Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation

Wenhui Li; Johan S. R. Nielsen; Sven Puchinger; Vladimir Sidorenko

Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation

Information Theory 2015-01-21 v1 math.IT

Authors: Wenhui Li , Johan S. R. Nielsen , Sven Puchinger , Vladimir Sidorenko

Abstract

For many algebraic codes the main part of decoding can be reduced to a shift register synthesis problem. In this paper we present an approach for solving generalised shift register problems over skew polynomial rings which occur in error and erasure decoding of $\ell$ -Interleaved Gabidulin codes. The algorithm is based on module minimisation and has time complexity $O(\ell \mu^2)$ where $\mu$ measures the size of the input problem.

Cite

@article{arxiv.1501.04797,
  title  = {Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation},
  author = {Wenhui Li and Johan S. R. Nielsen and Sven Puchinger and Vladimir Sidorenko},
  journal= {arXiv preprint arXiv:1501.04797},
  year   = {2015}
}

Comments

10 pages, submitted to WCC 2015

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