Analysis of error floors of LDPC codes under LP decoding over the BSC

Shashi Kiran Chilappagari, Bane V Vasic, Mikhail Stepanov, Michael Chertkov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

We consider Linear Programming (LP) decoding of a fixed Low-Density Parity-Check (LDPC) code over the Binary Symmetric Channel (BSC). The LP decoder fails when it outputs a pseudo-codeword which is not a codeword. We propose an efficient algorithm termed the Instanton Search Algorithm (ISA) which, given a random input, generates a set of flips called the BSC-instanton and prove that: (a) the LP decoder fails for any set of flips with support vector including an instanton; (b) for any input, the algorithm outputs an instanton in the number of steps upper-bounded by twice the number of flips in the input. We obtain the number of unique instantons of different sizes by running the ISA sufficient number of times. We then use the instanton statistics to predict the performance of the LP decoding over the BSC in the error floor region. We also propose an efficient semi-analytical method to predict the performance of LP decoding over a large range of transition probabilities of the BSC.

Original languageEnglish (US)
Title of host publicationIEEE International Symposium on Information Theory - Proceedings
Pages379-383
Number of pages5
DOIs
StatePublished - 2009
Event2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of
Duration: Jun 28 2009Jul 3 2009

Other

Other2009 IEEE International Symposium on Information Theory, ISIT 2009
CountryKorea, Republic of
CitySeoul
Period6/28/097/3/09

Fingerprint

Low-density Parity-check (LDPC) Codes
Instantons
Linear programming
Decoding
Binary
Flip
Search Algorithm
Semi-analytical Method
Predict
Support Vector
Output
Statistics
Transition Probability
Efficient Algorithms
Sufficient
Range of data

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Theoretical Computer Science
  • Information Systems

Cite this

Chilappagari, S. K., Vasic, B. V., Stepanov, M., & Chertkov, M. (2009). Analysis of error floors of LDPC codes under LP decoding over the BSC. In IEEE International Symposium on Information Theory - Proceedings (pp. 379-383). [5205739] https://doi.org/10.1109/ISIT.2009.5205739

Analysis of error floors of LDPC codes under LP decoding over the BSC. / Chilappagari, Shashi Kiran; Vasic, Bane V; Stepanov, Mikhail; Chertkov, Michael.

IEEE International Symposium on Information Theory - Proceedings. 2009. p. 379-383 5205739.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Chilappagari, SK, Vasic, BV, Stepanov, M & Chertkov, M 2009, Analysis of error floors of LDPC codes under LP decoding over the BSC. in IEEE International Symposium on Information Theory - Proceedings., 5205739, pp. 379-383, 2009 IEEE International Symposium on Information Theory, ISIT 2009, Seoul, Korea, Republic of, 6/28/09. https://doi.org/10.1109/ISIT.2009.5205739
Chilappagari SK, Vasic BV, Stepanov M, Chertkov M. Analysis of error floors of LDPC codes under LP decoding over the BSC. In IEEE International Symposium on Information Theory - Proceedings. 2009. p. 379-383. 5205739 https://doi.org/10.1109/ISIT.2009.5205739
Chilappagari, Shashi Kiran ; Vasic, Bane V ; Stepanov, Mikhail ; Chertkov, Michael. / Analysis of error floors of LDPC codes under LP decoding over the BSC. IEEE International Symposium on Information Theory - Proceedings. 2009. pp. 379-383
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