Abstract:
For decoding concatenated codes up to half their designed distance, generalized minimum distance (GMD) decoding can be used. GMD decoding applies multitrial error/erasure decoding of the outer code, where erased symbols depend on some reliability measure stemming from the inner decoders. We consider the case where the outer decoder is able to decode beyond half the minimum distance of the outer code. For a given number of outer decoding trials, we derive achievable decoding radii for GMD decoding. Vice versa, we give a lower bound on the number of required outer decoding trials to obtain the greatest possible decoding radius.
Citation:
C. Senger, V. R. Sidorenko, M. Bossert, V. V. Zyablov, “Multitrial decoding of concatenated codes using fixed thresholds”, Probl. Peredachi Inf., 46:2 (2010), 30–46; Problems Inform. Transmission, 46:2 (2010), 127–141
This publication is cited in the following 6 articles:
Chaaban A. Sidorenko V.R. Senger Ch., “on Multi-Trial Forney-Kovalev Decoding of Concatenated Codes”, Adv. Math. Commun., 8:1 (2014), 1–20
Martin Bossert, Sergey Bezzateev, “A Unified View on Known Algebraic Decoding Algorithms and New Decoding Concepts”, IEEE Trans. Inform. Theory, 59:11 (2013), 7320
J. Weber, V. R. Sidorenko, C. Senger, K. Abdel-Ghaffar, “Asymptotic single-trial strategies for GMD decoding with arbitrary error-erasure tradeoff”, Problems Inform. Transmission, 48:12 (2012), 324–333
Senger Ch., Sidorenko V.R., Bossert M., Zyablov V.V., “Optimal threshold-based multi-trial error/erasure decoding with the Guruswami-Sudan algorithm”, 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), 2011, 845–849
Senger Ch., Sidorenko V.R., Bossert M., Zyablov V.V., “Optimal thresholds for GMD decoding with l+1 over l-extended Bounded Distance decoders”, 2010 IEEE International Symposium on Information Theory, IEEE International Symposium on Information Theory, 2010, 1100–1104
Christian Senger, Vladimir R. Sidorenko, Steffen Schober, Martin Bossert, Victor V. Zyablov, 2010 International Symposium On Information Theory & Its Applications, 2010, 267