Parity bit means nothing but an additional bit added to the data at the transmitter before transmitting the data. Before adding the parity bit, number of 1’s or zeros is calculated in the data. Based on this calculation of data an extra bit is added to the actual information / data. The addition of parity bit to the data will result in the change of data string size.

This means if we have an 8 bit data, then after adding a parity bit to the data binary string it will become a 9 bit binary data string.

Parity check is also called as “Vertical Redundancy Check (VRC)”.

There is two types of parity bits in error detection, they are

 

2.Cyclic Redundancy Check (CRC)
 A cyclic code is a linear (n, k) block code with the property that every cyclic shift of a codeword results in another code word. Here k indicates the length of the message at transmitter (the number of information bits). n is the total length of the message after adding check bits. (actual data and the check bits). n, k is the number of check bits.
The codes used for cyclic redundancy check there by error detection are known as CRC codes (Cyclic redundancy check codes).Cyclic redundancy-check codes are shortened cyclic codes. These types of codes are used for error detection and encoding. They are easily implemented using shift-registers with feedback connections. That is why they are widely used for error detection on digital communication. CRC codes will provide effective and high level of protection. 

 

In longitudinal redundancy method, a BLOCK of bits are arranged in a table format (in rows and columns) and we will calculate the parity bit for each column separately. The set of these parity bits are also sent along with our original data bits.

Longitudinal redundancy check is a bit by bit parity computation, as we calculate the parity of each column individually.

This method can easily detect burst errors and single bit errors and it fails to detect the 2 bit errors occurred in same vertical slice.

4.Checksum
 

Checksums are similar to parity bits except, the number of bits in the sums is larger than parity and the result is always constrained to be zero. That means if the checksum is zero, error is detected. A checksum of a message is an arithmetic sum of code words of certain length. The sum is stated by means of 1’s compliment and stored or transferred as a code extension of actual code word. At receiver a new checksum is calculated by receiving the bit sequence from transmitter.

The checksum method includes parity bits, check digits and longitudinal redundancy check (LRC). For example, if we have to transfer and detect errors for a long data sequence (also called as Data string) then we divide that into shorter words and we can store the data with a word of same width. For each another incoming bit we will add them to the already stored data. At every instance, the newly added word is called “Checksum”.

At receiver side, the received bits checksum is same as that of transmitter’s, there is no error found.

We can also find the checksum by adding all data bits. For example, if we have 4 bytes of data as 25h, 62h, 3fh, 52h.

Then, adding all bytes we get 118H

Dropping the carry Nibble, we get 18H

Find the 2’s complement of the nibble, i.e. E8H

This is the checksum of the transmitted 4 bits of data.

At receiver side,to check whether the data is received without error or not, just add the checksum to the actual data bits (we will get 200H). By dropping the carry nibble we get 00H. This means the checksum is constrained to zero. So there is no error in the data.

In general, there are 5 types of checksum methods like:

As of now we discussed about the error detection codes. But to receive the exact and perfect data sequence without any errors, is not done enough only by detecting the errors occurred in the data. But also we need to correct the data by eliminating the presence of errors, if any. To do this we use some other codes. 

How to detect error : 

 CRC is a different approach to detect if the received frame contains valid data. This technique involves binary division of the data bits being sent.  

 One extra bit is sent along with the original bits to make number of 1s either even in case of even parity, or odd in case of odd parity.
 
i) Even parity - an even number of bits are 1 Even parity - data: 10010001, parity bit 1 

ii)Odd parity - an odd number of bits are 1 Odd parity - data: 10010111, parity bit 0 

 The sender while creating a frame counts the number of 1s in it. For example, if even parity is used and number of 1s is even then one bit with value 0 is added. This way number of 1s remains even.If the number of 1s is odd, to make it even a bit with value 1 is added.  

This is an error detection mechanism employed by upper layers. Here the

data word is arranged in the form of a matrix, each row containing n bits and modulo 2

addition is performed so that the sum is also having n bits (Ignoring the carry) . The sum

is then complemented. This is the checksum field. This is appended to the data unit and

sent. At the receiver, again the data after arranging in the form of a matrix,(including

checksum bits) modulo 2 addition is performed. If the sum is all 1s, it is assumed that

data is intact. 

How to do Error correction :

The world is noisy place, and errors can occur whenever information is stored or transmitted. Error detection techniques add extra parity bits to data to determine when errors have occurred.

This activity is a magic trick which most audiences find intriguing. In the trick the demonstrator is “magically” able to figure which one out of dozens of cards has been turned over, using the same methods that computers use to figure out if an error has occurred in data storage.

 

Error is a condition when the output information does not match with the input information. During transmission, digital signals suffer from noise that can introduce errors in the binary bits travelling from one system to other. That means a 0 bit may change to 1 or a 1 bit may change to 0.

Error-Detecting codes

Whenever a message is transmitted, it may get scrambled by noise or data may get corrupted. To avoid this, we use error-detecting codes which are additional data added to a given digital message to help us detect if an error occurred during transmission of the message. A simple example of error-detecting code is parity check.

Error-Correcting codes

Along with error-detecting code, we can also pass some data to figure out the original message from the corrupt message that we received. This type of code is called an error-correcting code. Error-correcting codes also deploy the same strategy as error-detecting codes but additionally, such codes also detect the exact location of the corrupt bit.

In error-correcting codes, parity check has a simple way to detect errors along with a sophisticated mechanism to determine the corrupt bit location. Once the corrupt bit is located, its value is reverted (from 0 to 1 or 1 to 0) to get the original message.


How to Detect and Correct Errors?

To detect and correct the errors, additional bits are added to the data bits at the time of transmission.

Parity Checking of Error Detection

It is the simplest technique for detecting and correcting errors. The MSB of an 8-bits word is used as the parity bit and the remaining 7 bits are used as data or message bits. The parity of 8-bits transmitted word can be either even parity or odd parity.

Even parity -- Even parity means the number of 1's in the given word including the parity bit should be even (2,4,6,....).

Odd parity -- Odd parity means the number of 1's in the given word including the parity bit should be odd (1,3,5,....).

Use of Parity Bit

The parity bit can be set to 0 and 1 depending on the type of the parity required.

How Does Error Detection Take Place?

Parity checking at the receiver can detect the presence of an error if the parity of the receiver signal is different from the expected parity. That means, if it is known that the parity of the transmitted signal is always going to be "even" and if the received signal has an odd parity, then the receiver can conclude that the received signal is not correct. If an error is detected, then the receiver will ignore the received byte and request for retransmission of the same byte to the transmitter.

 

Error Detection

Errors in the received frames are detected by means of Parity Check and Cyclic Redundancy Check (CRC). In both cases, few extra bits are sent along with actual data to confirm that bits received at other end are same as they were sent. If the counter-check at receiver’ end fails, the bits are considered corrupted.

Parity Check

One extra bit is sent along with the original bits to make number of 1s either even in case of even parity, or odd in case of odd parity.

The sender while creating a frame counts the number of 1s in it. For example, if even parity is used and number of 1s is even then one bit with value 0 is added. This way number of 1s remains even.If the number of 1s is odd, to make it even a bit with value 1 is added.

The receiver simply counts the number of 1s in a frame. If the count of 1s is even and even parity is used, the frame is considered to be not-corrupted and is accepted. If the count of 1s is odd and odd parity is used, the frame is still not corrupted.

If a single bit flips in transit, the receiver can detect it by counting the number of 1s. But when more than one bits are erro neous, then it is very hard for the receiver to detect the error.

Cyclic Redundancy Check (CRC)

CRC is a different approach to detect if the received frame contains valid data. This technique involves binary division of the data bits being sent. The divisor is generated using polynomials. The sender performs a division operation on the bits being sent and calculates the remainder. Before sending the actual bits, the sender adds the remainder at the end of the actual bits. Actual data bits plus the remainder is called a codeword. The sender transmits data bits as codewords.

At the other end, the receiver performs division operation on codewords using the same CRC divisor. If the remainder contains all zeros the data bits are accepted, otherwise it is considered as there some data corruption occurred in transit.

Error Correction

In the digital world, error correction can be done in two ways:

The first one, Backward Error Correction, is simple and can only be efficiently used where retransmitting is not expensive. For example, fiber optics. But in case of wireless transmission retransmitting may cost too much. In the latter case, Forward Error Correction is used.

To correct the error in data frame, the receiver must know exactly which bit in the frame is corrupted. To locate the bit in error, redundant bits are used as parity bits for error detection.For example, we take ASCII words (7 bits data), then there could be 8 kind of information we need: first seven bits to tell us which bit is error and one more bit to tell that there is no error.

For m data bits, r redundant bits are used. r bits can provide 2r combinations of information. In m+r bit codeword, there is possibility that the r bits themselves may get corrupted. So the number of r bits used must inform about m+r bit locations plus no-error information, i.e. m+r+1.

 

 

A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect errors resulting in all-zero messages.

Checksum schemes include parity bits, check digits, and longitudinal redundancy checks. Some checksum schemes, such as the Damm algorithm, the Luhn algorithm, and the Verhoeff algorithm, are specifically designed to detect errors commonly introduced by humans in writing down or remembering identification numbers. 

-Cyclic Redundancy Check (CRC)
:- A cyclic code is a linear (n, k) block code with the property that every cyclic shift of a codeword results in another code word. Here k indicates the length of the message at transmitter (the number of information bits). n is the total length of the message after adding check bits. (actual data and the check bits). n, k is the number of check bits.
The codes used for cyclic redundancy check there by error detection are known as CRC codes (Cyclic redundancy check codes).Cyclic redundancy-check codes are shortened cyclic codes. These types of codes are used for error detection and encoding. They are easily implemented using shift-registers with feedback connections. That is why they are widely used for error detection on digital communication. CRC codes will provide effective and high level of protection.
-Longitudinal Redundancy Check (LRC)
:- In longitudinal redundancy method, a BLOCK of bits are arranged in a table format (in rows and columns) and we will calculate the parity bit for each column separately. The set of these parity bits are also sent along with our original data bits.
Longitudinal redundancy check is a bit by bit parity computation, as we calculate the parity of each column individually.
This method can easily detect burst errors and single bit errors and it fails to detect the 2 bit errors occurred in same vertical slice.
-Check Sum
:- Checksums are similar to parity bits except, the number of bits in the sums is larger than parity and the result is always constrained to be zero. That means if the checksum is zero, error is detected. A checksum of a message is an arithmetic sum of code words of certain length. The sum is stated by means of 1’s compliment and stored or transferred as a code extension of actual code word. At receiver a new checksum is calculated by receiving the bit sequence from transmitter.
The checksum method includes parity bits, check digits and longitudinal redundancy check (LRC). For example, if we have to transfer and detect errors for a long data sequence (also called as Data string) then we divide that into shorter words and we can store the data with a word of same width. For each another incoming bit we will add them to the already stored data. At every instance, the newly added word is called “Checksum”.
At receiver side, the received bits checksum is same as that of transmitter’s, there is no error found. 

•CRC can detect all burst errors that affect an odd number of bits 

•CRC can detect all burst errors of length less than or equal to the degree of the polynomial