7,138 research outputs found
Probabilistic Existence Results for Separable Codes
Separable codes were defined by Cheng and Miao in 2011, motivated by
applications to the identification of pirates in a multimedia setting.
Combinatorially, -separable codes lie somewhere between
-frameproof and -frameproof codes: all -frameproof codes are
-separable, and all -separable codes are
-frameproof. Results for frameproof codes show that (when is large)
there are -ary -separable codes of length with
approximately codewords, and that no -ary
-separable codes of length can have more than approximately
codewords.
The paper provides improved probabilistic existence results for
-separable codes when . More precisely, for all and all , there exists a constant (depending only on
and ) such that there exists a -ary -separable code of
length with at least codewords for all sufficiently
large integers . This shows, in particular, that the upper bound (derived
from the bound on -frameproof codes) on the number of codewords in a
-separable code is realistic.
The results above are more surprising after examining the situation when
. Results due to Gao and Ge show that a -ary -separable
code of length can contain at most codewords, and that codes with at
least codewords exist. So optimal -separable
codes behave neither like -frameproof nor -frameproof codes.
Also, the Gao--Ge bound is strengthened to show that a -ary
-separable code of length can have at most
codewords.Comment: 16 pages. Typos corrected and minor changes since last version.
Accepted by IEEE Transactions on Information Theor
Polynomial-Time, Semantically-Secure Encryption Achieving the Secrecy Capacity
In the wiretap channel setting, one aims to get information-theoretic privacy
of communicated data based only on the assumption that the channel from sender
to receiver is noisier than the one from sender to adversary. The secrecy
capacity is the optimal (highest possible) rate of a secure scheme, and the
existence of schemes achieving it has been shown. For thirty years the ultimate
and unreached goal has been to achieve this optimal rate with a scheme that is
polynomial-time. (This means both encryption and decryption are proven
polynomial time algorithms.) This paper finally delivers such a scheme. In fact
it does more. Our scheme not only meets the classical notion of security from
the wiretap literature, called MIS-R (mutual information security for random
messages) but achieves the strictly stronger notion of semantic security, thus
delivering more in terms of security without loss of rate
A single-photon sampling architecture for solid-state imaging
Advances in solid-state technology have enabled the development of silicon
photomultiplier sensor arrays capable of sensing individual photons. Combined
with high-frequency time-to-digital converters (TDCs), this technology opens up
the prospect of sensors capable of recording with high accuracy both the time
and location of each detected photon. Such a capability could lead to
significant improvements in imaging accuracy, especially for applications
operating with low photon fluxes such as LiDAR and positron emission
tomography.
The demands placed on on-chip readout circuitry imposes stringent trade-offs
between fill factor and spatio-temporal resolution, causing many contemporary
designs to severely underutilize the technology's full potential. Concentrating
on the low photon flux setting, this paper leverages results from group testing
and proposes an architecture for a highly efficient readout of pixels using
only a small number of TDCs, thereby also reducing both cost and power
consumption. The design relies on a multiplexing technique based on binary
interconnection matrices. We provide optimized instances of these matrices for
various sensor parameters and give explicit upper and lower bounds on the
number of TDCs required to uniquely decode a given maximum number of
simultaneous photon arrivals.
To illustrate the strength of the proposed architecture, we note a typical
digitization result of a 120x120 photodiode sensor on a 30um x 30um pitch with
a 40ps time resolution and an estimated fill factor of approximately 70%, using
only 161 TDCs. The design guarantees registration and unique recovery of up to
4 simultaneous photon arrivals using a fast decoding algorithm. In a series of
realistic simulations of scintillation events in clinical positron emission
tomography the design was able to recover the spatio-temporal location of 98.6%
of all photons that caused pixel firings.Comment: 24 pages, 3 figures, 5 table
Constraining the Number of Positive Responses in Adaptive, Non-Adaptive, and Two-Stage Group Testing
Group testing is a well known search problem that consists in detecting the
defective members of a set of objects O by performing tests on properly chosen
subsets (pools) of the given set O. In classical group testing the goal is to
find all defectives by using as few tests as possible. We consider a variant of
classical group testing in which one is concerned not only with minimizing the
total number of tests but aims also at reducing the number of tests involving
defective elements. The rationale behind this search model is that in many
practical applications the devices used for the tests are subject to
deterioration due to exposure to or interaction with the defective elements. In
this paper we consider adaptive, non-adaptive and two-stage group testing. For
all three considered scenarios, we derive upper and lower bounds on the number
of "yes" responses that must be admitted by any strategy performing at most a
certain number t of tests. In particular, for the adaptive case we provide an
algorithm that uses a number of "yes" responses that exceeds the given lower
bound by a small constant. Interestingly, this bound can be asymptotically
attained also by our two-stage algorithm, which is a phenomenon analogous to
the one occurring in classical group testing. For the non-adaptive scenario we
give almost matching upper and lower bounds on the number of "yes" responses.
In particular, we give two constructions both achieving the same asymptotic
bound. An interesting feature of one of these constructions is that it is an
explicit construction. The bounds for the non-adaptive and the two-stage cases
follow from the bounds on the optimal sizes of new variants of d-cover free
families and (p,d)-cover free families introduced in this paper, which we
believe may be of interest also in other contexts
Blind Multilinear Identification
We discuss a technique that allows blind recovery of signals or blind
identification of mixtures in instances where such recovery or identification
were previously thought to be impossible: (i) closely located or highly
correlated sources in antenna array processing, (ii) highly correlated
spreading codes in CDMA radio communication, (iii) nearly dependent spectra in
fluorescent spectroscopy. This has important implications --- in the case of
antenna array processing, it allows for joint localization and extraction of
multiple sources from the measurement of a noisy mixture recorded on multiple
sensors in an entirely deterministic manner. In the case of CDMA, it allows the
possibility of having a number of users larger than the spreading gain. In the
case of fluorescent spectroscopy, it allows for detection of nearly identical
chemical constituents. The proposed technique involves the solution of a
bounded coherence low-rank multilinear approximation problem. We show that
bounded coherence allows us to establish existence and uniqueness of the
recovered solution. We will provide some statistical motivation for the
approximation problem and discuss greedy approximation bounds. To provide the
theoretical underpinnings for this technique, we develop a corresponding theory
of sparse separable decompositions of functions, including notions of rank and
nuclear norm that specialize to the usual ones for matrices and operators but
apply to also hypermatrices and tensors.Comment: 20 pages, to appear in IEEE Transactions on Information Theor
Lectures on Designing Screening Experiments
Designing Screening Experiments (DSE) is a class of information - theoretical
models for multiple - access channels (MAC). We discuss the combinatorial model
of DSE called a disjunct channel model. This model is the most important for
applications and closely connected with the superimposed code concept. We give
a detailed survey of lower and upper bounds on the rate of superimposed codes.
The best known constructions of superimposed codes are considered in paper. We
also discuss the development of these codes (non-adaptive pooling designs)
intended for the clone - library screening problem. We obtain lower and upper
bounds on the rate of binary codes for the combinatorial model of DSE called an
adder channel model. We also consider the concept of universal decoding for the
probabilistic DSE model called a symmetric model of DSE.Comment: 66 page
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