Related papers: Syndrome-Based Error-Erasure Decoding of Interleav…
Integrated Interleaved (II) and Extended Integrated Interleaved (EII) codes are a versatile alternative for Locally Recoverable (LRC) codes, since they require fields of relatively small size. II and EII codes are generally defined over…
Generalized Reed-Solomon and extended generalized Reed-Solomon (abbreviation to GRS and EGRS) codes are the most well-known family of MDS codes with wide applications in coding theory and practice. Let $\mathbb{F}_q$ be the $q$ elements…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
Modern language models (LMs) are trained in an autoregressive manner, conditioned only on the prefix. In contrast, sequence labeling (SL) tasks assign labels to each individual input token, naturally benefiting from bidirectional context.…
Maximum distance separable (MDS) codes have significant combinatorial and cryptographic applications due to their certain optimality. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Twisted generalized Reed-Solomon…
Classical erasure codes, e.g. Reed-Solomon codes, have been acknowledged as an efficient alternative to plain replication to reduce the storage overhead in reliable distributed storage systems. Yet, such codes experience high overhead…
Understanding the limits of list-decoding and list-recovery of Reed-Solomon (RS) codes is of prime interest in coding theory and has attracted a lot of attention in recent decades. However, the best possible parameters for these problems…
In this paper, we propose a new linear-equation ordered-statistics decoding (LE-OSD). Unlike the OSD, LE-OSD uses high reliable parity bits rather than information bits to recover the codeword estimates, which is equivalent to solving a…
Hermitian hulls of linear codes are interesting for theoretical and practical reasons alike. In terms of recent application, linear codes whose hulls meet certain conditions have been utilized as ingredients to construct…
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
This work proves new results on the ability of binary Reed-Muller codes to decode from random errors and erasures. We obtain these results by proving improved bounds on the weight distribution of Reed-Muller codes of high degrees.…
Despite of tremendous research on decoding Reed-Solomon (RS) and algebraic geometry (AG) codes under the random and adversary substitution error models, few studies have explored these codes under the burst substitution error model. Burst…
Distributed storage systems for large clusters typically use replication to provide reliability. Recently, erasure codes have been used to reduce the large storage overhead of three-replicated systems. Reed-Solomon codes are the standard…
The interpolation based algebraic decoding for Reed-Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance. Using soft information, the algebraic soft decoding (ASD) further improves the decoding…
We speed up existing decoding algorithms for three code classes in different metrics: interleaved Gabidulin codes in the rank metric, lifted interleaved Gabidulin codes in the subspace metric, and linearized Reed-Solomon codes in the…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
We propose an alternative method for collaborative decoding of interleaved Reed-Solomon codes. Simulation results for a concatenated coding scheme using polar codes as inner codes are included.
Error-correcting codes are a method for representing data, so that one can recover the original information even if some parts of it were corrupted. The basic idea, which dates back to the revolutionary work of Shannon and Hamming about a…
For communication systems with heavy burst noise, an optimal Forward Error Correction (FEC) scheme is expected to have a large burst error correction capacity while simultaneously owning moderate random error correction capability. This…
Maximum distance separable (MDS) codes are widely used in distributed storage, but naively repairing a single failure in an $(n,k)$ MDS code requires downloading the full contents of $k$ surviving nodes. Minimum storage regenerating (MSR)…