This document discusses error detection and correction in digital communication. It describes how coding schemes add redundancy to messages through techniques like block coding and convolution coding to detect or correct errors. The encoder adds redundant bits to original messages to create relationships between bits that the decoder can use to check for errors. It also explains the use of modular arithmetic, specifically modulo-2 arithmetic which uses only 1s and 0s, for error detection and correction operations.

1. Error Detection and Correction

2. Coding:
Redundancy
is achieved through various
coding Scheme.
The sender adds the redundancy bit to
the original message and create
relationship.
The receiver checks the relationship b/w
two sets of bits to detect (or) correct the
errors.
Robustness of the process are important
factors in any coding scheme.

3. The Structure of encoder and
decoder

4. 2 categories
Block coding
2. Convolution coding-more complex(less
use)
1.

5. Modular Arithmetic
Use
only limited range of integers.
We, define upper limit, called a ,modulus
N.
Then use only the integers 0 to N-1.
This is modulo-N arithmetic.

6. Modulo-2 Arithmetic
Here
modulus N is 2. we can use only 0
and 1. operation in this arithmetic are
very simple.
The addition and subtraction give the
same results. Here, we use XOR
operation for both the add and sub.
The result of an XOR operation is 0(if
both the bits are same. The result is 1 if
the any of the two bit is different.)

7. Block coding
Divide
the message into blocks, each of k
bits, called datawords. Then add r
redundant bit to make length n=k+r
The resulting n-bit blocks are called
codewords.

8. Error Detection
The
receiver can detect a change in the
original codeword. by
1. The receiver has a list of valid codewords.
2. The original codeword has changed to an
invalid one.

9. Error Detection

10. Example code word

11. Error Correction