A low-complexity method of interleaver design, sub-vector interleaving, for both parallel and serially concatenated convolutional codes (PCCCs and SCCCs, respectively) is presented here. Since the method is low-complexity, it is uniquely suitable for designing long interleavers. Sub-vector interleaving is based on a dynamical system representation of the constituent encoders employed by PCCCs and SCCCs. Simultaneous trellis termination can be achieved with a single tail sequence using sub-vector interleaving for both PCCCs and SCCCs. In the case of PCCCs, the error floor can be lowered by sub-vector interleaving which allows for an increase in the weight of the free distance codeword and the elimination of the lowest weight codewords generated by weight-2 terminating input sequences that determine the error floor at low signal-to-noise ratios (SNRs). In the case of SCCCs, sub-vector interleaving lowers the error floor by increasing the weight of the free distance codewords. Interleaver gain can also be increased for SCCCs by interleaving the lowest weight codewords from the outer into non-terminating input sequences to the inner encoder. Sub-vector constrained S-random interleaving, a method for incorporating S-random interleaving into sub-vector interleavers, is also proposed. Simulations show that short interleavers incorporating S-random interleaving into sub-vector interleavers perform as well as or better than those designed by the best and most complex methods for designing short interleavers. A method for randomly generating sub-vector constrained S-random interleavers that maximizes the spreading factor, S, is also examined. The convergence of the turbo decoding algorithm to maximum-likelihood decisions on the decoded input sequence is required to demonstrate the improvement in BER performance caused by the use of sub-vector interleavers. Convergence to maximum-likelihood decisions by the decoder do not always occur in the regions where it is feasible to generate the statistically significant numbers of error events required to approximate the BER performance for a particular coding scheme employing a sub-vector interleaver. Therefore, a technique for classifying error events by the mode of convergence of the decoder is used to illuminate the effect of the sub-vector interleaver at SNRs where it is possible to simulate the BER performance of the coding scheme.

Diversity transmission is an effective technique to combat fading channels and this thesis introduces two main ideas. Firstly, a novel precoding technique is proposed to achieve diversity transmission and improve bit error rate (BER) performance over the existing linear constellation precoding (LCP) techniques. Experimental and theoretical results are presented to show that the proposed precoding schemes can outperform the existing LCP schemes in various fading channels and additive white Gaussian noise channels. Secondly, an interleaving technique to further improve the BER performance is proposed. The proposed diversity transmission techniques are implemented for both single-carrier and orthogonal frequency division multiplexing (OFDM) systems. The second part of the thesis focuses on the pairwise error probability analysis of the proposed and LCP schemes when receivers have imperfect channel state information (CSI). The BER performance of the proposed precoding and interleaver scheme are investigated in OFDM systems with minimum mean square error channel estimators and single-carrier systems with basis expansion model based channel estimators. It is demonstrated that while precoding schemes designed for receivers with perfect CSI yield near-optimum BER performance in the former system, the proposed phase-shift keying based precoding schemes perform well in the latter system. In both cases, the proposed precoding scheme, combined with the novel interleaving technique, outperforms the existing LCP schemes.

Diversity transmission is an effective technique to combat fading channels and this thesis introduces two main ideas. Firstly, a novel precoding technique is proposed to achieve diversity transmission and improve bit error rate (BER) performance over the existing linear constellation precoding (LCP) techniques. Experimental and theoretical results are presented to show that the proposed precoding schemes can outperform the existing LCP schemes in various fading channels and additive white Gaussian noise channels. Secondly, an interleaving technique to further improve the BER performance is proposed. The proposed diversity transmission techniques are implemented for both single-carrier and orthogonal frequency division multiplexing (OFDM) systems. The second part of the thesis focuses on the pairwise error probability analysis of the proposed and LCP schemes when receivers have imperfect channel state information (CSI). The BER performance of the proposed precoding and interleaver scheme are investigated in OFDM systems with minimum mean square error channel estimators and single-carrier systems with basis expansion model based channel estimators. It is demonstrated that while precoding schemes designed for receivers with perfect CSI yield near-optimum BER performance in the former system, the proposed phase-shift keying based precoding schemes perform well in the latter system. In both cases, the proposed precoding scheme, combined with the novel interleaving technique, outperforms the existing LCP schemes.