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

Publication ,  Conference
Pfister, HD; Vontobel, PO
Published in: IEEE International Symposium on Information Theory - Proceedings
December 19, 2013

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.

Duke Scholars

Published In

IEEE International Symposium on Information Theory - Proceedings

DOI

ISSN

2157-8095

ISBN

9781479904464

Publication Date

December 19, 2013

Start / End Page

3000 / 3004
 

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Pfister, H. D., & Vontobel, P. O. (2013). On the relevance of graph covers and zeta functions for the analysis of SPA decoding of cycle codes. In IEEE International Symposium on Information Theory - Proceedings (pp. 3000–3004). https://doi.org/10.1109/ISIT.2013.6620776
Pfister, H. D., and P. O. Vontobel. “On the relevance of graph covers and zeta functions for the analysis of SPA decoding of cycle codes.” In IEEE International Symposium on Information Theory - Proceedings, 3000–3004, 2013. https://doi.org/10.1109/ISIT.2013.6620776.
Pfister HD, Vontobel PO. On the relevance of graph covers and zeta functions for the analysis of SPA decoding of cycle codes. In: IEEE International Symposium on Information Theory - Proceedings. 2013. p. 3000–4.
Pfister, H. D., and P. O. Vontobel. “On the relevance of graph covers and zeta functions for the analysis of SPA decoding of cycle codes.” IEEE International Symposium on Information Theory - Proceedings, 2013, pp. 3000–04. Scopus, doi:10.1109/ISIT.2013.6620776.
Pfister HD, Vontobel PO. On the relevance of graph covers and zeta functions for the analysis of SPA decoding of cycle codes. IEEE International Symposium on Information Theory - Proceedings. 2013. p. 3000–3004.

Published In

IEEE International Symposium on Information Theory - Proceedings

DOI

ISSN

2157-8095

ISBN

9781479904464

Publication Date

December 19, 2013

Start / End Page

3000 / 3004