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Generic programming (GP) is an increasingly important trend in programming languages. Well-known GP mechanisms, such as type classes and the C++0x concepts proposal, usually combine two features: 1) a special type of interfaces; and 2)…
In order to provide high data reliability, distributed storage systems disperse data with redundancy to multiple storage nodes. Regenerating codes is a new class of erasure codes to introduce redundancy for the purpose of improving the data…
In this paper, we first propose a general interpolation algorithm in a free module of a linearized polynomial ring, and then apply this algorithm to decode several important families of codes, Gabidulin codes, KK codes and MV codes. Our…
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…
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…
Self-Repairing Codes (SRC) are codes designed to suit the need of coding for distributed networked storage: they not only allow stored data to be recovered even in the presence of node failures, they also provide a repair mechanism where as…
In this paper, we prove that the sub-field images of generalized Reed-Solomon (RS) codes can achieve the symmetric capacity of p-ary memoryless channels. Unlike the totally random linear code ensemble, as a class of maximum distance…
An alternative method for collaborative decoding of interleaved Reed-Solomon codes as well as Gabidulin codes for the case of high interleaving degree is proposed. As an example of application, simulation results are presented for a…
We consider regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the information stored at a subset of vertices of the graph for the…
Locality enables storage systems to recover failed nodes from small subsets of surviving nodes. The setting where nodes are partitioned into subsets, each allowing for local recovery, is well understood. In this work we consider a…
Concatenated backward ray mapping is an alternative for ray tracing in 2D. It is based on the phase-space description of an optical system. Phase space is the set of position and direction coordinates of light rays intersecting a surface.…
Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result…
Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a…
In the modern era of large-scale computing systems, a crucial use of error correcting codes is to judiciously introduce redundancy to ensure recoverability from failure. To get the most out of every byte, practitioners and theorists have…
Maximally Recoverable Local Reconstruction Codes (LRCs) are codes designed for distributed storage to provide maximum resilience to failures for a given amount of storage redundancy and locality. An $(n,r,h,a,g)$-MR LRC has $n$ coordinates…
We apply a dynamical systems approach to concatenation of quantum error correcting codes, extending and generalizing the results of Rahn et al. [1] to both diagonal and nondiagonal channels. Our point of view is global: instead of focusing…
Recently, locally repairable codes (LRCs) with local erasure correction constraints that are unequal and disjoint have been proposed. In this work, we study the same topic and provide some improved and additional results.
Constraint Programming (CP) has been successfully applied to both constraint satisfaction and constraint optimization problems. A wide variety of specialized global constraints provide critical assistance in achieving a good model that can…
In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…
We establish a duality result between linear index coding and Locally Repairable Codes (LRCs). Specifically, we show that a natural extension of LRCs we call Generalized Locally Repairable Codes (GLCRs) are exactly dual to linear index…