scholarly journals Minimal State-Space Representation of Convolutional Product Codes

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1410
Author(s):  
Joan-Josep Climent ◽  
Diego Napp ◽  
Raquel Pinto ◽  
Verónica Requena
Keyword(s):  
State Space ◽  
Convolutional Codes ◽  
Space Representation ◽  
Product Codes ◽  
Product Code ◽  
Minimal State ◽  
Systematic Procedure ◽  
State Space Representation ◽  
Minimal Dimension ◽  
Study Product

In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.

scholarly journals Realization of 2D (2,2)–Periodic Encoders by Means of 2D Periodic Separable Roesser Models

2019 ◽  
Vol 29 (3) ◽  
pp. 527-539
Author(s):  
Diego Napp ◽  
Ricardo Pereira ◽  
Raquel Pinto ◽  
Paula Rocha
Keyword(s):  
State Space ◽  
Necessary Conditions ◽  
Convolutional Codes ◽  
Space Representation ◽  
Realization Problem ◽  
One Dimensional ◽  
Minimal State ◽  
State Space Representation ◽  
Roesser Models ◽  
Time Invariant

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.

scholarly journals On Bumps and Reduction of Switching Transients in Multicontroller Systems

2007 ◽  
Vol 2007 ◽  
pp. 1-17 ◽  
Author(s):  
Joseph J. Yamé ◽  
Michel Kinnaert
Keyword(s):  
State Space ◽  
Closed Loop ◽  
Open Loop ◽  
Space Representation ◽  
Control Loop ◽  
Minimal State ◽  
State Space Representation ◽  
Common Memory ◽  
Linear Controllers

This paper is concerned with the realization and implementation of multicontroller systems, consisting of several linear controllers, subject to the bump phenomenon which occurs when switching between one controller acting in closed loop and another controller in the set of “offline” controllers waiting to take over the control loop. Based on a deep characterization of the bump phenomenon, the paper gives a novel and simple parameterization of such set of linear controllers, possibly having different state dimensions, to cope with bumps and their undesirable transients in switched-mode systems. The proposed technique is based on a non minimal state-space representation allowing a common memory and a unique dynamics shared by all controllers in that set. It also makes each initially open-loop unstable controller run in a stable way regardless of whether that controller is connected to the controlled process.

A Dynamic Systems Model for Gasifier in IGCC

2008 ◽  
Author(s):  
Mohit Aggarwal ◽  
B. Erik Ydstie ◽  
Lee R. White
Keyword(s):  
State Space ◽  
Dynamic Systems ◽  
Process Analysis ◽  
Main Idea ◽  
Space Representation ◽  
Level Control ◽  
Minimal State ◽  
State Space Representation ◽  
Systems Model ◽  
Shrinking Core

We combine the concepts of element mole balance, population balance and shrinking core mechanism to develop a dynamic systems model for the Gasifier in an IGCC process. There is need for such a model for process analysis, optimization and low level control studies. The main idea is to use invariants, like elements (atoms), instead of compounds. This reduces the size of state space and we are able to explore the idea of a minimal state space representation for a thermodynamic process. The idea of a minimal state plays an important role in control theory as it is closely related to the concepts of controllability and observability.

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