Fast Decoding of Interleaved Linearized ReedSolomon Codes and Variants
Abstract
We construct sinterleaved linearized ReedSolomon (ILRS) codes and variants and propose efficient decoding schemes that can correct errors beyond the unique decoding radius in the sumrank, sumsubspace and skew metric. The proposed interpolationbased scheme for ILRS codes can be used as a list decoder or as a probabilistic unique decoder that corrects errors of sumrank up to $t\leq\frac{s}{s+1}(nk)$, 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 LoidreauOverbecklike decoder for ILRS codes. The results are extended to decoding of lifted interleaved linearized ReedSolomon (LILRS) codes in the sumsubspace metric and interleaved skew ReedSolomon (ISRS) codes in 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 sumrank, sumsubspace and skew metric. The results for the proposed decoding schemes are validated via Monte Carlo simulations.
 Publication:

arXiv eprints
 Pub Date:
 January 2022
 arXiv:
 arXiv:2201.01339
 Bibcode:
 2022arXiv220101339B
 Keywords:

 Computer Science  Information Theory
 EPrint:
 submitted to IEEE Transactions on Information Theory, 57 pages, 10 figures