The Experts below are selected from a list of 30 Experts worldwide ranked by ideXlab platform
Arya Mazumdar - One of the best experts on this subject based on the ideXlab platform.
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nonadaptive group testing with random set of defectives
IEEE Transactions on Information Theory, 2016Co-Authors: Arya MazumdarAbstract:In a group testing scheme, a series of tests are designed to identify a small number $t$ of defective items that are present among a large number $N$ of items. Each test takes a group of items as input and produces a binary output indicating whether any defective item is present in the group. In a non-adaptive scheme, the tests have to be designed in one-shot. In this setting, designing a testing scheme is equivalent to the construction of a disjunct matrix , an $M \times N$ binary matrix where the union of supports of any $t$ columns does not contain the support of any other column. In principle, one wants to have such a matrix with a minimum possible number $M$ of rows. In this paper, we consider the scenario where defective items are random and follow simple probability distributions. In particular, we consider the cases where: 1) each item can be defective independently with probability $\frac {t}{N}$ and 2) each $t$ -set of items can be defective with uniform probability. In both the cases, our aim is to design a testing matrix that successfully identifies the set of defectives with high probability. Both of these models have been studied in the literature before, and it is known that $\Theta (t \log N)$ tests are necessary as well as sufficient (via random coding) in both the cases. Our main focus is explicit deterministic construction of the test matrices amenable to above scenarios. One of the most popular ways of constructing test matrices relies on Constant-Weight error-correcting Codes and their minimum distance . In particular, it is known that Codes result in test matrices with $O(t^{2} \log N)$ rows that identify any $t$ defectives. We go beyond the minimum distance analysis and connect the average distance of a constant weight Code to the parameters of the resulting test matrix. Indeed, we show how distance, a pairwise property of the columns of the matrix, translates to a $(t+1)$ -wise property of the columns. With our relaxed requirements, we show that using explicit Constant-Weight Codes (e.g., based on algebraic geometry Codes) we may achieve a number of tests equal to $O(t ({\log ^{2} N}/{ \log t}))$ for both the first and second cases. While only away by a factor of $({\log N}/{\log t})$ from the optimal number of tests, this is the best set of parameters that one can obtain from a deterministic construction, and our main contribution lies in relating the group testing properties to the average and minimum distances of Constant-Weight Codes.
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nonadaptive group testing with random set of defectives
arXiv: Information Theory, 2015Co-Authors: Arya MazumdarAbstract:In a group testing scheme, a set of tests is designed to identify a small number $t$ of defective items that are present among a large number $N$ of items. Each test takes as input a group of items and produces a binary output indicating whether any defective item is present in the group. In a non-adaptive scheme designing a testing scheme is equivalent to the construction of a disjunct matrix, an $M \times N$ binary matrix where the union of supports of any $t$ columns does not contain the support of any other column. In this paper we consider the scenario where defective items are random and follow simple probability distributions. In particular we consider the cases where 1) each item can be defective independently with probability $\frac{t}{N}$ and 2) each $t$-set of items can be defective with uniform probability. In both cases our aim is to design a testing matrix that successfully identifies the set of defectives with high probability. Both of these models have been studied in the literature before and it is known that $O(t\log N)$ tests are necessary as well as sufficient (via random coding) in both cases. Our main focus is explicit deterministic construction of the test matrices amenable to above scenarios. One of the most popular ways of constructing test matrices relies on \emph{Constant-Weight error-correcting Codes} and their minimum distance. We go beyond the minimum distance analysis and connect the average distance of a constant weight Code to the parameters of the resulting test matrix. With our relaxed requirements, we show that using explicit Constant-Weight Codes (e.g., based on algebraic geometry Codes) we may achieve a number of tests equal to $O(t \frac{\log^2 N}{ \log t})$ for both the first and the second cases.
Silberstein Natalia - One of the best experts on this subject based on the ideXlab platform.
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Error-Correcting Codes in Projective Spaces via Rank-Metric Codes and Ferrers Diagrams
2009Co-Authors: Etzion Tuvi, Silberstein NataliaAbstract:Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key role for solving coding problems in the projective space. In this paper we propose a method to design error-correcting Codes in the projective space. We use a multilevel approach to design our Codes. First, we select a constant weight Code. Each Codeword defines a skeleton of a basis for a subspace in reduced row echelon form. This skeleton contains a Ferrers diagram on which we design a rank-metric Code. Each such rank-metric Code is lifted to a constant dimension Code. The union of these Codes is our final constant dimension Code. In particular the Codes constructed recently by Koetter and Kschischang are a subset of our Codes. The rank-metric Codes used for this construction form a new class of rank-metric Codes. We present a decoding algorithm to the constructed Codes in the projective space. The efficiency of the decoding depends on the efficiency of the decoding for the constant weight Codes and the rank-metric Codes. Finally, we use puncturing on our final constant dimension Codes to obtain large Codes in the projective space which are not constant dimension.Comment: Revised for IEEE Transactions on Information Theor
Natalia Silberstein - One of the best experts on this subject based on the ideXlab platform.
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Error-Correcting Codes in Projective Spaces via Rank-Metric Codes and Ferrers Diagrams
2008Co-Authors: Tuvi Etzion, Natalia SilbersteinAbstract:Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key role for solving coding problems in the projective space. In this paper we propose a method to design error-correcting Codes in the projective space. We use a multilevel approach to design our Codes. First, we select a constant weight Code. Each Codeword defines a skeleton of a basis for a subspace in reduced row echelon form. This skeleton contains a Ferrers diagram on which we design a rank-metric Code. Each such rankmetric Code is lifted to a constant dimension Code. The union of these Codes is our final constant dimension Code. In particular the Codes constructed recently by Koetter and Kschischang are a subset of our Codes. All the proposed Codes can be efficiently enCoded and deCoded. Finally, we use puncturing on our final constant dimension Codes to obtain large Codes in the projective space which are not constant dimension
Craig S Levin - One of the best experts on this subject based on the ideXlab platform.
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compressed sensing for the multiplexing of large area silicon photomultiplier pet detectors acquisition and calibration
The Journal of Nuclear Medicine, 2012Co-Authors: Peter D Olcott, Ealgoo Kim, Garry Chinn, Craig S LevinAbstract:2388 Objectives Potential clinical silicon photomultiplier based PET systems will consist of tens of thousands of individual sensors. Compressed sensing electronics can be used to multiplex a large number of individual readout sensors to significantly reduce the number of readout channels. Methods Using brute force optimization method, a two level sensing matrix based on a 2-weight constant weight Code C1[128:32] followed by a 3 weight constant weight Code C2[32:16] was designed. These Codes consists of discrete resistor elements either connected or not connected to intermediate or output signals. A PET block detector PCB and electronics were fabricated that can multiplex 128 3.2 mm x 3.2 mm solid-state photomultiplier pixels arranged into a 16 x 8 array. Signals from the detector were acquired by a custom 16 channel simultaneously sampling 12-bit 65 Msps ADC acquisition system. Each of the signals was summed to form a trigger, and the peak value for each event on each channel was captured simultaneously. For calibration, we placed a single 4 x 4 array of 3.2 mm x 3.2 mm x 20 mm LYSO crystals onto one of the populated detectors and collected a uniform flood calibration dataset using a 125μCi Ge source. We used a KNN Density clustering method to calculate the centroids of the calibration flood irradiation that were mapped through the sensing matrix and captured by the 16 ADC channels. Results All 16 crystals were clearly segmented from the 16 dimensional output data using the new KNN-density clustering method. After correcting for the gain non-uniformities of the SiPM sensor, we measured a preliminary 23.7 +/- 1.2% FWHM energy resolution at 511 keV. Conclusions We have successfully fabricated, performed data acquisition, developed a new calibration method, and done preliminary calibration for a compressed sensing PET detector. Research Support This work was funded in part by a Stanford SIGF Bio-X Graduate Fellowship
Etzion Tuvi - One of the best experts on this subject based on the ideXlab platform.
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Error-Correcting Codes in Projective Spaces via Rank-Metric Codes and Ferrers Diagrams
2009Co-Authors: Etzion Tuvi, Silberstein NataliaAbstract:Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key role for solving coding problems in the projective space. In this paper we propose a method to design error-correcting Codes in the projective space. We use a multilevel approach to design our Codes. First, we select a constant weight Code. Each Codeword defines a skeleton of a basis for a subspace in reduced row echelon form. This skeleton contains a Ferrers diagram on which we design a rank-metric Code. Each such rank-metric Code is lifted to a constant dimension Code. The union of these Codes is our final constant dimension Code. In particular the Codes constructed recently by Koetter and Kschischang are a subset of our Codes. The rank-metric Codes used for this construction form a new class of rank-metric Codes. We present a decoding algorithm to the constructed Codes in the projective space. The efficiency of the decoding depends on the efficiency of the decoding for the constant weight Codes and the rank-metric Codes. Finally, we use puncturing on our final constant dimension Codes to obtain large Codes in the projective space which are not constant dimension.Comment: Revised for IEEE Transactions on Information Theor