16,264 research outputs found
Non-adaptive pooling strategies for detection of rare faulty items
We study non-adaptive pooling strategies for detection of rare faulty items.
Given a binary sparse N-dimensional signal x, how to construct a sparse binary
MxN pooling matrix F such that the signal can be reconstructed from the
smallest possible number M of measurements y=Fx? We show that a very low number
of measurements is possible for random spatially coupled design of pools F. Our
design might find application in genetic screening or compressed genotyping. We
show that our results are robust with respect to the uncertainty in the matrix
F when some elements are mistaken.Comment: 5 page
Lower bounds for constant query affine-invariant LCCs and LTCs
Affine-invariant codes are codes whose coordinates form a vector space over a
finite field and which are invariant under affine transformations of the
coordinate space. They form a natural, well-studied class of codes; they
include popular codes such as Reed-Muller and Reed-Solomon. A particularly
appealing feature of affine-invariant codes is that they seem well-suited to
admit local correctors and testers.
In this work, we give lower bounds on the length of locally correctable and
locally testable affine-invariant codes with constant query complexity. We show
that if a code is an -query
locally correctable code (LCC), where is a finite field and
is a finite alphabet, then the number of codewords in is
at most . Also, we show that if
is an -query locally testable
code (LTC), then the number of codewords in is at most
. The dependence on in these
bounds is tight for constant-query LCCs/LTCs, since Guo, Kopparty and Sudan
(ITCS `13) construct affine-invariant codes via lifting that have the same
asymptotic tradeoffs. Note that our result holds for non-linear codes, whereas
previously, Ben-Sasson and Sudan (RANDOM `11) assumed linearity to derive
similar results.
Our analysis uses higher-order Fourier analysis. In particular, we show that
the codewords corresponding to an affine-invariant LCC/LTC must be far from
each other with respect to Gowers norm of an appropriate order. This then
allows us to bound the number of codewords, using known decomposition theorems
which approximate any bounded function in terms of a finite number of
low-degree non-classical polynomials, upto a small error in the Gowers norm
Local Testing for Membership in Lattices
Motivated by the structural analogies between point lattices and linear error-correcting codes, and by the mature theory on locally testable codes, we initiate a systematic study of local testing for membership in lattices. Testing membership in lattices is also motivated in practice, by applications to integer programming, error detection in lattice-based communication, and cryptography. Apart from establishing the conceptual foundations of lattice testing, our results include the following: 1. We demonstrate upper and lower bounds on the query complexity of local testing for the well-known family of code formula lattices. Furthermore, we instantiate our results with code formula lattices constructed from Reed-Muller codes, and obtain nearly-tight bounds. 2. We show that in order to achieve low query complexity, it is sufficient to design one-sided non-adaptive canonical tests. This result is akin to, and based on an analogous result for error-correcting codes due to Ben-Sasson et al. (SIAM J. Computing 35(1) pp1-21)
Synapse: Synthetic Application Profiler and Emulator
We introduce Synapse motivated by the needs to estimate and emulate workload
execution characteristics on high-performance and distributed heterogeneous
resources. Synapse has a platform independent application profiler, and the
ability to emulate profiled workloads on a variety of heterogeneous resources.
Synapse is used as a proxy application (or "representative application") for
real workloads, with the added advantage that it can be tuned at arbitrary
levels of granularity in ways that are simply not possible using real
applications. Experiments show that automated profiling using Synapse
represents application characteristics with high fidelity. Emulation using
Synapse can reproduce the application behavior in the original runtime
environment, as well as reproducing properties when used in a different
run-time environments
Optimal Testing of Generalized Reed-Muller Codes in Fewer Queries
A local tester for an error correcting code is a
tester that makes oracle queries to a given word and
decides to accept or reject the word . An optimal local tester is a local
tester that has the additional properties of completeness and optimal
soundness. By completeness, we mean that the tester must accept with
probability if . By optimal soundness, we mean that if the tester
accepts with probability at least (where is small),
then it must be the case that is -close to some codeword
in Hamming distance.
We show that Generalized Reed-Muller codes admit optimal testers with queries. Here, for a prime power , the Generalized Reed-Muller code, RM[n,q,d], consists of the
evaluations of all -variate degree polynomials over .
Previously, no tester achieving this query complexity was known, and the best
known testers due to Haramaty, Shpilka and Sudan(which is optimal) and due to
Ron-Zewi and Sudan(which was not known to be optimal) both required
queries. Our tester achieves query
complexity which is polynomially better than by a power of , which is
nearly the best query complexity possible for generalized Reed-Muller codes.
The tester we analyze is due to Ron-Zewi and Sudan, and we show that their
basic tester is in fact optimal. Our methods are more general and also allow us
to prove that a wide class of testers, which follow the form of the Ron-Zewi
and Sudan tester, are optimal. This result applies to testers for all
affine-invariant codes (which are not necessarily generalized Reed-Muller
codes).Comment: 42 pages, 8 page appendi
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