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Error detection and correction
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.
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Error detection and correction
- 1. Error Detection andCorrection
- 2. Coding: Redundancy is achieved throughvarious 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 ofencoder and decoder
- 4. 2 categories Block coding 2.Convolution coding-more complex(less use) 1.
- 5. Modular Arithmetic Use only limitedrange 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 Nis 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 messageinto 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 candetect 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.
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