Vardy, Alexander
Overview
Works:  16 works in 26 publications in 2 languages and 184 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Correspondent 
Classifications:  TK5101, 621.382 
Publication Timeline
.
Most widely held works by
Alexander Vardy
Codes, curves, and signals : common threads in communications by
Alexander Vardy(
Book
)
9 editions published in 1998 in English and held by 119 WorldCat member libraries worldwide
Codes, Curves, and Signals is a tribute to the broad and profound influence of Richard E. Blahut on the fields of algebraic coding, information theory, and digital signal processing. All the contributors have individually and collectively dedicated their work to R.E. Blahut. Codes, Curves, and Signals is an excellent reference for researchers and professionals interested in information theory and communications
9 editions published in 1998 in English and held by 119 WorldCat member libraries worldwide
Codes, Curves, and Signals is a tribute to the broad and profound influence of Richard E. Blahut on the fields of algebraic coding, information theory, and digital signal processing. All the contributors have individually and collectively dedicated their work to R.E. Blahut. Codes, Curves, and Signals is an excellent reference for researchers and professionals interested in information theory and communications
Ordered binary decision diagrams and minimal trellises by
John Lafferty(
Book
)
2 editions published in 1998 in English and held by 3 WorldCat member libraries worldwide
Abstract: "Ordered binary decision diagrams (OBDDs) are graphbased data structures for representing Boolean functions. They have found widespread use in computeraided design and in formal verification of digital circuits. Minimal trellises are graphical representations of errorcorrecting codes that play a prominent role in coding theory. This paper establishes a close connection between these two graphical models, as follows. Let C be a binary code of length n, and let f[subscript c](x₁, ..., x[subscript n]) be the Boolean function that takes the value 0 at x₁, ..., x[subscript n] if and only if (x₁, ..., x[subscript n]) [element of] C. Given this natural onetoone correspondence between Boolean functions and binary codes, we prove that the minimal proper trellis for a code C with minimum distance d> 1 is isomorphic to the singleterminal OBDD for its Boolean indicator function f[subscript c](x₁, ..., x[subscript n]). Prior to this result, the extensive research during the past decade on binary decision diagrams  in computer engineering  and on minimal trellises  in coding theory  has been carried out independently. As outlined in this work, the realization that binary decision diagrams and minimal trellises are essentially the same data structure opens up a range of promising possibilities for transfer of ideas between these disciplines."
2 editions published in 1998 in English and held by 3 WorldCat member libraries worldwide
Abstract: "Ordered binary decision diagrams (OBDDs) are graphbased data structures for representing Boolean functions. They have found widespread use in computeraided design and in formal verification of digital circuits. Minimal trellises are graphical representations of errorcorrecting codes that play a prominent role in coding theory. This paper establishes a close connection between these two graphical models, as follows. Let C be a binary code of length n, and let f[subscript c](x₁, ..., x[subscript n]) be the Boolean function that takes the value 0 at x₁, ..., x[subscript n] if and only if (x₁, ..., x[subscript n]) [element of] C. Given this natural onetoone correspondence between Boolean functions and binary codes, we prove that the minimal proper trellis for a code C with minimum distance d> 1 is isomorphic to the singleterminal OBDD for its Boolean indicator function f[subscript c](x₁, ..., x[subscript n]). Prior to this result, the extensive research during the past decade on binary decision diagrams  in computer engineering  and on minimal trellises  in coding theory  has been carried out independently. As outlined in this work, the realization that binary decision diagrams and minimal trellises are essentially the same data structure opens up a range of promising possibilities for transfer of ideas between these disciplines."
Man lacht nicht nur in Eriwan : Anekdoten und WItze aus dem real existierenden Sozialismus(
Book
)
1 edition published in 1984 in German and held by 2 WorldCat member libraries worldwide
1 edition published in 1984 in German and held by 2 WorldCat member libraries worldwide
Highorder spectralnull codes : constructions and bounds by
Ron M Roth(
Book
)
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
Abstract: "Let S(n, k) denote the set of all sequences of length n over the alphabet [+1,1], having a kth order spectralnull at zero frequency. A subset of S(n, k) is a spectralnull code of length n and order k. Upper and lower bounds on the cardinality of S(n, k) are derived. In particular we prove that O(2[superscript k] log₂ n) [> or =] n  log₂ [absolute value of S(n, k)] [> or =] O(k log₂ n) for infinitely many values of n. On the other hand we show that if n is not divisible by 2[superscript m] for m = [log₂ k] + 1, then S(n, k) is empty. Furthermore, bounds on the minimum Hamming distance d of S(n, k) are provided, showing that 2k [<or =] d [<or =] k(k1)+2 for infinitely many n. We also investigate the minimum number of sign changes in a sequence [subset x] [element of] S(n, k) and provide an equivalent definition of S(n, k) in terms of the positions of these sign changes. An efficient algorithm for encoding arbitrary information sequences into a secondorder spectralnull code of redundancy 3 log₂ n + O(log log n) is presented. Furthermore, we prove that the first nonzero moment of any sequence in S(n, k) is divisible by k! and then show how to construct a sequence with a spectral null of order k whose first nonzero moment is any even multiple of k!. This leads to an encoding scheme for spectralnull codes of length n and any fixed order k, with rate approaching unity as n [approaches] [infinity]."
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
Abstract: "Let S(n, k) denote the set of all sequences of length n over the alphabet [+1,1], having a kth order spectralnull at zero frequency. A subset of S(n, k) is a spectralnull code of length n and order k. Upper and lower bounds on the cardinality of S(n, k) are derived. In particular we prove that O(2[superscript k] log₂ n) [> or =] n  log₂ [absolute value of S(n, k)] [> or =] O(k log₂ n) for infinitely many values of n. On the other hand we show that if n is not divisible by 2[superscript m] for m = [log₂ k] + 1, then S(n, k) is empty. Furthermore, bounds on the minimum Hamming distance d of S(n, k) are provided, showing that 2k [<or =] d [<or =] k(k1)+2 for infinitely many n. We also investigate the minimum number of sign changes in a sequence [subset x] [element of] S(n, k) and provide an equivalent definition of S(n, k) in terms of the positions of these sign changes. An efficient algorithm for encoding arbitrary information sequences into a secondorder spectralnull code of redundancy 3 log₂ n + O(log log n) is presented. Furthermore, we prove that the first nonzero moment of any sequence in S(n, k) is divisible by k! and then show how to construct a sequence with a spectral null of order k whose first nonzero moment is any even multiple of k!. This leads to an encoding scheme for spectralnull codes of length n and any fixed order k, with rate approaching unity as n [approaches] [infinity]."
MDS array codes with independent parity symbols by
Mario Blaum(
Book
)
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
Abstract: "A new family of MDS array codes is presented. The code arrays contain p information columns and r independent parity columns, each column consisting of p1 bits, where p is a prime. We extend a previously known construction for the case r = 2 to three and more parity columns. It is shown that when r = 3 such extension is possible for any prime p. For larger values of r we give necessary and sufficient conditions for our codes to be MDS, and then prove that if p belongs to a certain class of primes these conditions are satisfied up to r = 8. One of the advantages of the new codes is that encoding and decoding may be accomplished using simple cyclic shifts and XOR operations on the columns of the code array. We develop efficient decoding procedures for the case of two and three column errors. This again extends the previously known results for the case of a single column error. Another primary advantage of our codes is related to the problem of efficient information updates. We present upper and lower bounds on the average number of parity bits which have to be updated in an MDS code over GF(2[superscript m]), following an update in a single information bit. This average number is of importance in many storage applications which require frequent updates of information. We show that the upper bound obtained from our codes is close to the lower bound and, most importantly, does not depend on the size of the code symbols. All these properties of the new MDS array codes make them very well suited for applications where the size of the code symbols is required to be large."
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
Abstract: "A new family of MDS array codes is presented. The code arrays contain p information columns and r independent parity columns, each column consisting of p1 bits, where p is a prime. We extend a previously known construction for the case r = 2 to three and more parity columns. It is shown that when r = 3 such extension is possible for any prime p. For larger values of r we give necessary and sufficient conditions for our codes to be MDS, and then prove that if p belongs to a certain class of primes these conditions are satisfied up to r = 8. One of the advantages of the new codes is that encoding and decoding may be accomplished using simple cyclic shifts and XOR operations on the columns of the code array. We develop efficient decoding procedures for the case of two and three column errors. This again extends the previously known results for the case of a single column error. Another primary advantage of our codes is related to the problem of efficient information updates. We present upper and lower bounds on the average number of parity bits which have to be updated in an MDS code over GF(2[superscript m]), following an update in a single information bit. This average number is of importance in many storage applications which require frequent updates of information. We show that the upper bound obtained from our codes is close to the lower bound and, most importantly, does not depend on the size of the code symbols. All these properties of the new MDS array codes make them very well suited for applications where the size of the code symbols is required to be large."
Proceedings : Thirtyfifth Annual Allerton Conference on Communication, Control, and Computing : conference held September
29, September 30, and October 1, 1997 Allerton House, Monticello, Illinois by Control, and Computing Allerton Conference on Communication(
Book
)
2 editions published in 1997 in English and held by 1 WorldCat member library worldwide
2 editions published in 1997 in English and held by 1 WorldCat member library worldwide
The NordstromRobinson code: representation over GF(4) and efficient decoding by
Thomas J. Watson IBM Research Center(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Communication, control and computing : proceedings by control and computing Annual Allerton conference on communication(
Book
)
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
The uniqueness of the Best code by
Thomas J. Watson IBM Research Center(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Thirtyfifth annual Allerton conference on communication, control and computing : proceedings(
Book
)
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
Upper bounds for constantweight codes by
Erik Agrell(
Book
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
Binary codes with large symbols by
Thomas J. Watson IBM Research Center(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Conservative arrays: multidimensional modulation codes for holographic recording by
Thomas J. Watson IBM Research Center(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Das Eisloch (Prorub,dt.) Dt. [aus d. Russ.] v. Josef Hahn by
Alexander Vardy(
Book
)
1 edition published in 1966 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1966 in Undetermined and held by 1 WorldCat member library worldwide
Brieven van Alexander Vardy aan Karel van het Reve (19211999) by
Alexander Vardy(
)
1 edition published in 1969 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1969 in Undetermined and held by 1 WorldCat member library worldwide
Ordered Binary Decision Diagrams and Minimal Trellises(
)
1 edition published in 1998 in English and held by 0 WorldCat member libraries worldwide
Ordered binary decision diagrams (OBDDs) are graph based data structures for representing Boolean functions. They have found widespread use in computer aided design and in formal verification of digital circuits. Minimal trellises are graphical representations of error correcting codes that play a prominent role in coding theory. This paper establishes a close connection between these two graphical models, as follows. Let C be a binary code of length n, and let fc(x1 ..., xn) be the Boolean function that takes the value 0 at x1 ..., xn if and only if (x1 ..., xn)epsilonC. Given this natural one to one correspondence between Boolean functions and binary codes, we prove that the minimal proper trellis for a code C with minimum distance d> 1 is isomorphic to the single terminal OBDD for its Boolean indicator function fC(x1 ..., xn). Prior to this result, the extensive research during the past decade on binary decision diagrams in computer engineering and on minimal trellises in coding theory has been carried out independently. As outlined in this work, the realization that binary decision diagrams and minimal trellises are essentially the same data structure opens up a range of promising possibilities for transfer of ideas between these disciplines
1 edition published in 1998 in English and held by 0 WorldCat member libraries worldwide
Ordered binary decision diagrams (OBDDs) are graph based data structures for representing Boolean functions. They have found widespread use in computer aided design and in formal verification of digital circuits. Minimal trellises are graphical representations of error correcting codes that play a prominent role in coding theory. This paper establishes a close connection between these two graphical models, as follows. Let C be a binary code of length n, and let fc(x1 ..., xn) be the Boolean function that takes the value 0 at x1 ..., xn if and only if (x1 ..., xn)epsilonC. Given this natural one to one correspondence between Boolean functions and binary codes, we prove that the minimal proper trellis for a code C with minimum distance d> 1 is isomorphic to the single terminal OBDD for its Boolean indicator function fC(x1 ..., xn). Prior to this result, the extensive research during the past decade on binary decision diagrams in computer engineering and on minimal trellises in coding theory has been carried out independently. As outlined in this work, the realization that binary decision diagrams and minimal trellises are essentially the same data structure opens up a range of promising possibilities for transfer of ideas between these disciplines
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Related Identities
 Lafferty, John Author
 Thomas J. Watson IBM Research Center Research Division
 Blaum, Mario 1951 Author
 Basar, Tamer Editor
 Bruck, Jehoshua
 Siegel, Paul H.
 Roth, Ron M. Author
 University of Illinois at UrbanaChampaign Department of Electrical and Computer Engineering
 University of Illinois at UrbanaChampaign Coordinated Science Laboratory
 Zeger, Kenneth