Minimal state-space realizations of 2D convolutional codes

  1. Pinho, Telma Daniela Pereira de
Dirigida per:
  1. Paula Rocha Director/a
  2. María Raquel Rocha Pinto Codirector/a

Universitat de defensa: Universidade de Aveiro (UA)

Fecha de defensa: 21 de de maig de 2014

Tribunal:
  1. Vitor José Babau Torres President/a
  2. Teresa Paula Coelho Azevedo Perdicoúlis Vocal
  3. Diego Napp Avelli Vocal
  4. Ettore Fornasini Vocal
  5. Joan-Josep Climent Coloma Vocal

Tipus: Tesi

Resum

In this thesis we consider two-dimensional (2D) convolutional codes. As happens in the one-dimensional (1D) case one of the major issues is obtaining minimal state-space realizations for these codes. It turns out that the problem of minimal realization of codes is not equivalent to the minimal realization of encoders. This is due to the fact that the same code may admit different encoders with different McMillan degrees. Here we focus on the study of minimality of the realizations of 2D convolutional codes by means of separable Roesser models. Such models can be regarded as a series connection between two 1D systems. As a first step we provide an algorithm to obtain a minimal realization of a 1D convolutional code starting from a minimal realization of an encoder of the code. Then, we restrict our study to two particular classes of 2D convolutional codes. The first class to be considered is the one of codes which admit encoders of type n 1. For these codes, minimal encoders (i.e., encoders for which a minimal realization is also minimal as a code realization) are characterized enabling the construction of minimal code realizations starting from such encoders. The second class of codes to be considered is the one constituted by what we have called composition codes. For a subclass of these codes, we propose a method to obtain minimal realizations by means of separable Roesser models.