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The approximate maximum-likelihood certificate
Information Theory · Submitted 16 May 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim When the AMLC holds, our approach thus provides the decoder with extra error detection capability, which is especially important in applications requiring high data integrity.
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The abstract, sentence by sentence
A new property which relies on the linear programming (LP) decoder, the approximate maximum-likelihood certificate (AMLC), is introduced. When using the belief propagation decoder, this property is a measure of how close the decoded codeword is to the LP solution. Using upper bounding techniques, it is demonstrated that the conditional frame error probability given that the AMLC holds is, with some degree of confidence, below a threshold. In channels with low noise, this threshold is several orders of magnitude lower than the simulated frame error rate, and our bound holds with very high degree of confidence. In contrast, showing this error performance by simulation would require very long Monte Carlo runs. When the AMLC holds, our approach thus provides the decoder with extra error detection capability, which is especially important in applications requiring high data integrity.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A new property which relies on the linear programming (LP) decoder, the approximate maximum-likelihood certificate (AMLC), is introduced. | contribution 1.00 | 0.91 | 0.12 | asserted 0.99 |
| s1 | When using the belief propagation decoder, this property is a measure of how close the decoded codeword is to the LP solution. | interpretation 0.45 | 0.35 | 0.05 | asserted 1.00 |
| s2 | Using upper bounding techniques, it is demonstrated that the conditional frame error probability given that the AMLC holds is, with some degree of confidence, below a threshold. | result 0.90 | 0.92 | 0.42 | asserted 0.95 |
| s3 | In channels with low noise, this threshold is several orders of magnitude lower than the simulated frame error rate, and our bound holds with very high degree of confidence. | result 0.95 | 0.92 | 0.21 | asserted 0.98 |
| s4 | In contrast, showing this error performance by simulation would require very long Monte Carlo runs. | interpretation 0.56 | 0.48 | 0.04 | asserted 0.96 |
| s5 | When the AMLC holds, our approach thus provides the decoder with extra error detection capability, which is especially important in applications requiring high data integrity. | interpretation 1.00 | 0.76 | 0.40 | asserted 0.98 |
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The paper
Original abstract
A new property which relies on the linear programming (LP) decoder, the approximate maximum-likelihood certificate (AMLC), is introduced. When using the belief propagation decoder, this property is a measure of how close the decoded codeword is to the LP solution. Using upper bounding techniques, it is demonstrated that the conditional frame error probability given that the AMLC holds is, with some degree of confidence, below a threshold. In channels with low noise, this threshold is several orders of magnitude lower than the simulated frame error rate, and our bound holds with very high degree of confidence. In contrast, showing this error performance by simulation would require very long Monte Carlo runs. When the AMLC holds, our approach thus provides the decoder with extra error detection capability, which is especially important in applications requiring high data integrity.
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Uses the method or tool of 1 paper
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To do this, we use the procedure described in [ref] which obtains a lower bound $LB(_1)$ on the minimum distance of the randomly-drawn code $_1$.
Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance · Application of the AMLC to expurgated LDPC ensembles · 1.00
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