Proceedings ArticleDOI
On the relationship between algebraic systems theory and coding theory: representations of codes
E.V. York,Joachim Rosenthal,Johannes Schumacher +2 more
- Vol. 3, pp 3271-3276
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This paper will look at various classes of codes and derive some new results concerning the representations of these codes and the relationship between systems theory and coding theory.Abstract:
In this paper we will explore the relationship between systems theory and coding theory. In particular, we will look at various classes of codes and derive some new results concerning the representations of these codes.read more
Citations
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On behaviors and convolutional codes
TL;DR: This paper defines a convolutional code as the dual of a complete linear behavior in the sense of Willems (1979) and describes a set of generalized first-order descriptions for convolutionan codes using ideas from systems theory.
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On behaviors and convolutional codes
TL;DR: In this paper, the authors define a convolutional code as the dual of a complete linear behavior in the sense of Willems (1979), and describe a set of generalized first-order descriptions for convolutions.
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Finite-state machine embeddings for nonconcurrent error detection and identification
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Nonconcurrent error detection and correction in fault-tolerant linear finite-state machines
TL;DR: This paper develops a scheme that uses Bose-Chaudhuri-Hocquenghem coding and obtains fault-tolerant LFSMs that require 2D additional state variables and have the ability to correct up to D errors in any state variable at any time step in the time interval consisting of the latest N time steps of operation.
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Some interesting problems in systems theory which are of fundamental importance in coding theory
TL;DR: In this article, the authors explain in a tutorial way some major research questions in the area of convolutional coding theory from a perspective of systems theory and show that those questions are related to some classical control problems e.g. the quadratic regulator problem and the tracking problem.
References
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TL;DR: This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.
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TL;DR: To understand the theoretical framework upon which error-control codes are built and then Algebraic Codes for Data Transmission by Richard E. Blahut, needed, several examples to illustrate the performance of the approximation scheme in practice are needed.
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Paradigms and puzzles in the theory of dynamical systems
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