computer Networks Error Detection and Correction.ppt

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This document discusses error detection and correction in data transmission. It covers the following key points: - There are two main types of errors: single-bit errors and burst errors. Burst errors are more common in serial transmission. - Error detection verifies data accuracy without having the original message. It uses redundancy like vertical and longitudinal redundancy checks. Cyclic redundancy checks use polynomial division to detect errors. - Error correction automatically fixes certain errors. Single-bit error correction reverses the value of the altered bit. Hamming codes use additional redundant bits to detect and correct single-bit errors.

Error Detection
and Correction
• Types of Errors
• Detection
• Correction

Basic concepts
 Networks must be able to transfer data from
one device to another with complete accuracy.
 Data can be corrupted during transmission.
 For reliable communication, errors must be
detected and corrected.
 Error detection and correction
are implemented either at the data link
layer or the transport layer of the OSI
model.

Single bit errors are the least likely type of
errors in serial data transmission because
the noise must have a very short duration
which is very rare. However this kind of
errors can happen in parallel transmission.

computer Networks Error Detection and Correction.ppt

The term burst error means that two or
more bits in the data unit have changed
from 1 to 0 or from 0 to 1.
Burst errors does not necessarily mean that
the errors occur in consecutive bits, the
length of the burst is measured from the first
corrupted bit to the last corrupted bit. Some
bits in between may not have been
corrupted.

Burst error is most likely to happen in serial
transmission since the duration of noise is
normally longer than the duration of a bit.
The number of bits affected depends on the data
rate and duration of noise.

Error detection
Error detection means to decide whether the
received data is correct or not without having a
copy of the original message.
Error detection uses the concept of redundancy,
which means adding extra bits for detecting
errors at the destination.

Four types of redundancy checks are used
in data communications

Performance
It can detect single bit error
It can detect burst errors only if the total
number of errors is odd.

Performance
LCR increases the likelihood of detecting
burst errors.
If two bits in one data units are damaged
and two bits in exactly the same positions in
another data unit are also damaged, the LRC
checker will not detect an error.

Cyclic Redundancy Check
• Given a k-bit frame or message, the
transmitter generates an n-bit sequence,
known as a frame check sequence (FCS), so
that the resulting frame, consisting of (k+n)
bits, is exactly divisible by some
predetermined number.
• The receiver then divides the incoming
frame by the same number and, if there is
no remainder, assumes that there was no
error.

At the sender
The unit is divided into k sections, each of n
bits.
All sections are added together using one’s
complement to get the sum.
The sum is complemented and becomes the
checksum.
The checksum is sent with the data

At the receiver
The unit is divided into k sections, each of n
bits.
All sections are added together using one’s
complement to get the sum.
The sum is complemented.
If the result is zero, the data are accepted:
otherwise, they are rejected.

Performance
The checksum detects all errors involving an
odd number of bits.
It detects most errors involving an even number
of bits.
If one or more bits of a segment are damaged
and the corresponding bit or bits of opposite
value in a second segment are also damaged, the
sums of those columns will not change and the
receiver will not detect a problem.

Error Correction
It can be handled in two ways:
1) receiver can have the sender retransmit the
entire data unit.
2) The receiver can use an error-correcting
code, which automatically corrects certain
errors.

Single-bit error correction
To correct an error, the receiver reverses the value
of the altered bit. To do so, it must know which bit
is in error.
Number of redundancy bits needed
• Let data bits = m
• Redundancy bits = r
Total message sent = m+r
The value of r must satisfy the following relation:
2r ≥ m+r+1

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In modern aerospace engineering, uncertainty is not an inconvenience — it is a defining feature. Lightweight structures, composite materials, and tight performance margins demand a deeper understanding of how variability in material properties, geometry, and boundary conditions affects dynamic response. This keynote presentation tackles the grand challenge: how can we model, quantify, and interpret uncertainty in structural dynamics while preserving physical insight? This talk reflects over two decades of research at the intersection of structural mechanics, stochastic modelling, and computational dynamics. Rather than adopting black-box probabilistic methods that obscure interpretation, the approaches outlined here are rooted in engineering-first thinking — anchored in modal analysis, physical realism, and practical implementation within standard finite element frameworks. The talk is structured around three major pillars: 1. Parametric Uncertainty via Random Eigenvalue Problems * Analytical and asymptotic methods are introduced to compute statistics of natural frequencies and mode shapes. * Key insight: eigenvalue sensitivity depends on spectral gaps — a critical factor for systems with clustered modes (e.g., turbine blades, panels). 2. Parametric Uncertainty in Dynamic Response using Modal Projection * Spectral function-based representations are presented as a frequency-adaptive alternative to classical stochastic expansions. * Efficient Galerkin projection techniques handle high-dimensional random fields while retaining mode-wise physical meaning. 3. Nonparametric Uncertainty using Random Matrix Theory * When system parameters are unknown or unmeasurable, Wishart-distributed random matrices offer a principled way to encode uncertainty. * A reduced-order implementation connects this theory to real-world systems — including experimental validations with vibrating plates and large-scale aerospace structures. Across all topics, the focus is on reduced computational cost, physical interpretability, and direct applicability to aerospace problems. The final section outlines current integration with FE tools (e.g., ANSYS, NASTRAN) and ongoing research into nonlinear extensions, digital twin frameworks, and uncertainty-informed design. Whether you're a researcher, simulation engineer, or design analyst, this presentation offers a cohesive, physics-based roadmap to quantify what we don't know — and to do so responsibly. Key words Stochastic Dynamics, Structural Uncertainty, Aerospace Structures, Uncertainty Quantification, Random Matrix Theory, Modal Analysis, Spectral Methods, Engineering Mechanics, Finite Element Uncertainty, Wishart Distribution, Parametric Uncertainty, Nonparametric Modelling, Eigenvalue Problems, Reduced Order Modelling, ASME SSDM2025

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computer Networks Error Detection and Correction.ppt

1. Error Detection and Correction • Types of Errors • Detection • Correction

2. Basic concepts  Networks must be able to transfer data from one device to another with complete accuracy.  Data can be corrupted during transmission.  For reliable communication, errors must be detected and corrected.  Error detection and correction are implemented either at the data link layer or the transport layer of the OSI model.

3. Types of Errors

4. Single-bit error

5. Single bit errors are the least likely type of errors in serial data transmission because the noise must have a very short duration which is very rare. However this kind of errors can happen in parallel transmission.

6. Burst error

8. The term burst error means that two or more bits in the data unit have changed from 1 to 0 or from 0 to 1. Burst errors does not necessarily mean that the errors occur in consecutive bits, the length of the burst is measured from the first corrupted bit to the last corrupted bit. Some bits in between may not have been corrupted.

9. Burst error is most likely to happen in serial transmission since the duration of noise is normally longer than the duration of a bit. The number of bits affected depends on the data rate and duration of noise.

10. Error detection Error detection means to decide whether the received data is correct or not without having a copy of the original message. Error detection uses the concept of redundancy, which means adding extra bits for detecting errors at the destination.

11. Redundancy

12. Four types of redundancy checks are used in data communications

13. Vertical Redundancy Check VRC

14. Performance It can detect single bit error It can detect burst errors only if the total number of errors is odd.

15. Longitudinal Redundancy Check LRC

16. Performance LCR increases the likelihood of detecting burst errors. If two bits in one data units are damaged and two bits in exactly the same positions in another data unit are also damaged, the LRC checker will not detect an error.

17. VRC and LRC

18. Cyclic Redundancy Check CRC

19. Cyclic Redundancy Check • Given a k-bit frame or message, the transmitter generates an n-bit sequence, known as a frame check sequence (FCS), so that the resulting frame, consisting of (k+n) bits, is exactly divisible by some predetermined number. • The receiver then divides the incoming frame by the same number and, if there is no remainder, assumes that there was no error.

20. Binary Division

21. Polynomial

22. Polynomial and Divisor

23. Standard Polynomials

24. Checksum

25. At the sender The unit is divided into k sections, each of n bits. All sections are added together using one’s complement to get the sum. The sum is complemented and becomes the checksum. The checksum is sent with the data

26. At the receiver The unit is divided into k sections, each of n bits. All sections are added together using one’s complement to get the sum. The sum is complemented. If the result is zero, the data are accepted: otherwise, they are rejected.

27. Performance The checksum detects all errors involving an odd number of bits. It detects most errors involving an even number of bits. If one or more bits of a segment are damaged and the corresponding bit or bits of opposite value in a second segment are also damaged, the sums of those columns will not change and the receiver will not detect a problem.

28. Error Correction It can be handled in two ways: 1) receiver can have the sender retransmit the entire data unit. 2) The receiver can use an error-correcting code, which automatically corrects certain errors.

29. Single-bit error correction To correct an error, the receiver reverses the value of the altered bit. To do so, it must know which bit is in error. Number of redundancy bits needed • Let data bits = m • Redundancy bits = r Total message sent = m+r The value of r must satisfy the following relation: 2r ≥ m+r+1

30. Error Correction

31. Hamming Code

32. Hamming Code

33. Hamming Code

34. Example of Hamming Code

35. Single-bit error

36. Error Detection