7,472 research outputs found
Locality via Partially Lifted Codes
In error-correcting codes, locality refers to several different ways of quantifying how easily a small amount of information can be recovered from encoded data. In this work, we study a notion of locality called the s-Disjoint-Repair-Group Property (s-DRGP). This notion can interpolate between two very different settings in coding theory: that of Locally Correctable Codes (LCCs) when s is large - a very strong guarantee - and Locally Recoverable Codes (LRCs) when s is small - a relatively weaker guarantee. This motivates the study of the s-DRGP for intermediate s, which is the focus of our paper. We construct codes in this parameter regime which have a higher rate than previously known codes. Our construction is based on a novel variant of the lifted codes of Guo, Kopparty and Sudan. Beyond the results on the s-DRGP, we hope that our construction is of independent interest, and will find uses elsewhere
Lifted Multiplicity Codes and the Disjoint Repair Group Property
Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We consider a generalization of their construction, which we call lifted multiplicity codes. These are multivariate polynomial codes whose restriction to any line is a codeword of a multiplicity code (Kopparty, Saraf, Yekhanin 2014). We show that lifted multiplicity codes have a better trade-off between redundancy and a notion of locality called the t-disjoint-repair-group property than previously known constructions. More precisely, we show that, for t <=sqrt{N}, lifted multiplicity codes with length N and redundancy O(t^{0.585} sqrt{N}) have the property that any symbol of a codeword can be reconstructed in t different ways, each using a disjoint subset of the other coordinates. This gives the best known trade-off for this problem for any super-constant t < sqrt{N}. We also give an alternative analysis of lifted Reed Solomon codes using dual codes, which may be of independent interest
Load management strategy for Particle-In-Cell simulations in high energy particle acceleration
In the wake of the intense effort made for the experimental CILEX project,
numerical simulation cam- paigns have been carried out in order to finalize the
design of the facility and to identify optimal laser and plasma parameters.
These simulations bring, of course, important insight into the fundamental
physics at play. As a by-product, they also characterize the quality of our
theoretical and numerical models. In this paper, we compare the results given
by different codes and point out algorithmic lim- itations both in terms of
physical accuracy and computational performances. These limitations are illu-
strated in the context of electron laser wakefield acceleration (LWFA). The
main limitation we identify in state-of-the-art Particle-In-Cell (PIC) codes is
computational load imbalance. We propose an innovative algorithm to deal with
this specific issue as well as milestones towards a modern, accurate high-per-
formance PIC code for high energy particle acceleration
Algebraic hierarchical locally recoverable codes with nested affine subspace recovery
Codes with locality, also known as locally recoverable codes, allow for
recovery of erasures using proper subsets of other coordinates. Theses subsets
are typically of small cardinality to promote recovery using limited network
traffic and other resources. Hierarchical locally recoverable codes allow for
recovery of erasures using sets of other symbols whose sizes increase as needed
to allow for recovery of more symbols. In this paper, we construct codes with
hierarchical locality from a geometric perspective, using fiber products of
curves. We demonstrate how the constructed hierarchical codes can be viewed as
punctured subcodes of Reed-Muller codes. This point of view provides natural
structures for local recovery at each level in the hierarchy
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