English

Hierarchies of Local-Optimality Characterizations in Decoding of Tanner Codes

Information Theory 2012-08-15 v2 math.IT

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 hh iterations is decoded with a certificate after khk\cdot h iterations, for every integer kk.

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