New constructions of superimposed codes

D’yachkov, Arkadii G.; Macula, Anthony J.; Rykov, Vladimir

doi:10.1109/18.817530

Cited by 56 publications

(28 citation statements)

References 10 publications

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“…A binary matrix X definesdisjunct code if and only if the Boolean sum of any -subset of columns of X does not cover any other column of X that is not in -subset [18,19].…”

Section: -Disjunct Code Given a Binarymentioning

confidence: 99%

A Reliable Broadcast Protocol in Vehicular Ad Hoc Networks

Fan

Wang

et al. 2015

International Journal of Distributed Sensor Networks

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Periodical broadcasts of individual vehicle's safety information such as velocity and acceleration are critical in vehicular ad hoc networks (VANETs). However, current contention-based media access control (MAC) protocols cannot guarantee high performance in high density VANETs. In this paper, we propose a MAC protocol based on s-disjunct code to achieve reliable and real-time broadcasts via assigning a channel to each vehicle as the vehicle enters the network. Our protocol is adaptive as vehicles are required to adjust their communication ranges according to the network density in order to avert the interference among them. We conduct an extensive simulation study, and our results indicate that the proposed scheme can successfully achieve the requirements of the dedicated short range communication (DSRC) standard, that is, to broadcast safety information 10 times per second. Even at a high vehicle density, our scheme still guarantees that the success rates of both transmission and reception are greater than 95%, and the collision rates of access collision and merging collision are lower than 10 collisions/period.

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“…A binary matrix X definesdisjunct code if and only if the Boolean sum of any -subset of columns of X does not cover any other column of X that is not in -subset [18,19].…”

Section: -Disjunct Code Given a Binarymentioning

confidence: 99%

A Reliable Broadcast Protocol in Vehicular Ad Hoc Networks

Fan

Wang

et al. 2015

International Journal of Distributed Sensor Networks

View full text Add to dashboard Cite

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“…Well-known constructions of superimposed codes are based on algebraic ReedSolomon codes [4,8]. In this paper, we present a new class of superimposed codes recursively constructed by combinatorial method.…”

Section: Introductionmentioning

confidence: 99%

“…Since then, these combinatorial structures have been studied extensively and appeared to have many applications in information theory, molecular biology [5] and cryptography including information retrieval, data communication, magnetic memories [8], group testing [1,2], key distribution [7,9,10], DNA library screening [3,4], tracing pirate media [12] and conflict resolution in multiple access channels [1]. In these applications, it is desirable to construct superimposed codes that have large number of codewords of relatively small length.…”

Section: Introductionmentioning

confidence: 99%

Some Constructions of Mutually Orthogonal Latin Squares and Superimposed Codes

Seberry

Tonien

2012

Discrete Math. Algorithm. Appl.

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Superimposed codes is a special combinatorial structure that has many applications in information theory, data communication and cryptography. On the other hand, mutually orthogonal latin squares is a beautiful combinatorial object that has deep connection with design theory. In this paper, we draw a connection between these two structures. We give explicit construction of mutually orthogonal latin squares and we show a method of generating new larger superimposed codes from an existing one by using mutually orthogonal latin squares. If n denotes the number of codewords in the existing code then the new code contains n2 codewords. Recursively, using this method, we can construct a very large superimposed code from a small simple code. Well-known constructions of superimposed codes are based on algebraic Reed-Solomon codes and our new construction gives a combinatorial alternative approach. Superimposed codes is a special combinatorial structure that has many applications in information theory, data communication and cryptography. On the other hand, mutually orthogonal latin squares is a beautiful combinatorial object that has deep connection with design theory. In this paper, we draw a connection between these two structures. We give explicit construction of mutually orthogonal latin squares and we show a method of generating new larger superimposed codes from an existing one by using mutually orthogonal latin squares. If n denotes the number of codewords in the existing code then the new code contains n 2 codewords. Recursively, using this method, we can construct a very large superimposed code from a small simple code. Well-known constructions of superimposed codes are based on algebraic Reed-Solomon codes and our new construction gives a combinatorial alternative approach.

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“…The same structure is also called cover free family [9,10,15] in combinatorics, and superimposed code [6,8,12] in information theory. It is called a d-disjunct matrix in group testing [4,11,13].…”

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confidence: 99%

On the upper bounds of the minimum number of rows of disjunct matrices

Cheng

Lin

2008

Optim Lett

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A 0-1 matrix is d-disjunct if no column is covered by the union of any d other columns. A 0-1 matrix is (d; z)-disjunct if for any column C and any d other columns, there exist at least z rows such that each of them has value 1 at column C and value 0 at all the other d columns. Let t (d, n) and t (d, n; z) denote the minimum number of rows required by a d-disjunct matrix and a (d; z)-disjunct matrix with n columns, respectively. We give a very short proof for the currently best upper bound on t (d, n). We also generalize our method to obtain a new upper bound on t (d, n; z).

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New constructions of superimposed codes

Cited by 56 publications

References 10 publications

A Reliable Broadcast Protocol in Vehicular Ad Hoc Networks

A Reliable Broadcast Protocol in Vehicular Ad Hoc Networks

Some Constructions of Mutually Orthogonal Latin Squares and Superimposed Codes

On the upper bounds of the minimum number of rows of disjunct matrices

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