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# Error detection and correction

Computer Network

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### Error detection and correction

1. 1. Error Detection and Correction
2. 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. 3. The Structure of encoder and decoder
4. 4. 2 categories Block coding 2. Convolution coding-more complex(less use) 1.
5. 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. 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. 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. 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. 9. Error Detection
10. 10. Example code word
11. 11. Error Correction