Types of error:
1. Single bit
error: Means that only one bit of a given data unit is changed from 1 to 0
or from 0 to 1.
2. Burst error: Means that 2 or
more bits in the data unit have changed.
Redundancy: To detect or correct errors, we need to send extra (redundant) bits with data.
Detection and correction: the correction of errors is more difficult than the detection.
Redundancy: To detect or correct errors, we need to send extra (redundant) bits with data.
Detection and correction: the correction of errors is more difficult than the detection.
Method of error correction:
There are two methods of error
correction:
1. Forward error
correction, and
2. Correction by
retransmission.
- Forward error correction: Forward error correction is the process in which the receiver tries to guess the message by using redundant bits. This is possible if the number of errors is small.
- Correction by retransmission: It is a technique in which the receiver detects the occurrence of an error and asks the sender to resend the message. Resending is repeated until a message arrives that the receiver believes its error free.
Coding:
Redundancy is achieved through various
coding schemes.
The sender adds redundant bits through a process that creates a relationships between the bits and the actual data. The receiver checks the relationships to detect and correct the errors accordingly.
The sender adds redundant bits through a process that creates a relationships between the bits and the actual data. The receiver checks the relationships to detect and correct the errors accordingly.
Coding scheme are divided into two broad
categories:
1. Block coding
2. Convolution
coding
Block coding: in block coding,
we divide our message in to blocks, each of k bits, called Datawords and
add r redundant bits to each block to make the length n=k+r. The
resulting n bit blocks are called Codewords.
From the moment, it is important to know that we have a set of Datawords each of size k and a set of Codewords each of size n.
With k bits we can create a combination
of (2)k Datawords;
With n bits we can create a combination
of (2)n Codewords.
Since
n>k, the number of possible Codewords is larger than the number of possible
Datawords.
The
block coding process is one to one, the same Dataword is always encoded as the
same Codeword. This means that we have (2)n-(2)k Codewords
that are not used. We call this Codewords invalid or illegal.
Hamming distance:
The hamming distance between two words is the number of differences between corresponding bits.
The hamming distance between two words is the number of differences between corresponding bits.
