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Dwijendra K. Ray-Chaudhuri

Bio: Dwijendra K. Ray-Chaudhuri is an academic researcher from IBM. The author has contributed to research in topics: Group code & Redundancy (engineering). The author has an hindex of 6, co-authored 6 publications receiving 1622 citations. Previous affiliations of Dwijendra K. Ray-Chaudhuri include University of North Carolina at Chapel Hill & Case Western Reserve University.

Papers
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Journal ArticleDOI
TL;DR: A general method of constructing error correcting binary group codes is obtained and an example is worked out to illustrate the method of construction.
Abstract: A general method of constructing error correcting binary group codes is obtained. A binary group code with n places, k of which are information places is called an (n,k) code. An explicit method of constructing t-error correcting (n,k) codes is given for n = 2m−1 and k = 2m−1−R(m,t) ≧ 2m−1−mt where R(m,t) is a function of m and t which cannot exceed mt. An example is worked out to illustrate the method of construction.

1,246 citations

Journal ArticleDOI
TL;DR: In this paper, a generalization of Fisher's Inequality for 2-designs and Petrenjuk's inequality for 4-design is presented, with the property that there are exactly t possible values for the size of the intersection of two distinct blocks, these values being computed from the parameters.
Abstract: We present the generalization (conjectured by A. Ja. Petrenjuk) of Fisher's Inequality b>v for 2-designs and Petrenjuk's Inequality ^^(2) f°r 4-designs. The ί-designs satisfying the inequality with equality may be considered as generalizatio ns of the symmetric 2-designs (b=v) and have the property that there are exactly — t possible values for the size of the intersection of two distinct blocks, these values being computable from the parameters. * This research was supported in part by ONR NOOO14-67-A-0232-0016 (OSURF

279 citations

Journal ArticleDOI
TL;DR: The present paper generalizes the methods of the earlier paper and gives a method of constructing a t-error correcting code with n places for any arbitrary n and k = n − R(m,t) ≧ [(2m − 1)/c] − mt information places where m is the least integer such that cn = 2m −1 for some integer c.
Abstract: The present paper is a sequel to the paper “On a class of error-correcting binary group codes”, by R. C. Base and D. K. Ray-Chaudhuri, appearing in Information and Control in which an explicit method of constructing a t-error correcting binary group code with n = 2m − 1 places and k = 2m − 1 − R(m,t) ≧ 2m − 1 − mt information places is given. The present paper generalizes the methods of the earlier paper and gives a method of constructing a t-error correcting code with n places for any arbitrary n and k = n − R(m,t) ≧ [(2m − 1)/c] − mt information places where m is the least integer such that cn = 2m − 1 for some integer c. A second method of constructing t-error correcting codes for n places when n is not of the form 2m − 1 is also given.

133 citations

Journal ArticleDOI
TL;DR: Some new schemes, possessing certain desirable properties, for organizing records with binary-valued attributes have been defined and it has been shown that it is possible to construct these filing schemes using finite geometires.
Abstract: Some new schemes, possessing certain desirable properties, for organizing records with binary-valued attributes have been defined. It has been shown that it is possible to construct these filing schemes using finite geometires. The search time for a query involving any k attributes for these filing schemes based on finite geometries is very small in comparison wih existing filing schemes. Moreover, the search time does not depend on the number of records. The problem of updating is also quite simple.

60 citations

Patent
10 Apr 1967
TL;DR: In this paper, the authors present a data processing method in which a plurality of records, each having a number of different attributes, are stored in the memory file of the machine and the file is then interrogated to retrieve those records which include a particular combination of attributes.
Abstract: The method is embodied in a data processing apparatus in which a plurality of records, each having a number of different attributes, are stored in the memory file of the machine and the file is then interrogated to retrieve those records which include a particular combination of attributes. The records are first prepared in machine readable form and applied as an input to the machine. The machine circuitry is controlled to store each input record in the memory file of the machine. The attributes for each record are analyzed in predetermined combinations of two or more attributes, and the address for each stored record is stored in one or more buckets in the memory file according to the combination(s) of attributes in each record. After the records are stored, the file is interrogated by applying input queries which specify certain combinations of attributes. From each input query, the machine circuitry is controlled to locate the bucket in which the addresses of all records which satisfy the query are stored. These addresses are then read out and used to retrieve the records themselves from the record file. In order to minimize the redundancy of storage of the addresses of the records, the addresses are grouped in buckets in the memory file in predetermined unique combinations of k+1 (e.g. 4) attributes, where k (e.g. 3) is the number of attributes in the queries for which the system is principally designed. In each such bucket the record addresses are arranged in k+2 (e.g. 5) subbuckets. The addresses for all records including all of the k+1 (e.g. 4) attributes are stored in one subbucket and the remaining addresses in that bucket are stored in the remaining k+1 (e.g. 4) subbuckets according to which of the combinations of k (e.g. 3) only of the k+1 (e.g. 4) attributes are present in the record identified by this particular address.

40 citations


Cited by
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Book
01 Jan 1963
TL;DR: A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
Abstract: A low-density parity-check code is a code specified by a parity-check matrix with the following properties: each column contains a small fixed number j \geq 3 of l's and each row contains a small fixed number k > j of l's. The typical minimum distance of these codes increases linearly with block length for a fixed rate and fixed j . When used with maximum likelihood decoding on a sufficiently quiet binary-input symmetric channel, the typical probability of decoding error decreases exponentially with block length for a fixed rate and fixed j . A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described. Both the equipment complexity and the data-handling capacity in bits per second of this decoder increase approximately linearly with block length. For j > 3 and a sufficiently low rate, the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length. Some experimental results show that the actual probability of decoding error is much smaller than this theoretical bound.

11,592 citations

Journal ArticleDOI
TL;DR: In this article, error-correcting output codes are employed as a distributed output representation to improve the performance of decision-tree algorithms for multiclass learning problems, such as C4.5 and CART.
Abstract: Multiclass learning problems involve finding a definition for an unknown function f(x) whose range is a discrete set containing k > 2 values (i.e., k "classes"). The definition is acquired by studying collections of training examples of the form (xi, f(xi)). Existing approaches to multiclass learning problems include direct application of multiclass algorithms such as the decision-tree algorithms C4.5 and CART, application of binary concept learning algorithms to learn individual binary functions for each of the k classes, and application of binary concept learning algorithms with distributed output representations. This paper compares these three approaches to a new technique in which error-correcting codes are employed as a distributed output representation. We show that these output representations improve the generalization performance of both C4.5 and backpropagation on a wide range of multiclass learning tasks. We also demonstrate that this approach is robust with respect to changes in the size of the training sample, the assignment of distributed representations to particular classes, and the application of overfitting avoidance techniques such as decision-tree pruning. Finally, we show that--like the other methods--the error-correcting code technique can provide reliable class probability estimates. Taken together, these results demonstrate that error-correcting output codes provide a general-purpose method for improving the performance of inductive learning programs on multiclass problems.

2,542 citations

Posted Content
TL;DR: It is demonstrated that error-correcting output codes provide a general-purpose method for improving the performance of inductive learning programs on multiclass problems.
Abstract: Multiclass learning problems involve finding a definition for an unknown function f(x) whose range is a discrete set containing k > 2 values (i.e., k ``classes''). The definition is acquired by studying collections of training examples of the form [x_i, f (x_i)]. Existing approaches to multiclass learning problems include direct application of multiclass algorithms such as the decision-tree algorithms C4.5 and CART, application of binary concept learning algorithms to learn individual binary functions for each of the k classes, and application of binary concept learning algorithms with distributed output representations. This paper compares these three approaches to a new technique in which error-correcting codes are employed as a distributed output representation. We show that these output representations improve the generalization performance of both C4.5 and backpropagation on a wide range of multiclass learning tasks. We also demonstrate that this approach is robust with respect to changes in the size of the training sample, the assignment of distributed representations to particular classes, and the application of overfitting avoidance techniques such as decision-tree pruning. Finally, we show that---like the other methods---the error-correcting code technique can provide reliable class probability estimates. Taken together, these results demonstrate that error-correcting output codes provide a general-purpose method for improving the performance of inductive learning programs on multiclass problems.

2,455 citations

Journal Article
TL;DR: It is argued that a simple "one-vs-all" scheme is as accurate as any other approach, assuming that the underlying binary classifiers are well-tuned regularized classifiers such as support vector machines.
Abstract: We consider the problem of multiclass classification. Our main thesis is that a simple "one-vs-all" scheme is as accurate as any other approach, assuming that the underlying binary classifiers are well-tuned regularized classifiers such as support vector machines. This thesis is interesting in that it disagrees with a large body of recent published work on multiclass classification. We support our position by means of a critical review of the existing literature, a substantial collection of carefully controlled experimental work, and theoretical arguments.

1,841 citations

Journal ArticleDOI
TL;DR: Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.
Abstract: This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.

1,401 citations