10,716 research outputs found
Symmetric Disjunctive List-Decoding Codes
A binary code is said to be a disjunctive list-decoding -code (LD
-code), , , if the code is identified by the incidence
matrix of a family of finite sets in which the union (or disjunctive sum) of
any sets can cover not more than other sets of the family. In this
paper, we consider a similar class of binary codes which are based on a {\em
symmetric disjunctive sum} (SDS) of binary symbols. By definition, the
symmetric disjunctive sum (SDS) takes values from the ternary alphabet , where the symbol~ denotes "erasure". Namely: SDS is equal to ()
if all its binary symbols are equal to (), otherwise SDS is equal
to~. List decoding codes for symmetric disjunctive sum are said to be {\em
symmetric disjunctive list-decoding -codes} (SLD -codes). In the
given paper, we remind some applications of SLD -codes which motivate the
concept of symmetric disjunctive sum. We refine the known relations between
parameters of LD -codes and SLD -codes. For the ensemble of binary
constant-weight codes we develop a random coding method to obtain lower bounds
on the rate of these codes. Our lower bounds improve the known random coding
bounds obtained up to now using the ensemble with independent symbols of
codewords.Comment: 18 pages, 1 figure, 1 table, conference pape
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
2-cancellative hypergraphs and codes
A family of sets F (and the corresponding family of 0-1 vectors) is called
t-cancellative if for all distict t+2 members A_1,... A_t and B,C from F the
union of A_1,..., A_t and B differs from the union of A_1, ..., A_t and C. Let
c(n,t) be the size of the largest t-cancellative family on n elements, and let
c_k(n,t) denote the largest k-uniform family. We significantly improve the
previous upper bounds, e.g., we show c(n,2) n_0). Using an
algebraic construction we show that the order of magnitude of c_{2k}(n,2) is
n^k for each k (when n goes to infinity).Comment: 20 page
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
Construction of Almost Disjunct Matrices for Group Testing
In a \emph{group testing} scheme, a set of tests is designed to identify a
small number of defective items among a large set (of size ) of items.
In the non-adaptive scenario the set of tests has to be designed in one-shot.
In this setting, designing a testing scheme is equivalent to the construction
of a \emph{disjunct matrix}, an matrix where the union of supports
of any columns does not contain the support of any other column. In
principle, one wants to have such a matrix with minimum possible number of
rows (tests). One of the main ways of constructing disjunct matrices relies on
\emph{constant weight error-correcting codes} and their \emph{minimum
distance}. In this paper, we consider a relaxed definition of a disjunct matrix
known as \emph{almost disjunct matrix}. This concept is also studied under the
name of \emph{weakly separated design} in the literature. The relaxed
definition allows one to come up with group testing schemes where a
close-to-one fraction of all possible sets of defective items are identifiable.
Our main contribution is twofold. First, we go beyond the minimum distance
analysis and connect the \emph{average distance} of a constant weight code to
the parameters of an almost disjunct matrix constructed from it. Our second
contribution is to explicitly construct almost disjunct matrices based on our
average distance analysis, that have much smaller number of rows than any
previous explicit construction of disjunct matrices. The parameters of our
construction can be varied to cover a large range of relations for and .Comment: 15 Page
Cross-Sender Bit-Mixing Coding
Scheduling to avoid packet collisions is a long-standing challenge in
networking, and has become even trickier in wireless networks with multiple
senders and multiple receivers. In fact, researchers have proved that even {\em
perfect} scheduling can only achieve . Here
is the number of nodes in the network, and is the {\em medium
utilization rate}. Ideally, one would hope to achieve ,
while avoiding all the complexities in scheduling. To this end, this paper
proposes {\em cross-sender bit-mixing coding} ({\em BMC}), which does not rely
on scheduling. Instead, users transmit simultaneously on suitably-chosen slots,
and the amount of overlap in different user's slots is controlled via coding.
We prove that in all possible network topologies, using BMC enables us to
achieve . We also prove that the space and time
complexities of BMC encoding/decoding are all low-order polynomials.Comment: Published in the International Conference on Information Processing
in Sensor Networks (IPSN), 201
Asymptotic Error Free Partitioning over Noisy Boolean Multiaccess Channels
In this paper, we consider the problem of partitioning active users in a
manner that facilitates multi-access without collision. The setting is of a
noisy, synchronous, Boolean, multi-access channel where active users (out
of a total of users) seek to access. A solution to the partition problem
places each of the users in one of groups (or blocks) such that no two
active nodes are in the same block. We consider a simple, but non-trivial and
illustrative case of active users and study the number of steps used
to solve the partition problem. By random coding and a suboptimal decoding
scheme, we show that for any , where and
are positive constants (independent of ), and can be
arbitrary small, the partition problem can be solved with error probability
, for large . Under the same scheme, we also bound from
the other direction, establishing that, for any ,
the error probability for large ; again and
are constants and can be arbitrarily small. These bounds on the number
of steps are lower than the tight achievable lower-bound in terms of for group testing (in which all active users are identified,
rather than just partitioned). Thus, partitioning may prove to be a more
efficient approach for multi-access than group testing.Comment: This paper was submitted in June 2014 to IEEE Transactions on
Information Theory, and is under review no
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