Error Detection and Error Correction by MHM.ppt
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This document discusses error detection and correction in data transmission. It defines error detection as detecting errors caused by noise during transmission, while error correction detects and fixes errors to reconstruct the original data. There are two main types of errors: single-bit errors, where one bit is changed, and burst errors, where multiple contiguous bits are changed. Hamming codes are described as a common error detection and correction method, being able to detect up to two-bit errors and correct single-bit errors, but not correct burst errors. The document provides examples of calculating Hamming distance to detect errors and the minimum distance required for error correction.
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This document discusses error detection and correction techniques in digital communications. It covers Hamming distance, block codes, linear block codes, cyclic codes, cyclic redundancy checks (CRCs), and checksums. Key points include:
- The Hamming distance between words is the number of differing bits
- Minimum Hamming distance determines a code's error detection/correction capability
- Linear block codes allow valid codewords to be created by XORing other codewords
- Cyclic codes maintain codeword validity under cyclic shifts
- CRCs use polynomial division to embed a checksum in transmitted data for error detection
- Checksums provide simple error detection by transmitting a sum of message bits
Ch10 2 v1
This document discusses error detection and correction techniques in digital communications. It covers Hamming distance, block codes, linear block codes, cyclic codes, cyclic redundancy checks (CRCs), and checksums. Key points include:
- The Hamming distance between words is the number of differing bits
- Minimum Hamming distance determines a code's error detection/correction capability
- Linear block codes allow valid codewords to be created by XORing other codewords
- Cyclic codes maintain codeword validity under cyclic shifts
- CRCs use polynomial division to embed a checksum in transmitted data
- Checksums provide error detection by transmitting a calculated value over transmitted data
crc_checksum.pdf
This document discusses various techniques for error detection and correction in communication networks, including:
1. Types of errors such as single-bit errors and burst errors that can occur when transmitting data.
2. The central concept of redundancy, where extra bits are added to the data and used at the receiver to detect or correct errors.
3. Popular error detection and correction codes including parity-check codes, cyclic redundancy checks (CRCs), checksums, and linear block codes. These codes add redundant bits in ways that allow the receiver to identify errors.
4. How encoders add redundant bits using techniques like modulo-2 addition and division, and how decoders analyze received codewords to detect errors based on
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- 1. 10.1 Error Detection and Error Correction Md Mosharof Hosen CSE dept.
- 2. 1 Introduction Error detection is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. Error correction is the detection of errors and reconstruction of the original, error free data.
- 3. 2 Types of Errors Single bit error : -Only one bit in the data unit has changed. Burst error : - It means that two or more bits in the data unit has changed.
- 4. 3 Single-bit error Only one bit in the data unit has changed.
- 5. 4 Burst error means two or more bits in the data unit has changed.
- 6. 5 Error detection/correction Error detection -Check if any error has occurred -Don’t care the number of errors -Don’t care the positions of errors Error correction -Need to know the number of errors -Need to know the positions of errors -More difficult
- 7. 6 Using Hamming Method Hamming code is a popular error detection and error correction method in data communication. Hamming code can only detect 2 bit error and correct a single bit error which means it is unable to correct burst errors if may occur while transmission of data.
- 8. 7 Continue . . . Where r is the number of redundant bits required and m is the number of data bits. R is calculated by putting r = 1, 2, 3 … until the above equation becomes true. R1 bit is appended at position 20 R2 bit is appended at position 21 R3 bit is appended at position 22 and so on.
- 9. 8 We can count the number of 1s in the Xoring of two words 1. The Hamming distance d(000, 011) is 2 because 2. The Hamming distance d(10101, 11110) is 3 because
- 10. 9 Geometric concept for finding dmin in error detection
- 11. 10 Geometric concept for finding dmin in error correction To guarantee correction of up to t errors in all cases, the minimum Hamming distance in a block code must be dmin = 2t + 1.
- 13. Thanks to all