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The aim of coding theory is to design codes which can achieve the fundamental limits of communication [52] and yet are simple to implement. On average randomly constructed codes can achieve this goal, but with a decoding complexity that is impractical. Consequently, highly structured codes with practical decoding algorithms have been extensively studied. Unfortunately the vast majority of these codes do not approach capacity. Recent advances involving simple 'random like' codes with practical iterative decoding algorithms have closely approached capacity as the blocklength increases. This thesis investigates single parity check (SPC) product codes and introduces the class of randomly interleaved (RI) SPC product codes. It will be shown that RI SPC product codes can asymptotically force the probability of error to zero, at code rates up to capacity, for almost all codewords. Furthermore the structure of these codes allows a very simple, sub-optimal, iterative decoding algorithm to be used. This thesis also derives an asymptotic analysis on SPC product codes from the decoding point of view. It is shown that the probability of error can be driven to zero, as the blocklength increases, for signal to noise ratios within 2dB of capacity on the additive white Gaussian noise (AWGN) channel. Simulation results for both SPC and RI SPC product codes in an AWGN channel are presented. These results indicate that RI SPC product codes perform very well, typically within 1.5dB of capacity over a wide range of blocklengths and code rates. Further analysis on the weight enumerator of finite length RI SPC product codes is used to confirm the error floor of these codes. Extensions to parallel and serially concatenated SPC product codes are also investigated. Simulation results show an advantageous trade-off between code rate, blocklength and performance for three dimensional parallel concatenated SPC product codes. The design of irregular SPC product codes is also considered, and some simulation results are presented.

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Thesis (M.S.)--University of Hawaii at Manoa, 2007. / Includes bibliographical references (leaves 50-51). / vii, 51 leaves, bound ill. 29 cm

The main focus of this thesis is the investigation of a number of different space-time coding scenarios based on predominately the application of turbo codes and low density parity check (LDPC) codes to a multi-antenna system. Both codes structures make use of the BPSK stacking construction that readily applies binary linear codes to the space-time channel while also providing a check on the suitability of the resulting code in order to achieve maximum diversity advantage. The turbo-like codes investigated are based upon the application of a parallel concatenated scheme to directly map the data and parity bits generated by the encoder to one of three possible antennas outputs. It is further highlighted in this case how the interleaver plays a crucial role in determining overall performance as this determines whether the resulting space-time codes achieve maximum diversity advantage or otherwise. Performance results are presented for a number of different constituent codes and interleaver design. The LDPC space-time codes considered herein again are based on satisfying the BPSK stacking construction to ensure full diversity advantage is achieved. The code design is based on a recursive application of the Shur complement in order to devise block based codes that have a resulting parity check matrix that is relatively sparse. A number of various code constructions that satisfy the conditions are then simulated in order to determine performance in both slow and fast fading channel conditions. This thesis also investigates the use of certain non-linear codes termed “chaotic codes” and their application as constituent codes within a parallel concatenated (turbo-like) coding scheme. Performance of such codes is shown to be readily analysed via the use extrinsic information transfer (EXIT) techniques. The modified codes are simulated over an AWGN channel using BPSK modulation for a number of different block lengths. / Thesis (PhDTelecommunications)--University of South Australia, 2006.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Mass., Massachusetts Inst. of Technology, Diss.--Cambridge, 2001. / Literaturverz. S. [337] - 347.

Thèse (M.Sc.)--Université Laval, 2008. / Bibliogr.: f. [102]-103. Publié aussi en version électronique dans la Collection Mémoires et thèses électroniques.