Weighted external difference families and R-optimal AMD codes

In this paper, we provide a mathematical framework for characterizing AMD codes that are R-optimal. We introduce a new combinatorial object, the reciprocally-weighted external difference family (RWEDF), which corresponds precisely to an R-optimal weak AMD code. This definition subsumes known examples of existing optimal codes, and also encompasses combinatorial objects not covered by previous definitions in the literature. By developing structural group-theoretic characterizations, we exhibit infinite families of new RWEDFs, and new construction methods for known objects such as near-complete EDFs. Examples of RWEDFs in non-abelian groups are also discussed

Characterising bimodal collections of sets in finite groups

A collection of disjoint subsets A = {A 1 ,A 2 ,...,A m } of a finite abelian group is said to have the bimodal property if, for any non-zero group element δ, either δ never occurs as a difference between an element of A i and an element of some other set A j , or else for every element a i in A i there is an element a j ∈ A j for some j 6= i such that a i − a j = δ. This property arises in various familiar situations, such as the cosets of a fixed subgroup or in a group partition, and has applications to the construction of optimal algebraic manipulation detection (AMD) codes. In this paper, we obtain a structural characterisation for bimodal collections of sets

Contributions to the efficient use of general purpose coprocessors: kernel density estimation as case study

142 p.The high performance computing landscape is shifting from assemblies of homogeneous nodes towards heterogeneous systems, in which nodes consist of a combination of traditional out-of-order execution cores and accelerator devices. Accelerators provide greater theoretical performance compared to traditional multi-core CPUs, but exploiting their computing power remains as a challenging task.This dissertation discusses the issues that arise when trying to efficiently use general purpose accelerators. As a contribution to aid in this task, we present a thorough survey of performance modeling techniques and tools for general purpose coprocessors. Then we use as case study the statistical technique Kernel Density Estimation (KDE). KDE is a memory bound application that poses several challenges for its adaptation to the accelerator-based model. We present a novel algorithm for the computation of KDE that reduces considerably its computational complexity, called S-KDE. Furthermore, we have carried out two parallel implementations of S-KDE, one for multi and many-core processors, and another one for accelerators. The latter has been implemented in OpenCL in order to make it portable across a wide range of devices. We have evaluated the performance of each implementation of S-KDE in a variety of architectures, trying to highlight the bottlenecks and the limits that the code reaches in each device. Finally, we present an application of our S-KDE algorithm in the field of climatology: a novel methodology for the evaluation of environmental models

EPSILOD: efficient parallel skeleton for generic iterative stencil computations in distributed GPUs

Producción CientíficaIterative stencil computations are widely used in numerical simulations. They present a high degree of parallelism, high locality and mostly-coalesced memory access patterns. Therefore, GPUs are good candidates to speed up their computa- tion. However, the development of stencil programs that can work with huge grids in distributed systems with multiple GPUs is not straightforward, since it requires solv- ing problems related to the partition of the grid across nodes and devices, and the synchronization and data movement across remote GPUs. In this work, we present EPSILOD, a high-productivity parallel programming skeleton for iterative stencil computations on distributed multi-GPUs, of the same or different vendors that sup- ports any type of n-dimensional geometric stencils of any order. It uses an abstract specification of the stencil pattern (neighbors and weights) to internally derive the data partition, synchronizations and communications. Computation is split to better overlap with communications. This paper describes the underlying architecture of EPSILOD, its main components, and presents an experimental evaluation to show the benefits of our approach, including a comparison with another state-of-the-art solution. The experimental results show that EPSILOD is faster and shows good strong and weak scalability for platforms with both homogeneous and heterogene- ous types of GPUJunta de Castilla y León, Ministerio de Economía, Industria y Competitividad, y Fondo Europeo de Desarrollo Regional (FEDER): Proyecto PCAS (TIN2017-88614-R) y Proyecto PROPHET-2 (VA226P20).Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación y “European Union NextGenerationEU/PRTR” : (MCIN/ AEI/10.13039/501100011033) - grant TED2021-130367B-I00CTE-POWER and Minotauro and the technical support provided by Barcelona Supercomputing Center (RES-IM-2021-2-0005, RES-IM-2021-3-0024, RES- IM-2022-1-0014).Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCL

Pauli Manipulation Detection codes and Applications to Quantum Communication over Adversarial Channels

We introduce and explicitly construct a quantum code we coin a "Pauli Manipulation Detection" code (or PMD), which detects every Pauli error with high probability. We apply them to construct the first near-optimal codes for two tasks in quantum communication over adversarial channels. Our main application is an approximate quantum code over qubits which can efficiently correct from a number of (worst-case) erasure errors approaching the quantum Singleton bound. Our construction is based on the composition of a PMD code with a stabilizer code which is list-decodable from erasures. Our second application is a quantum authentication code for "qubit-wise" channels, which does not require a secret key. Remarkably, this gives an example of a task in quantum communication which is provably impossible classically. Our construction is based on a combination of PMD codes, stabilizer codes, and classical non-malleable codes (Dziembowski et al., 2009), and achieves "minimal redundancy" (rate $1-o(1)$)