Performance Evaluation of Error Correcting Codes

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Performance Evaluation of Error Correcting Codes
Claudia OsmannInternational Computer Science
Instituteosmann_at_icsi.berkeley.edu
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Contents

• 1. Motivation and main problem
• 2. Development of an evaluation scheme
• Channel models for the error process
• Definition of a performance measure
• Development of a recursive scheme
• 3. Comparison of different coding techniques
• 4. Derivation of an approximation formular
• 5. View into the future

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Motivation
Error process
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Main problem
Find an optimal error correcting technique !
Evaluation of different error correcting
techniques regarding their performance
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Evaluation scheme
Requirements

• Adequate channel model
• Appropriate performance measure
• Recursive scheme

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Channel models
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Gilbert model
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Finite (semi-) Markov model
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Performance measure
Residual error rate
probability that despite of the use of an error
correcting code there are still errors left in
the received information
Find an efficient way for calculation !
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Recursive scheme I
If is the set of all correctable error
patterns , then calculate the probability of
a single error pattern of size n .Therefore,
let

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Recursive scheme II
Recursive scheme for the probability of an error
pattern

• Initialization

• If

, then

• If

, then
Computational expense of order
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Comparison of codes
Residual error rate
b-BEC-codecorrecting all burst errors up to
length b in adjacent positions
r-REC-code correcting up to r random errors in
arbitrary positions
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Results I
Distribution of mean burst size geometrical
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Results II
Distribution of mean burst size Poissonian
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First conclusions

• Analysis of different channel models
• Development of recursive equations
• Determination of an optimal code

Problemcomplexity and computational expense
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Approximation formular I
Is it necessary to exactly calculate the
residual errorrate of a code ?
Derive an approximation formular for the
residual error rate !
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Approximation formular II
Residual error rate
Probability that
generates one or more bad-phases
Probabilitythat uncorrectable error patterns
appear in one of the bad-phases
r-REC-code
b-BEC-code
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Results
Deviation of about 1
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View into the future

• Channel noise on signal level
• Video transmission as an example

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Noise on signal level
Error process onsignal level
Amplitude of thechannel noise
Adaptation of finiteMarkov processes to
autoregressiveerror processes
Representation by an autoregressive process
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Example video data
Data of different priority levels
Video data
Adapted errorcorrecting methods
Modification of the developed evaluation concept
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Conclusions

• Determination of an optimal error correcting
  code
• by evaluating its performance
• depending on the properties of the
  transmission channel
• based on adequate models for the error
  process on bit level as well as on signal level
• Derivation of an approximation formular