P. Weiner. Multidimensional Convolutional Codes. PhD thesis, University of Notre Dame, 1998. Available at http://www.nd.edu/~rosen/preprints.html. Home/Search Document Details and Download
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Connections between Linear Systems and Convolutional Codes - Rosenthal (2000) (2 citations) (Correct)
....de nitions given in Section 2 and 3. In Section 5 we will give a de nition for convolutional codes in which it is required that the code words have nite support. Such a de nition was considered by Fornasini and Valcher [48, 5] and by the author in collaboration with Schumacher, Weiner and York [42, 44, 49]. The study of behaviors with nite support has been done earlier in the context of automata theory and we refer to Eilenberg s book [1] We show in Section 5 how this moduletheoretic de nition relates to complete, linear and time invariant behaviors by Pontryagin duality. In Section 6 we will ....
....the algebraic properties of the di erent de nitions. We will also restrict ourselves to the concrete setting of convolutional codes de ned over nite elds. It is however known that many of the concepts in this paper generalize to group codes [3, 12, 9] and multidimensional convolutional codes [4, 5, 16, 48, 49]. All of the de nitions which we are going to give are quite similar, but there are some notable di erences. Since the paper draws from results from quite di erent research areas, one is faced with the problem that there is no uniform notation. In this paper we will adopt the convention used in ....
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P. Weiner. Multidimensional Convolutional Codes. PhD thesis, University of Notre Dame, 1998. Available at http://www.nd.edu/~rosen/preprints.html.
An Algebraic Decoding Algorithm for Convolutional Codes - Rosenthal (1998) (1 citation) (Correct)
....: z m ) In [4, 18] Fornasini and Valcher define a code as a submodule of R n , where R = F[z 1 ; z 2 ; z Gamma1 1 ; z Gamma1 2 ] is the ring of Laurent polynomials in the variables z 1 ; z 2 . In this way codes become dual to complete linear behaviors defined on Z Theta Z. Weiner [19] defines a convolutional code as a submodule of R n , where R is the polynomial ring R = F[z 1 ; z m ] In this framework codes are dual to linear complete behaviors defined on N m . Since submodules of F n [z] i.e. convolutional codes, are dual to linear complete behaviors they ....
P. Weiner (1998). Multidimensional Convolutional Codes. Ph.D. thesis, University of Notre Dame, Available at http://www.nd.edu/~rosen/preprints.html.
Duality between Multidimensional Convolutional Codes.. - Gluesing-Luerssen.. (1999) Self-citation (Weiner) (Correct)
....as w : y Gamma e. 3 Duality between Codes and Behaviors There have been several instances in the recent literature about coding theory, in which certain types of duality between convolutional codes and behaviors in the system theoretical sense of [13] have been mentioned or used, see, e.g. [3, 8, 11, 12]. In this section we are going to make this duality precise by introducing the appropriate bilinear form. Exploiting the very comprehensive and powerful paper of Oberst [5] quite a lot of results about this duality are available even in the multidimensional case. However, as it seems to us, most ....
P. Weiner. Multidimensional Convolutional Codes. PhD thesis, University of Notre Dame, 1998. Available at http://www.nd.edu/~rosen/preprints.html.
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