Error-Erasure Decoding of Linearized Reed-Solomon Codes in the Sum-Rank Metric

02/14/2022
by   Felicitas Hörmann, et al.
0

Codes in the sum-rank metric have various applications in error control for multishot network coding, distributed storage and code-based cryptography. Linearized Reed-Solomon (LRS) codes contain Reed-Solomon and Gabidulin codes as subclasses and fulfill the Singleton-like bound in the sum-rank metric with equality. We propose the first known error-erasure decoder for LRS codes to unleash their full potential for multishot network coding. The presented syndrome-based Berlekamp-Massey-like error-erasure decoder can correct t_F full errors, t_R row erasures and t_C column erasures up to 2t_F + t_R + t_C ≤ n-k in the sum-rank metric requiring at most 𝒪(n^2) operations in 𝔽_q^m, where n is the code's length and k its dimension. We show how the proposed decoder can be used to correct errors in the sum-subspace metric that occur in (noncoherent) multishot network coding.

READ FULL TEXT
research
03/30/2023

On Decoding High-Order Interleaved Sum-Rank-Metric Codes

We consider decoding of vertically homogeneous interleaved sum-rank-metr...
research
09/30/2021

Efficient Decoding of Folded Linearized Reed-Solomon Codes in the Sum-Rank Metric

Recently, codes in the sum-rank metric attracted attention due to severa...
research
01/04/2022

Fast Decoding of Interleaved Linearized Reed-Solomon Codes and Variants

We construct s-interleaved linearized Reed-Solomon (ILRS) codes and vari...
research
02/18/2022

Fast Kötter-Nielsen-Høholdt Interpolation over Skew Polynomial Rings

Skew polynomials are a class of non-commutative polynomials that have se...
research
05/16/2022

Genomic Compression with Read Alignment at the Decoder

We propose a new compression scheme for genomic data given as sequence f...
research
08/22/2023

Fast Gao-like Decoding of Horizontally Interleaved Linearized Reed-Solomon Codes

Both horizontal interleaving as well as the sum-rank metric are currentl...
research
03/23/2022

Rank-Metric Codes and Their Applications

The rank metric measures the distance between two matrices by the rank o...

Please sign up or login with your details

Forgot password? Click here to reset