Upper bounding the performance of arbitrary finite LDPC codes on binary erasure channels

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

7 Scopus citations

Abstract

Assuming iterative decoding for binary erasure channels (BECs), a novel tree-based technique for upper bounding the bit error rates (BERs) of arbitrary, finite low-density parity-check (LDPC) codes is provided and the resulting bound can be evaluated for all operating erasure probabilities, including both the waterfall and the error floor regions. This upper bound can also be viewed as a narrowing search of stopping sets, which is an approach different from the stopping set enumeration used for lower bounding the error floor. When combined with optimal leaf-finding modules, this upper bound is guaranteed to be tight in terms of the asymptotic order. The Boolean framework proposed herein further admits a composite search for even tighter results. For comparison, a refinement of the algorithm is capable of exhausting all stopping sets of size ≤ 13 for irregular LDPC codes of length n ≈ 500, which requires (500/13) ≈ 1.67 × 1025 trials if a brute force approach is taken. These experiments indicate that this upper bound can be used both as an analytical tool and as a deterministic worst-performance (error floor) guarantee, the latter of which is crucial to optimizing LDPC codes for extremely low BER applications, e.g., optical/satellite communications.

Original languageEnglish (US)
Title of host publicationProceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006
Pages411-415
Number of pages5
DOIs
StatePublished - Dec 1 2006
Event2006 IEEE International Symposium on Information Theory, ISIT 2006 - Seattle, WA, United States
Duration: Jul 9 2006Jul 14 2006

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8101

Other

Other2006 IEEE International Symposium on Information Theory, ISIT 2006
CountryUnited States
CitySeattle, WA
Period7/9/067/14/06

All Science Journal Classification (ASJC) codes

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

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    Wang, C. C., Kulkarni, S. R., & Vincent Poor, H. (2006). Upper bounding the performance of arbitrary finite LDPC codes on binary erasure channels. In Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006 (pp. 411-415). [4035993] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2006.261701