Multidimensional convolutional codes generalize (one dimensional)
convolutional codes and they correspond under a natural duality to
multidimensional systems widely studied in the systems literature.Comment: 16 pages LaTe

Gluesing-Luerssen, Heide

Rosenthal, Joachim

Weiner, Paul

English

arXiv

this paper. The following example will illustrate the usefulness of multidimensional convolutional codes.  Example 1.1 Let D = F[z 1 ; z 2 ; z 3 ] be the polynomial ring in the indeterminate

Heide Gluesing-Luerssen

Joachim Rosenthal

Paul A. Weiner

CiteSeerX

Duality between Multidimensional Convolutional Codes and Systems

Abstract: Multidimensional convolutional codes arise as a generalization of “classical” onedimensional codes. We will introduce m-dimensional convolutional codes of length n as submodules of D n where D is the polynomial ring in m variables over a finite field. Besides their coding theoretic significance, they can also be regarded as the annihilating modules of systems of partial difference equations, the latter being studied in much detail in discrete-time multidimensional systems theory. We will apply the duality theorem of Oberst [5] to this particular case and employ the duality to investigate certain first-order representations of onedimensional convolutional codes

Heide Gluesing-luerssen

Duality between multidimensional convolutional codes and systems

Duality between Multidimensional Convolutional Codes and Systems

Abstract

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