FONSECA NETO, J.; http://lattes.cnpq.br/1843035768725746; FONSECA NETO, João.
Resumo:
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.