Applications of chaotic maps in communications and biomedical signal processing

The dissertation proposes a novel technique of using chaotic functions to solve pivotal issues in wireless communications and biomedical signal processing applications. In this dissertation three critical issues are discussed. The dissertation proposes an effective interleaver structure which uses the chaotic circle map to generate scrambled uncorrelated randomized data. An Interleaver is a functional entity which improves the performance of error correcting codes under short bursts error due to channel effects. The information is interleaved after the orthogonal frequency division multiplexing (OFDM) modulation block. The contribution of the proposed technique is better randomization with minimal information requirement between transmitter and receiver for de-interleaving. The performance improvement of the proposed technique is compared in terms of the bit error rate and field programmable gate array (FPGA) implementation resource utilization.;The dissertation proposes an approach to alleviate the impact of distortion on the transmitted signal caused by peak to average power ration (PAPR) in OFDM systems. This is achieved with the aid of chaotic functional map, called circle map. The proposed approach is compared with the well known techniques, such as selective mapping (SLM), amplitude clipping, tone reservation (TR), partial transmit sequence (PTS), and active constellation extension (ACE). The previous methods require large side information vector and high complexity. The proposed approach reduces the PAPR by exploiting the inherent properties of chaotic signals. It is shown that the proposed method results in an overall error rate that is superior to those of the existing techniques at a lower overhead cost of the side information.;In recent years, numerous studies have been carried out on effective means of pattern detection and characterization for biomedical signal sets. With the aid of chaos theory, the dissertation presents two significant contributions in characterizing electrocardiogram (ECG) signal sets. The first contribution is the introduction of a functional map representation of atrial fibrillation ECG signal sets, which in turn can be brought to bear for the estimation of the probabilities of the future state vectors. The effectiveness of the proposed model is tested using mean-squared error metric. The Second contribution is to demonstrate the effectiveness of the recurrence period density entropy (RPDE) index as an effective tool in tracking the onset of changes in the condition of the patient from the state of normal ECG rhythm to the state of atrial fibrillation and sudden cardiac arrest.