11-08-2012, 02:47 PM
ERROR DETECTION AND CORRECTION USING HAMMING CODE(7,4)
[attachment=31136]
OSI MODEL (open systems interconnection) Position & Function of Data-Link layer
Frame Synchronization: The source machine sends data in block called frames to the destination machine. The starting and ending on each frame must be recognized by the destination machine.
Flow Control: The source machine should not send data frames at a rate faster than the destination machine can accept them.
Addressing: On multipoint line, such as many machine connected together (LAN), the identity of the individual machines must be specified while transmitting the data frames.
Error Control: The error made in the bits during transmission from the source to destination machines must be detected and corrected.
CAUSE OF ERROR
Noise
Unwanted Extra bit which is inserted somewhere in the communication channel causing error .
TYPES OF NOISE
Thermal Noise : Due to thermal agitation of electrons. Present in
all electronic devices and is the function of temperature.
Impulse Noise: Due to electromagnetic interference(EMI). They may
be present in power lines, or in nature (lightning.. etc)
Delay Distortion : Due to non-uniform velocities of signals of
different frequencies traveling in a guided media. Various frequencies
of a message signal will arrive at different delays resulting in distortion.
ERROR DETECTION SCHEMES
Repetition Schemes: The data is broken up into blocks of bits , and sent some predetermined number of times.
Parity Schemes: A parity bit is error detection mechanism that can only detect an odd number of errors. The stream of data is broken up into blocks of bits and the number of “1” bits are counted.
Checksum: A checksum of a message is an arithmetic sum of the message code words of a certain word length. The sum is negated by means of one’s compliment, and stored or transferred as an extra code word extending the message.
Cyclic redundancy checks: The cyclic redundancy check considers a block of data as the coefficients to a polynomial and then divides by fixed, predetermined polynomial.
Hamming Distance based checks: If we want to detect d bit error in an n bit word we can map every n bit word into bigger n+d+1 bit word so that the minimum Hamming Distance between is valid mapping is d+1. This way, if one receives a n+d+1 word that doesn’t match any word in the mapping (with the Hamming distance x<=d+1 from any word in the mapping) it can successfully detect it’s as an error word.
HAMMING CODE(7,4)
In telecommunication a Hamming code is a linear error correction code named after its inventor, Richard Hamming. Since 1946 Richard Hamming (1915-1998) works on a model of calculator to perforated card low reliability.
Hamming codes can detect and correct single bit errors.
SOLUTION OR FUTURE USE DEVELOPMENT
This limitation can be overcome by developing the code or extending the code from (7,4) to (11,8).
In Modern time this code has very less limit which can be developed and reconstructed by expanding the limit of the code.
[attachment=31136]
OSI MODEL (open systems interconnection) Position & Function of Data-Link layer
Frame Synchronization: The source machine sends data in block called frames to the destination machine. The starting and ending on each frame must be recognized by the destination machine.
Flow Control: The source machine should not send data frames at a rate faster than the destination machine can accept them.
Addressing: On multipoint line, such as many machine connected together (LAN), the identity of the individual machines must be specified while transmitting the data frames.
Error Control: The error made in the bits during transmission from the source to destination machines must be detected and corrected.
CAUSE OF ERROR
Noise
Unwanted Extra bit which is inserted somewhere in the communication channel causing error .
TYPES OF NOISE
Thermal Noise : Due to thermal agitation of electrons. Present in
all electronic devices and is the function of temperature.
Impulse Noise: Due to electromagnetic interference(EMI). They may
be present in power lines, or in nature (lightning.. etc)
Delay Distortion : Due to non-uniform velocities of signals of
different frequencies traveling in a guided media. Various frequencies
of a message signal will arrive at different delays resulting in distortion.
ERROR DETECTION SCHEMES
Repetition Schemes: The data is broken up into blocks of bits , and sent some predetermined number of times.
Parity Schemes: A parity bit is error detection mechanism that can only detect an odd number of errors. The stream of data is broken up into blocks of bits and the number of “1” bits are counted.
Checksum: A checksum of a message is an arithmetic sum of the message code words of a certain word length. The sum is negated by means of one’s compliment, and stored or transferred as an extra code word extending the message.
Cyclic redundancy checks: The cyclic redundancy check considers a block of data as the coefficients to a polynomial and then divides by fixed, predetermined polynomial.
Hamming Distance based checks: If we want to detect d bit error in an n bit word we can map every n bit word into bigger n+d+1 bit word so that the minimum Hamming Distance between is valid mapping is d+1. This way, if one receives a n+d+1 word that doesn’t match any word in the mapping (with the Hamming distance x<=d+1 from any word in the mapping) it can successfully detect it’s as an error word.
HAMMING CODE(7,4)
In telecommunication a Hamming code is a linear error correction code named after its inventor, Richard Hamming. Since 1946 Richard Hamming (1915-1998) works on a model of calculator to perforated card low reliability.
Hamming codes can detect and correct single bit errors.
SOLUTION OR FUTURE USE DEVELOPMENT
This limitation can be overcome by developing the code or extending the code from (7,4) to (11,8).
In Modern time this code has very less limit which can be developed and reconstructed by expanding the limit of the code.