A construction of superimposed codes for the Euclidean channel

Anderson, P.-O.

doi:10.1109/isit.1994.394783

Cited by 6 publications

(12 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Probabilistic constructions as well as explicit constructions are provided for these two families of codes when the number of defectives is much smaller than the total number of subjects. In addition, the important special case of SQGT with equidistant thresholds is discussed in detail, and test constructions are provided for this model as well 4 .…”

Section: A Challenges In Genotyping and Semi-quantitative Group Tesmentioning

confidence: 99%

“…As such, GT has found many applications in communication theory [2]- [5], signal processing [6]- [8], computer science [9]- [11], and mathematics [12]. Some examples of these applications include error-correcting coding [4], [13], [14], identifying users accessing a multiple access channel (MAC) [15], [16], reconstructing sparse signals from low-dimensional projections [6], [7], and many others.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Semiquantitative Group Testing

Emad

Milenković

2014

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

We propose a novel group testing method, termed semi-quantitative group testing, motivated by a class of problems arising in genome screening experiments. Semi-quantitative group testing (SQGT) is a (possibly) non-binary pooling scheme that may be viewed as a concatenation of an adder channel and an integer-valued quantizer. In its full generality, SQGT may be viewed as a unifying framework for group testing, in the sense that most group testing models are special instances of SQGT. For the new testing scheme, we define the notion of SQ-disjunct and SQ-separable codes, representing generalizations of classical disjunct and separable codes. We describe several combinatorial and probabilistic constructions for such codes. While for most of these constructions we assume that the number of defectives is much smaller than total number of test subjects, we also consider the case in which there is no restriction on the number of defectives and they may be as large as the total number of subjects. For the codes constructed in this paper, we describe a number of efficient decoding algorithms. In addition, we describe a belief propagation decoder for sparse SQGT codes for which no other efficient decoder is currently known. Finally, we define the notion of capacity of SQGT and evaluate it for some special choices of parameters using information theoretic methods. The authors are with the

show abstract

Section: A Challenges In Genotyping and Semi-quantitative Group Tesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Semiquantitative Group Testing

Emad

Milenković

2014

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…The goal is to find the number of tests required to satisfy (5). We define the error event E as the event that there exists a set of subjects D = D such that P (y|C, D ) ≥ P (y|C, D).…”

Section: Summary Of the Results And Discussionmentioning

confidence: 99%

“…It can be easily verified that P (E) ≤ P (E ). As a result, a number of tests that guarantees lim n→∞ P (E ) = 0 also guarantees (5). Given D = d, 1 ≤ d ≤ n, let E i , 1 ≤ i ≤ d, denote the event that there exists a set of subjects with cardinality d, that differ from D in exactly i items and is at least as likely as D to the decoder.…”

Section: Summary Of the Results And Discussionmentioning

confidence: 99%

“…In what follows, we propose two nonadaptive test matrix constructions and decoding algorithms to guarantee that the aforementioned condition is met 1 . In order to evaluate how effectively each method uses its tests, we first find a lower bound on the minimum number of tests required by a nonadaptive algorithm to ensure (5), and then use this bound as a benchmark. The constructive methods provide upper bounds on the minimum number of tests.…”

Section: Poisson Probabilistic Group Testingmentioning

confidence: 99%

See 1 more Smart Citation

Poisson Group Testing: A Probabilistic Model for Boolean Compressed Sensing

Emad

Milenković

2015

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including dynamic testing with diminishing relative rates of defectives. We consider both nonadaptive and semi-adaptive identification methods. For nonadaptive methods, we derive a lower bound on the number of tests required to identify the defectives with a probability of error that asymptotically converges to zero; in addition, we propose test matrix constructions for which the number of tests closely matches the lower bound. For semiadaptive methods, we describe a lower bound on the expected number of tests required to identify the defectives with zero error probability. In addition, we propose a stage-wise reconstruction algorithm for which the expected number of tests is only a constant factor away from the lower bound. The methods rely only on an estimate of the average number of defectives, rather than on the individual probabilities of subjects being defective.

show abstract

An improved upper bound of the rate of Euclidean superimposed codes

Füredi

Ruszinkó

1999

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

A family of n-dimensional unit norm vectors is a Euclidean superimposed code, if the sums of any two distinct at most m-tuples of vectors are separated by a certain minimum Euclidean distance d. Ericson and Györfi [8] proved that the rate of such a code is between (log m)/4m and (log m)/m for m large enough. In this paper-improving the above longstanding best upper bound for the rate-it is shown that the rate is always at most (log m)/2m, i.e., the size of a possible superimposed code is at most the root of the size given in [8]. We also generalize these codes to other normed vector spaces. 1 Superimposed codes Binary superimposed codes were introduced by Kautz and Singleton [18]. They studied binary codewords with the property that the disjunctions (bitwise OR) of any pair of distinct at most m tuples of codewords have to be different. Later this question has been investigated in several papers on multiple access communication (see, e.g.

show abstract

A construction of superimposed codes for the Euclidean channel

Cited by 6 publications

References 2 publications

Semiquantitative Group Testing

Semiquantitative Group Testing

Poisson Group Testing: A Probabilistic Model for Boolean Compressed Sensing

An improved upper bound of the rate of Euclidean superimposed codes

Contact Info

Product

Resources

About