Repeat--punctured turbo codes and superorthogonal convolutional turbo codes.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2007.The use of error-correction coding techniques in communication systems has become extremely imperative. Due to the heavy constraints faced by systems engineers more attention has been given to developing codes that converge closer to the Shannon theoretical limit. Turbo codes exhibit a performance a few tenths of a decibel from the theoretical limit and has motivated a lot of good research in the channel coding area in recent years. In the under-mentioned dissertation, motivated by turbo codes, we study the use of three new error-correction coding schemes: Repeat-Punctured Superorthogonal Convolutional Turbo Codes, Dual-Repeat-Punctured Turbo Codes and Dual-Repeat-Punctured Superorthogonal Convolutional Turbo Codes, applied to the additive white Gaussian noise channel and the frequency non-selective or flat Rayleigh fading channel. The performance of turbo codes has been shown to be near the theoretical limit in the AWGN channel. By using orthogonal signaling, which allows for bandwidth expansion, the performance of the turbo coding scheme can be improved even further. Since the resultant is a low-rate code, the code is mainly suitable for spread-spectrum modulation applications. In conventional turbo codes the frame length is set equal to the interleaver size; however, the codeword distance spectrum of turbo codes improves with an increasing interleaver size. It has been reported that the performance of turbo codes can be improved by using repetition and puncturing. Repeat-punctured turbo codes have shown a significant increase in performance at moderate to high signal-to-noise ratios. In this thesis, we study the use of orthogonal signaling and parallel concatenation together with repetition (dual and single) and puncturing, to improve the performance of the superorthogonal convolutional turbo code and the conventional turbo code for reliable and effective communications. During this research, three new coding schemes were adapted from the conventional turbo code; a method to evaluate the union bounds for the AWGN channel and flat Rayleigh fading channel was also established together with a technique for the weight-spectrum evaluation

Repeat-punctured turbo trellis-coded modulation.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2010.Ever since the proposal of turbo code in 1993, there has been extensive research carried out to improve both the performance and spectrum efficiency. One of the methods used to improve the spectrum efficiency was to combine turbo code with a trellis-coded modulation scheme, called turbo trellis-coded modulation (TTCM). The scheme is used in various applications such as deep-space communication, wireless communication and other fields. It is a well established fact that an increase in an interleaver size of a TTCM system results in an improved performance in the bit error rate (BER). In this thesis repeat-punctured turbo trellis-coded modulation (RPTTCM) is proposed. In RPTTCM, the effect of repeat-puncture is investigated on a TTCM system, repetition of the information bits increases the interleaver size, followed by an appropriate puncturing scheme to maintain the respective code rate. The TTCM and RPTTCM systems are simulated in an Additive White Gaussian Noise (AWGN) channel. To understand how the RPTTCM scheme will perform in a wireless channel, the Rayleigh flat fading channel (with channel state information known at the receiver) will be used. The BER performance bound for the TTCM scheme is derived for AWGN and Rayleigh flat fading channels. Thereafter repeat-punctured is introduced into the TTCM system. The BER performance bound is then extended to include repeat-puncturing. The performances of the TTCM and RPTTCM systems are then compared. It was found that the RPTTCM system performed better at high signal-to-noise ratio (SNR) in both AWGN and Rayleigh flat fading channels. The RPTTCM scheme achieved a coding gain of approximately 0.87 dB at a BER of for an AWGN channel and 1.9 dB at a BER of for a Rayleigh flat fading channel, for an information size of N=800

Code design based on metric-spectrum and applications

We introduced nested search methods to design (n, k) block codes for arbitrary channels by optimizing an appropriate metric spectrum in each iteration. For a given k, the methods start with a good high rate code, say k/(k + 1), and successively design lower rate codes up to rate k/2^k corresponding to a Hadamard code. Using a full search for small binary codes we found that optimal or near-optimal codes of increasing length can be obtained in a nested manner by utilizing Hadamard matrix columns. The codes can be linear if the Hadamard matrix is linear and non-linear otherwise. The design methodology was extended to the generic complex codes by utilizing columns of newly derived or existing unitary codes. The inherent nested nature of the codes make them ideal for progressive transmission. Extensive comparisons to metric bounds and to previously designed codes show the optimality or near-optimality of the new codes, designed for the fading and the additive white Gaussian noise channel (AWGN). It was also shown that linear codes can be optimal or at least meeting the metric bounds; one example is the systematic pilot-based code of rate k/(k + 1) which was proved to meet the lower bound on the maximum cross-correlation. Further, the method was generalized such that good codes for arbitrary channels can be designed given the corresponding metric or the pairwise error probability. In synchronous multiple-access schemes it is common to use unitary block codes to transmit the multiple users information, especially in the downlink. In this work we suggest the use of newly designed non-unitary block codes, resulting in increased throughput efficiency, while the performance is shown not to be substantially sacrificed. The non-unitary codes are again developed through suitable nested searches. In addition, new multiple-access codes are introduced that optimize certain criteria, such as the sum-rate capacity. Finally, the introduction of the asymptotically optimum convolutional codes for a given constraint length, reduces dramatically the search size for good convolutional codes of a certain asymptotic performance, and the consequences to coded code-division multiple access (CDMA) system design are highlighted