论文标题
交织线性化的芦苇 - 固体代码和变体的快速解码
Fast Decoding of Interleaved Linearized Reed-Solomon Codes and Variants
论文作者
论文摘要
我们构建了$ s $ - 间接线性化的芦苇 - 固体（ILRS）代码和变体，并提出有效的解码方案，这些方案可以纠正超出sum-rank度量中唯一解码半径的错误。提出的基于ILRS代码的基于插值的方案可以用作列表解码器，也可以用作概率的独特解码器，该解码器纠正总和级的错误，最高可达$ t \ leq \ frac {s} {s+1}（s+1}（n-k）$，$ s $是$ n $ n $ n $ the $ n $ the $ k $ the dimemension和$ k $ the dimemention of dimemention of dimperimension of dimesimens。列表大小的上限和解码故障概率是基于新型的loidreau（类似于ILRS代码的贝克样解码器）的情况下给出的。我们展示了如何使用所提出的解码方案来解码误差超出偏斜度量的唯一解码半径，并使用总和度量和偏斜度量的均衡法。 我们概括了快速最小的近似基插值技术，以获取具有代码长度中具有亚二次复杂性的ILRS代码（和变体）的有效解码方案。 据我们所知，提出的解码方案是第一个能够纠正超出和偏移度量的独特解码区域以外的错误。通过蒙特卡洛模拟验证了所提出的解码方案的性能和解码失效概率上的上限的紧密度。
We construct $s$-interleaved linearized Reed--Solomon (ILRS) codes and variants and propose efficient decoding schemes that can correct errors beyond the unique decoding radius in the sum-rank metric. The proposed interpolation-based scheme for ILRS codes can be used as a list decoder or as a probabilistic unique decoder that corrects errors of sum-rank up to $t\leq\frac{s}{s+1}(n-k)$, where $s$ is the interleaving order, $n$ the length and $k$ the dimension of the code. Upper bounds on the list size and the decoding failure probability are given where the latter is based on a novel Loidreau--Overbeck-like decoder for ILRS codes. We show how the proposed decoding schemes can be used to decode errors beyond the unique decoding radius in the skew metric by using an isometry between the sum-rank metric and the skew metric. We generalize fast minimal approximant basis interpolation techniques to obtain efficient decoding schemes for ILRS codes (and variants) with subquadratic complexity in the code length. Up to our knowledge, the presented decoding schemes are the first being able to correct errors beyond the unique decoding region in the sum-rank and skew metric. The performance of the proposed decoding schemes and the tightness of the upper bound on the decoding failure probability are validated via Monte Carlo simulations.
