The error-floor of LDPC codes in the Laplacian channel

M. G. Stepanov, M. Chertkov

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

2 Scopus citations

Abstract

We analyze the performance of Low-Density-Parity-Check codes in the error-floor domain where the Signal-to-Noise-Ratio, s, is large, s ≥ 1. We describe how the instanton method of theoretical physics, recently adapted to coding theory, solves the problem of characterizing the error-floor domain in the Laplacian channel. An example of the (155,64,20) LDPC code with four iterations (each iteration consisting of two semi-steps: from bits-tochecks and from checks-to-bits) of the min-sum decoding is discussed. A generalized computational tree analysis is devised to explain the rational structure of the leading instantons. The asymptotic for the symbol Bit-Error-Rate in the error-floor domain is comprised of individual instanton contributions, each estimated as ∼ exp(-linst;L s), where the effective distances, linst;L, of the the leading instantons are 7.6,8.0 and 8.0 respectively. (The Hamming distance of the code is 20.) The analysis shows that the instantons are distinctly different from the ones found for the same coding/decoding scheme performing over the Gaussian channel. We validate instanton results against direct simulations and offer an explanation for remarkable performance of the instanton approximation not only in the extremal, s→∞, limit but also at the moderate s values of practical interest.

Original languageEnglish (US)
Title of host publication43rd Annual Allerton Conference on Communication, Control and Computing 2005
PublisherUniversity of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering
Pages1795-1804
Number of pages10
ISBN (Electronic)9781604234916
StatePublished - Jan 1 2005
Externally publishedYes
Event43rd Annual Allerton Conference on Communication, Control and Computing 2005 - Monticello, United States
Duration: Sep 28 2005Sep 30 2005

Publication series

Name43rd Annual Allerton Conference on Communication, Control and Computing 2005
Volume4

Other

Other43rd Annual Allerton Conference on Communication, Control and Computing 2005
CountryUnited States
CityMonticello
Period9/28/059/30/05

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications

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