282 research outputs found
Download and Access Trade-offs in Lagrange Coded Computing
Lagrange Coded Computing (LCC) is a recently
proposed technique for resilient, secure, and private computation
of arbitrary polynomials in distributed environments. By
mapping such computations to composition of polynomials, LCC
allows the master node to complete the computation by accessing
a minimal number of workers and downloading all of their
content, thus providing resiliency to the remaining stragglers.
However, in the most common case in which the number of
stragglers is less than in the worst case scenario, much of the
computational power of the system remains unexploited. To
amend this issue, in this paper we expand LCC by studying a
fundamental trade-off between download and access, and present
two contributions. In the first contribution, it is shown that
without any modification to the encoding process, the master
can decode the computations by accessing a larger number of
nodes, however downloading less information from each node in
comparison with LCC (i.e., trading access for download). This
scheme relies on decoding a particular polynomial in the ideal
that is generated by the polynomials of interest, a technique we
call Ideal Decoding. This new scheme also improves LCC in the
sense that for systems with adversaries, the overall downloaded
bandwidth is smaller than in LCC. In the second contribution
we study a real-time model of this trade-off, in which the data
from the workers is downloaded sequentially. By clustering nodes
of similar delays and encoding the function with Universally
Decodable Matrices, the master can decode once sufficient data is
downloaded from every cluster, regardless of the internal delays
within that cluster. This allows the master to utilize the partial
work that is done by stragglers, rather than to ignore it, a feature
that most past works in coded computing are lacking
On the Design of Future Communication Systems with Coded Transport, Storage, and Computing
Communication systems are experiencing a fundamental change. There are novel applications that require an increased performance not only of throughput but also latency, reliability, security, and heterogeneity support from these systems. To fulfil the requirements, future systems understand communication not only as the transport of bits but also as their storage, processing, and relation. In these systems, every network node has transport storage and computing resources that the network operator and its users can exploit through virtualisation and softwarisation of the resources. It is within this context that this work presents its results. We proposed distributed coded approaches to improve communication systems. Our results improve the reliability and latency performance of the transport of information. They also increase the reliability, flexibility, and throughput of storage applications. Furthermore, based on the lessons that coded approaches improve the transport and storage performance of communication systems, we propose a distributed coded approach for the computing of novel in-network applications such as the steering and control of cyber-physical systems. Our proposed approach can increase the reliability and latency performance of distributed in-network computing in the presence of errors, erasures, and attackers
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