Contribuições à codificação de canal por matrizes wavelet.

Abstract

The channel code by wavelet matrices, for digital communications, WCC, has the following advantages: the reduced computational complexity to encode and decode the information and the ease of adaptation of the coding rates. However, in spite of several publications on the subject, there were some open points that needed to be attacked, among them: mathematical systematization of the process, increase in spectral efficiency, and to compare, by simulations, its performance, in terms of the error rate of bits, relative to other systems that transmit over flat fading channel, to verify their competitiveness and employability in current digital communication systems. In order to achieve the proposed objectives, we used as methodology study the channel-coding technique by wavelet matrices, a literature review on channel coding techniques currently in use and the implementation of algorithms and the development of computer programs in the Phyton language, for simulations. In WCC coding, real planar wavelets matrices derived from a Haar matrix are used. Thus, the main contributions of this thesis are: 1) general algebraic description of the WCC process; 2) increase in spectral efficiency for up to 4 bits/s/Hz; 3) evaluation of the effectiveness and employability of WCC systems, on flat fading and Gaussian noise (AWGN) channels; 4) execution of sequence decoding; 5) extension of previously obtained results, with unit coding rate, for coding rates 1/2 and 1/4. In this study, the encoder input symbols are complex producing complex wavelet symbols. Besides coding and decoding are been described algebraically, a probability distribution function of the coded symbols is formulated, and used to calculate the average energy of constellations proposed for the transmission of the symbols. The performance of the system, in Rayleigh flat channel, is analyzed and compared with space-time block coding (STBC) system, with two diversity. In order to perform the sequence decoding a procedure was developed to obtain a trellis corresponding to the wavelet coding. The results of the simulations show that for a signal to noise ratio, Eb/N0 < 15 dB, the WCC, with spectral efficiency of 1 bit/s/Hz, has compatible performance with STBC used as a reference and that increasing the spectral efficiency by applying a data formatting process prior to WCC coding, degrades system performance when the number of bits, nb, is greater than four. In general, it is concluded that CWC systems can be used as an alternative in current digital communications systems.