Error detecting and correcting codes are used to detect and correct errors during data transmission. Hamming codes allow for single bit error correction and double bit error detection. Hamming codes work by assigning parity bits to specific bit positions, with each parity bit checking a set of data bit positions. If a single bit error occurs, the receiver can detect which bit is in error by checking the parity bits and make the correction. Hamming codes provide an easy way to detect and correct single bit errors during data transmission.

1. Error detecting and correcting codes, hamming codes.
1 Error detecting and correcting codes, hamming codes.
Error Detection and Correction Codes
Main Approaches are:
Echoplex
Automatic detection & retransmission
Forward Error Correction
Echoplex
Used in Telnet--When a character is entered in a Telnet session, the character is sent to the computer
and the computer will echo the character--a crude way of check error
Automatic detection & retransmission
Use an error detection code to detect error
Error Detection Codes
(a) Parity Code(VRC--Vertical Redundancy Check)
-A Parity bit is used
-Odd or Even parity
-Detects all odd number of error(1 bit error, 3 bit error, …)
-Even number of errors can not be detected
(b) LRC(Longitudinal Redundancy Check)

2. -Sometimes called “Block Check Code” or “Checksum”
-A block of characters are parity checked
-Often used along with VRC, -It is 2-demensional code
(c) CRC(Cyclic Redundancy Check)
-Divide a block(block size is determined by LAN requirements--Ethernetà 1500Bytes, Token
Ringà 8000Bytes, ….) by a predetermined Divisor and calculate the Remainder and attach the
Remainder at the end of data bits -Receiver will also divide the data bits with the same Divisor and
calculatesRemainder and compares the received Remainder with the calculated one -If they matchà No
error detected, If no match à Error detected and the frame is deleted.

3. The above calculations can easily be done using hardware Shift Registers
--Binary division = a series of Shift followed by adds
Example shift register:
-A carefully designed(chosen) divisor is used
-A divisor is usually represented using a polynomial notation

4. There are several standard Divisors that are adopted International standards
-CRC-32 is used in LAN protocols---Ethernet, Token Ring, ….
Forward Error Correction:
Hamming code
It is a Single bit Error Correction and Double bit Error Detection Code.
Hamming designed to have several parity bits in the following position:
2**0, 2**1, 2**2, 2**3 positions will have parity bits
Other bit positions are for data bits
The parity bit at 2**0 position checks positions 1, 3, 5, 7, 9, 11
The parity bit at 2**1 position checks positions 2, 3, 6, 7, 10, 11
The parity bit at 2**0 position checks positions 4, 5, 6, 7
The parity bit at 2**0 position checks positions 8, 9, 10, 11
Let’s use Even Parity for this example:

5. Let’s say a single-bit error occurs in bit position 7:
The receiver checks parity bits to find the error:
Thus it is very easy to detect and correct code using Hamming Code.