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Realization of 2D (2,2)–Periodic Encoders by Means of 2D Periodic Separable Roesser Models
- Source :
- International Journal of Applied Mathematics and Computer Science, Vol 29, Iss 3, Pp 527-539 (2019)
- Publication Year :
- 2019
- Publisher :
- Sciendo, 2019.
-
Abstract
- It is well known that convolutional codes are linear systems when they are defined over a finite field. A fundamental issue in the implementation of convolutional codes is to obtain a minimal state representation of the code. Compared with the literature on one-dimensional (1D) time-invariant convolutional codes, there exist relatively few results on the realization problem for time-varying 1D convolutional codes and even fewer if the convolutional codes are two-dimensional (2D). In this paper we consider 2D periodic convolutional codes and address the minimal state space realization problem for this class of codes. This is, in general, a highly nontrivial problem. Here, we focus on separable Roesser models and show that in this case it is possible to derive, under weak conditions, concrete formulas for obtaining a 2D Roesser state space representation. Moreover, we study minimality and present necessary conditions for these representations to be minimal. Our results immediately lead to constructive algorithms to build these representations.
Details
- Language :
- English
- ISSN :
- 20838492
- Volume :
- 29
- Issue :
- 3
- Database :
- Directory of Open Access Journals
- Journal :
- International Journal of Applied Mathematics and Computer Science
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.8969f04015064767a294b0f5007e8ee1
- Document Type :
- article
- Full Text :
- https://doi.org/10.2478/amcs-2019-0039