even parity sets the eighth bit to 1 if needed to give an even number
of 1s in the byte.
 Two-dimensional parity does a similar calculation for each bit
position across each of the bytes contained in the frame
 This results in an extra parity byte for the entire frame, in addition
to a parity bit for each byte
 Two-dimensional parity catches all 1-, 2-, and 3-bit errors and
most 4-bit errors
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9. Internet Checksum:
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In internet checksum n=16

10.  Add up all the words that are transmitted and then transmit the
result of that sum
o The result is called the checksum.
 The receiver performs the same calculation on the received data
and compares the result with the received checksum
 If any transmitted data, including the checksum itself, is
corrupted, then the results will not match, so the receiver knows
that an error occurred
 Consider the data being checksummed as a sequence of 16-bit
integers.
• Add them together using 16-bit ones complement arithmetic and
then take the ones complement of the result. That 16-bit number
is the checksum.
• In ones complement arithmetic, a negative integer −x is
represented as the complement of x;
– Each bit of x is inverted.
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11.  When adding numbers in ones complement arithmetic, a
carryout from the most significant bit needs to be added to the
result (Wrapping).
Sender Side:
 The message is divided into 16-bit words.
 The value of the checksum word is set to 0.
 All words including the checksum are added using one's complement
addition.
 The sum is complemented and becomes the checksum.
 The checksum is sent with the data.
Receiver Side:
 The message (including checksum) is divided into 16-bit words.
 All words are added using one's complement addition.
 The sum becomes the new checksum.
 If the value of checksum is 0, the message is accepted; otherwise, it is
rejected.
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12. Example:
Frame Data: 01101101 10010011 01101101
n=8
Sender Side:
Calculating Checksum,
01101101
10010011
01101101
---------------------------
01101101 --------1’s Compliment-- 10010010---------------------------
Checksum = 10010001
So data transmitted over the link is: 01101101 10010011 01101101 10010010
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13. Receiver Side: (without Error)
Received Data: 01101101 10010011 01101101 10010001
Calculating Sum,
01101101
10010011
01101101
10010010
---------------------------
11111111 ----> All 1’s So accepted (No error)---------------------------
Receiver Side: (with Error)
Received Data: 11101101 10010011 01101101
11101101
10010011
01101101
10010010
---------------------------
01111111 ---> Not all 1’s. So not accepted (Contains Error)---------------------------
Error Control Contd…