41,244 research outputs found
A General Upper Bound on the Size of Constant-Weight Conflict-Avoiding Codes
Conflict-avoiding codes are used in the multiple-access collision channel
without feedback. The number of codewords in a conflict-avoiding code is the
number of potential users that can be supported in the system. In this paper, a
new upper bound on the size of conflict-avoiding codes is proved. This upper
bound is general in the sense that it is applicable to all code lengths and all
Hamming weights. Several existing constructions for conflict-avoiding codes,
which are known to be optimal for Hamming weights equal to four and five, are
shown to be optimal for all Hamming weights in general.Comment: 10 pages, 1 figur
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
Approximate generalized Steiner systems and near-optimal constant weight codes
Constant weight codes (CWCs) and constant composition codes (CCCs) are two
important classes of codes that have been studied extensively in both
combinatorics and coding theory for nearly sixty years. In this paper we show
that for {\it all} fixed odd distances, there exist near-optimal CWCs and CCCs
asymptotically achieving the classic Johnson-type upper bounds.
Let denote the maximum size of -ary CWCs of length with
constant weight and minimum distance . One of our main results shows
that for {\it all} fixed and odd , one has
,
where . This implies the existence of near-optimal
generalized Steiner systems originally introduced by Etzion, and can be viewed
as a counterpart of a celebrated result of R\"odl on the existence of
near-optimal Steiner systems. Note that prior to our work, very little is known
about for . A similar result is proved for the maximum
size of CCCs.
We provide different proofs for our two main results, based on two
strengthenings of the well-known Frankl-R\"odl-Pippenger theorem on the
existence of near-optimal matchings in hypergraphs: the first proof follows by
Kahn's linear programming variation of the above theorem, and the second
follows by the recent independent work of Delcour-Postle, and
Glock-Joos-Kim-K\"uhn-Lichev on the existence of near-optimal matchings
avoiding certain forbidden configurations.
We also present several intriguing open questions for future research.Comment: 15 pages, introduction revise
A new generation 99 line Matlab code for compliance Topology Optimization and its extension to 3D
Compact and efficient Matlab implementations of compliance Topology
Optimization (TO) for 2D and 3D continua are given, consisting of 99 and 125
lines respectively. On discretizations ranging from to
elements, the 2D version, named top99neo, shows speedups from
2.55 to 5.5 times compared to the well-known top88 code (Andreassen-etal 2011).
The 3D version, named top3D125, is the most compact and efficient Matlab
implementation for 3D TO to date, showing a speedup of 1.9 times compared to
the code of Amir-etal 2014, on a discretization with elements.
For both codes, improvements are due to much more efficient procedures for the
assembly and implementation of filters and shortcuts in the design update step.
The use of an acceleration strategy, yielding major cuts in the overall
computational time, is also discussed, stressing its easy integration within
the basic codes.Comment: 17 pages, 8 Figures, 4 Table
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