The Approximate Maximum-Likelihood Certificate

The confidence in the reliability of a codeword output by some (not necessarily optimal) decoding algorithm is discussed. A new property which relies on the linear programming (LP) decoder, the approximate maximum-likelihood certificate (AMLC), is introduced to address this issue as follows. First,...

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Vydáno v:IEEE transactions on information theory Ročník 59; číslo 9; s. 6049 - 6059
Hlavní autoři: Goldenberg, Idan, Burshtein, David
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.09.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Applied sciences
Approximation
Coding theory
Coding, codes
Data integrity
Error probability
Exact sciences and technology
Information theory
Information, signal and communications theory
Linear programming
Linear programming (LP) decoding
low-density parity-check (LDPC) codes
maximum likelihood (ML) decoding
Maximum likelihood decoding
Maximum likelihood method
minimum distance
Monte Carlo methods
Monte Carlo simulation
Parity check codes
Signal and communications theory
Telecommunications and information theory
Upper bound
upper bounds on error probability
Vectors
Performance evaluation
Monte Carlo method
Error probability
Optimal algorithm
upper bounds on error probability
Error rate
Linear programming
Frame rate
Conditional probability
Maximum likelihood decoding
maximum likelihood (ML) decoding
Credal approach
Upper bound
Data integrity
low-density parity-check (LDPC) codes
minimum distance
Error detection
Numerical simulation
Error correcting code
Parity check codes
Minimal distance
Linear programming (LP) decoding
Maximum likelihood
Reliability
ISSN:0018-9448, 1557-9654
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Popis
Shrnutí:The confidence in the reliability of a codeword output by some (not necessarily optimal) decoding algorithm is discussed. A new property which relies on the linear programming (LP) decoder, the approximate maximum-likelihood certificate (AMLC), is introduced to address this issue as follows. First, the channel output vector is decoded by some symmetric decoder D, e.g., belief propagation or min-sum algorithm decoding. Second, the channel output vector is decoded by LP decoding. Third, if the decoding result of D is a codeword, its LP value is compared to the LP value of the LP decoding result (the latter need not be a codeword). If these two values are close, the AMLC holds. Using upper bounding techniques, we show 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 orders of magnitude lower than the simulated frame error rate, and our bound holds with a very high degree of confidence. This is in stark contrast with standard Monte Carlo simulation, which would require excessively long runs to demonstrate like performance. 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.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2263462