Convergence analysis of serial message-passing schedules for LDPC decoding

Eran Sharon, Simon Litsyn, Jacob Goldberger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Serial decoding schedules for low-density parity-check (LDPC) codes are described and analyzed. Conventionally, in each iteration all the variable nodes and subsequently all the check nodes send messages to their neighbors (“flooding schedule”). In contrast, in the considered methods, the updating of the nodes is implemented according to a serial schedule. The evolution of the decoding algorithm's computation tree under serial scheduling is analyzed. The analysis shows that it grows twice as fast in comparison to the flooding schedule's computation tree, indicating that the serial schedule propagates information twice as fast in the code's underlying graph. Furthermore, asymptotic analysis of the serial schedule's convergence rate is done using the Density Evolution (DE) algorithm. Applied to various ensembles of LDPC codes, it shows that when working near the ensemble's threshold, for long enough codes the serial schedule is expected to converge in half the number of iterations compared to the standard flooding schedule. This observation is generally proved for the Binary Erasure Channel (BEC) under some likely assumptions. Finally, an accompanying concentration theorem is proved, justifying the asymptotic DE analysis assumptions.

Original languageEnglish
Title of host publicationTURBO - CODING 2006 - 4th International Symposium on Turbo Codes and Related Topics and 6th International ITG-Conference on Source and Channel Coding
PublisherVDE Verlag GmbH
ISBN (Electronic)3800729474, 9783800729470
StatePublished - 2006
Event4th International Symposium on Turbo Codes and Related Topics and 6th International ITG-Conference on Source and Channel Coding, TURBOCODING 2006 - Munich, Germany
Duration: 3 Apr 20067 Apr 2006

Publication series

NameTURBO - CODING 2006 - 4th International Symposium on Turbo Codes and Related Topics and 6th International ITG-Conference on Source and Channel Coding

Conference

Conference4th International Symposium on Turbo Codes and Related Topics and 6th International ITG-Conference on Source and Channel Coding, TURBOCODING 2006
Country/TerritoryGermany
CityMunich
Period3/04/067/04/06

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