Hierarchies of Local-Optimality Characterizations in Decoding of Tanner Codes
Abstract
Recent developments in decoding of Tanner codes with maximum-likelihood certificates are based on a sufficient condition called local-optimality. We define hierarchies of locally-optimal codewords with respect to two parameters. One parameter is related to the minimum distance of the local codes in Tanner codes. The second parameter is related to the finite number of iterations used in iterative decoding. We show that these hierarchies satisfy inclusion properties as these parameters are increased. In particular, this implies that a codeword that is decoded with a certificate using an iterative decoder after iterations is decoded with a certificate after iterations, for every integer .
Keywords
Cite
@article{arxiv.1202.2251,
title = {Hierarchies of Local-Optimality Characterizations in Decoding of Tanner Codes},
author = {Nissim Halabi and Guy Even},
journal= {arXiv preprint arXiv:1202.2251},
year = {2012}
}
Comments
Extended abstract appears in the proceedings of the IEEE International Symposium on Information Theory, Cambridge, MA,USA, 2012