A contribution to the theory of convolutional codes from systems theory piont of view
- Autores: Laurence Emilie Um
- Directores de la Tesis: El Mamoun Souidi (dir. tes.), María Isabel García Planas (dir. tes.)
- Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2015
- Idioma: inglés
- Tribunal Calificador de la Tesis: El Bernoussi Souad (presid.), El Mamoun Souidi (voc.), Mohd Omar Ab Kadir (voc.), María Isabel García Planas (voc.), María Dolors Magret Planas (voc.)
- Materias:
- Enlaces
- Tesis en acceso abierto en: TDX
- Resumen
Information is such a valuable good of our time. Given that the transmission of information has always been subject to precision problems, knowing the obstacles existing between the transmitter and the receiver, eventual disruptions can happen anywhere in between, the physical means, channels involved with the exchange are never perfect and they are subject to errors that might result in loss of important data. Error correcting codes are a key element in the transmission and storage of digital information. In this thesis we study the possibility to redefine and improve properties of convolutional codes in terms of coding and decoding, with the help of the systems and control theory. For that matter, in chapter 1, we recall notions on coding theory, more specifically, on linear codes, both block and convolutional, redefining the convolutional codes as submodules of the F^n_{q} which is our main workspace. And we go through the prerequisites involved in the process of encoding and decoding, both for block and convolutional codes. And in order to approach them with tools of the systems theory, in chapter 2, we give the equivalence of the generating matrix in the form of a realization (A,B,C,D) of an input-output system. Then, we studied the concatenation because it has been proved to improve the transmission. In this work, we consider two big families of concatenation: serial concatenation, and parallel concatenation and two other models of concatenation called systematic serial concatenation and parallel interleaver concatenation. In chapter 3, we study control properties for each case. Nevertheless, we focus on the property of output-observability, and conditions to obtain it, particularly an easy iterative test is presented in order to discuss whether a code is output-observable. This test consists in calculating certain ranks of block matrices constructed from the matrices A, B, C, D. The output-observability property is very beneficial for the decoding as discussed in the next chapter. Moreover, in chapter 4, we assess two methods for a complete decoding operating on an iterative fashion, then suggest conditions for a step by step decoding in a case of concatenation, in order to recover exactly each and every original sequence after operation of every implied code. Following this concept, we study the convolutional decoding in general, and in particular the one of concatenated models in serial, in parallel, in systematic serial and finally in interleaver parallel implementation. In chapter 5, we suggest an application in steganography, in which we implement a steganographic scheme, inspired by the linear system representation of convolutional codes. Having the output-observability matrix being the backbone behind the construction of our decoding algorithms, coupled with the syndrome method, we formed some embedding/retrieval algorithms inspired by that construction. Those methods display the protection of communication within time-related transfer of information, with interesting possibilities and results. Finally, a chapter summarizing all our achievements and a short list of possible future lines of work upon aspects that we would like to continue studying in order to achieve new related goals.
