The Design of the MaximumLikelihood Decoding Algorithm of LDPC Codes over BEC

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The Design of the Maximum-Likelihood Decoding
Algorithm of LDPC Codes over BEC

• KiMoon Lee, Hayder Radha

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Contents

• Decoding of LDPC Codes over BEC
• The Maximum-Likelihood Decoding Algorithms (MLDA)
• Separated MLDA
• Computational Complexities
• Simulation Results
• Conclusion

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1. Linear Systems and Decoding of LDPC Codes over
BEC
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2. Maximum-Likelihood Decoding Algorithms
The original MLDA by Burshtein and Miller

• Equivalent to Gaussian Elimination (GE) on M
• Natural Extension of the Message Passing
  Algorithm (MPA)

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2. Maximum-Likelihood Decoding Algorithms
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2. Maximum-Likelihood Decoding Algorithms
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2. Maximum-Likelihood Decoding Algorithms
Advantages
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2. Maximum-Likelihood Decoding Algorithms
Disadvantages??
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3. Separated MLDA
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3. Separated MLDA
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4. Computational Complexity
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5. Simulation Results
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5. Simulation Results
2. The MPA vs the MLDA in Performances

• derr percentage of decoding failures in 100
  trials
• Red performances by the MPA
• Blue performances by the MLDA

• By the MLDA, for all (n, plt0.492),
• derr 0.
• By the MPA, for all (n, pgt0.45),
• derr gt 0.

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5. Simulation Results
3. Number of Symbol Additions by the Post-Decoding

• By the separated MLDA, for any (n,p) , ns lt 20
• By the original MLDA, ns increases rapidly as p
  -gt 0.5
• The ns by the original MLDA is dominated by the
  ns from the FFS as p -gt 0.5

Note The ns from the GE is not considere??
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5. Simulation Results
4. Number of References by the MLDA

• rf ( of references) /n.
• For any (n,p),
• rf lt 0.032, or r lt (0.032)n.

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5. Simulation Results
5. Rank Deficient Case Number of Free Variables

• For any (n,p),
• Nf lt 43.
• 2. X can be recovered by retransmission of less
  than 43 symbols of free variables.
• 3. This feature is not possible by the MPA alone.

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5. Simulation Results
6. An Exemplary Application from Simulation
Results.
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5. Simulation Results
6. continued.
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Conclusion

• The MPA is (Not) optimal for short block lengths
  ??
• The MLDA is very efficient compared to the
  conventional GE.
• The performance of codes by the MLDA is close to
  m/n.
• The GE may not be a major drawback to the
  efficiency of the MLDA??

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Thank You

• Questions?