On the relevance of graph covers and zeta functions for the analysis of SPA decoding of cycle codes

Conference Paper

For an arbitrary binary cycle code, we show that sum-product algorithm (SPA) decoding after infinitely many iterations equals symbolwise graph-cover decoding. We do this by characterizing the Bethe free energy function of the underlying normal factor graph (NFG) and by stating a global convergence proof of the SPA. We also show that the set of log-likelihood ratio vectors for which the SPA converges to the all-zero codeword is given by the region of convergence of the edge zeta function associated with the underlying NFG. The results in this paper justify the use of graph-cover pseudo-codewords and edge zeta functions to characterize the behavior of SPA decoding of cycle codes. These results have also implications for the analysis of attenuated sum-product and max-product algorithm decoding of low-density parity-check (LDPC) codes beyond cycle codes. © 2013 IEEE.

Full Text

Duke Authors

Cited Authors

  • Pfister, HD; Vontobel, PO

Published Date

  • December 19, 2013

Published In

Start / End Page

  • 3000 - 3004

International Standard Serial Number (ISSN)

  • 2157-8095

International Standard Book Number 13 (ISBN-13)

  • 9781479904464

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2013.6620776

Citation Source

  • Scopus