Related papers: Repairing Reed-Solomon Codes
MDS codes have diverse practical applications in communication systems, data storage, and quantum codes due to their algebraic properties and optimal error-correcting capability. In this paper, we focus on a class of linear codes and…
The I/O cost, defined as the amount of data accessed at helper nodes during the repair process, is a crucial metric for repair efficiency of Reed-Solomon (RS) codes. Recently, a formula that relates the I/O cost to the Hamming weight of…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
MDS (maximum distance separable) array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with r redundancy nodes can correct any r erasures by accessing (reading)…
In distributed storage systems reliability is achieved through redundancy stored at different nodes in the network. Then a data collector can reconstruct source information even though some nodes fail. To maintain reliability, an autonomous…
We construct an explicit family of locally repairable and locally regenerating codes whose existence was proven in a recent work by Kamath et al. about codes with local regeneration but no explicit construction was given. This explicit…
In this paper, we study distributed storage problems over unidirectional ring networks. A lower bound on the reconstructing bandwidth to recover total original data for each user is proposed, and it is achievable for arbitrary parameters.…
Folded Reed-Solomon codes are an explicit family of codes that achieve the optimal trade-off between rate and error-correction capability: specifically, for any $\eps > 0$, the author and Rudra (2006,08) presented an $n^{O(1/\eps)}$ time…
Piggybacking codes are a special class of MDS array codes that can achieve small repair bandwidth with small sub-packetization by first creating some instances of an $(n,k)$ MDS code, such as a Reed-Solomon (RS) code, and then designing the…
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…
Folded Reed-Solomon (FRS) codes are a well-studied family of codes, known for achieving list decoding capacity. In this work, we give improved deterministic and randomized algorithms for list decoding FRS codes of rate $R$ up to radius…
For high-rate linear systematic maximum distance separable (MDS) codes, most early constructions could initially optimally repair all the systematic nodes but not all the parity nodes. Fortunately, this issue was first solved by Li et al.…
Cooperative regenerating codes are regenerating codes designed to tradeoff storage for repair bandwidth in case of multiple node failures. Minimum storage cooperative regenerating (MSCR) codes are a class of cooperative regenerating codes…
Regenerating code is a class of code very suitable for distributed storage systems, which can maintain optimal bandwidth and storage space. Two types of important regenerating code have been constructed: the minimum storage regeneration…
In a distributed storage systems (DSS), regenerating codes are used to optimize bandwidth in the repair process of a failed node. To optimize other DSS parameters such as computation and disk I/O, Distributed Replication-based Simple…
This paper presents a new explicit construction for locally repairable codes (LRCs) for distributed storage systems which possess all-symbols locality and maximal possible minimum distance, or equivalently, can tolerate the maximal number…
Linearized Reed-Solomon (LRS) codes are evaluation codes based on skew polynomials. They achieve the Singleton bound in the sum-rank metric and therefore are known as maximum sum-rank distance (MSRD) codes. In this work, we give necessary…
In this paper, we propose two new constructions of exact-repair minimum storage regenerating (exact-MBR) codes. Both constructions obtain the encoded symbols by first treating the message vector over GF(q) as a linearized polynomial and…
Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…