The slope scaling parameter for general channels, decoders, and ensembles

Jérémie Ezri, Andrea Montanari, Sewoong Oh, Ruediger Urbanke

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

Abstract

Scaling laws are a powerful way to analyze the performance of moderately sized iteratively decoded sparse graph codes. Our aim is to provide an easily usable finitelength optimization tool that is applicable to the wide variety of channels, blocklengths, error probability requirements, and decoders that one encounters for practical systems. The tool is aimed at non-experts in the field, who need to quickly find code designs that are comparable with the best known codes available today but do not have the luxury of spending months in doing so. In previous work we have shown how to compute scaling parameters for transmission over the binary erasure channel, as well as general channels and general quantized messagepassing decoders when applied to regular ensembles. In this paper we show how to compute the message variance for a fixed number of iterations for irregular low-density parity-check ensembles. From these calculations the basic scaling parameter α can be deduced by determining the leading term of the limiting expression when the number of iterations tends to infinity and the channel parameter approaches the density evolution threshold.

Original languageEnglish (US)
Title of host publicationProceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008
Pages1443-1447
Number of pages5
DOIs
StatePublished - Sep 29 2008
Event2008 IEEE International Symposium on Information Theory, ISIT 2008 - Toronto, ON, Canada
Duration: Jul 6 2008Jul 11 2008

Publication series

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

Other

Other2008 IEEE International Symposium on Information Theory, ISIT 2008
CountryCanada
CityToronto, ON
Period7/6/087/11/08

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ASJC Scopus subject areas

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

Cite this

Ezri, J., Montanari, A., Oh, S., & Urbanke, R. (2008). The slope scaling parameter for general channels, decoders, and ensembles. In Proceedings - 2008 IEEE International Symposium on Information Theory, ISIT 2008 (pp. 1443-1447). [4595226] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2008.4595226