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As wireless communication systems continue to push the limits of energy and spectral efficiency, increased demands are placed on the capabilities of the receiver. At the same time, the computational resources available for processing received signals will continue to grow. This opens the door for iterative algorithms to play an increasing role in the next generation of communication receivers. In the context of receivers, the goal of iterative probabilistic processing is to approximate maximum a posteriori (MAP) symbol-by-symbol detection of the information bits and estimation of the unknown channel or signal parameters. The sum-product algorithm is capable of efficiently approximating the marginal posterior probabilities desired for MAP detection and provides a unifying framework for the development of iterative receiver algorithms. However, in some applications the sum-product algorithm is computationally infeasible. Specifically, this is the case when both continuous and discrete parameters are present within the model. Also, the complexity of the sum-product algorithm is exponential in the number of variables connected to a particular factor node and can be prohibitive in multi-user and multi-antenna applications. In this dissertation we identify three key problems which can benefit from iterative probabilistic processing, but for which the sum-product algorithm is too complex. They are (1) joint synchronization and detection in multipath channels with emphasis on frame timing, (2) detection in co-channel interference and non-Gaussian noise, and (3) joint channel estimation and multi-signal detection. This dissertation presents the advances we have made in iterative probabilistic processing in order to tackle these problems. The motivation behind the work is to (a) compromise as little as possible on the performance that is achieved while limiting the computational complexity and (b) maintain good theoretical justification to the algorithms that are developed. / Ph. D.

In this thesis, I describe the iterative service design process I used in identifying and understanding the needs of diverse stakeholders, the development of technologies to support their mutually beneficial needs, and the evaluation of the end-user experience with these technologies. Over three iterative design cycles, the set of identified end-user customers expanded to include the patient, the supervising therapist, the annotating therapist, and other members of the development team. Multiple versions of interactive movement capture and annotation tools were developed as the needs of these stakeholders were clarified and evolved, and the optimal data forms and structures became evident. Interactions between the stakeholders and the developed technologies operating in various environments were evaluated and assessed to help improve and optimize the entire service ecosystem. Results and findings from these three design cycles are being used to direct and shape my ongoing and future doctoral research / Master of Science / In this thesis, I describe the iterative service design process I used in identifying and understanding the needs of diverse stakeholders, the development of technologies to support their mutually beneficial needs, and the evaluation of the end-user experience with these technologies. Over three iterative design cycles, the set of identified end-user customers expanded to include the patient, the supervising therapist, the annotating therapist, and other members of the development team. Multiple versions of interactive movement capture and annotation tools were developed as the needs of these stakeholders were clarified and evolved, and the optimal data forms and structures became evident Interactions between the stakeholders and the developed technologies operating in various environments were evaluated and assessed to help improve and optimize the entire service ecosystem. Results and findings from these three design cycles are being used to direct and shape my ongoing and future doctoral research.

Globally convergent homotopy methods are used to solve difficult nonlinear systems of equations by tracking the zero curve of a homotopy map. Homotopy curve tracking involves solving a sequence of linear systems, which often vary greatly in difficulty. In this research, a popular iterative solution tool, GMRES(k), is adapted to deal with the sequence of such systems. The proposed adaptive strategy of GMRES(k) allows tuning of the restart parameter k based on the GMRES convergence rate for the given problem. Adaptive GMRES(k) is shown to be superior to several other iterative techniques on analog circuit simulation problems and on postbuckling structural analysis problems. Developing parallel techniques for robust but expensive sequential computations, such as globally convergent homotopy methods, is important. The design of these techniques encompasses the functionality of the iterative method (adaptive GMRES(k)) implemented sequentially and is based on the results of a parallel performance analysis of several implementations. An implementation of adaptive GMRES(k) with Householder reflections in its orthogonalization phase is developed. It is shown that the efficiency of linear system solution by the adaptive GMRES(k) algorithm depends on the change in problem difficulty when the problem is scaled. In contrast, a standard GMRES(k) implementation using Householder reflections maintains a constant efficiency with increase in problem size and number of processors, as concluded analytically and experimentally. The supporting numerical results are obtained on three distributed memory homogeneous parallel architectures: CRAY T3E, Intel Paragon, and IBM SP2. / Ph. D.

Usually, image compression techniques that use only one transform exhibit some poor properties. For instance, the Discrete Cosine Transform (DCT) cannot efficiently represent high frequency components, resulting in blurred images. The Multiple Bases Representation (MBR) compression technique, which uses two or more transforms, is found to be superior to the single transform techniques in terms of representation efficiency. However, some bits in the MBR representation are needed to track the basis information. The MBR image quality is deteriorated by discontinuities at block boundaries, as is the standard DCT transform. In this thesis, test images are distorted by MBR compression using a Recursive Residual Projection algorithm. This algorithm is a sub-optimal method to find the best basis vector subset for representing images based on multiple orthogonal bases. The MBR distorted images are reconstructed by the iterative method of Projection onto Convex Sets (POCS). Many constraints that form convex sets are reviewed and examined. Due to the high distortion at the block boundaries, some constraints are introduced particularly to reduce artifacts at the boundaries. Some constraints add energy to the reconstructed images while others remove energy. Thus, the initial vectors play a key role in the performance of the POCS method for better MBR reconstruction. This thesis also determines the most appropriate initial vector for each constraint. Finally, the composite projections associated with the sign, minimum decreasing and norm-of-slope constraints are used to improve the reconstruction of the MBR distorted images and the effect of ordering of the projections is investigated. / Master of Science

Timing recovery is the processing of synchronizing the sampler with the received analog signal. Sampling at the wrong times can have a devastating impact on performance. Conventional timing recovery techniques are based on a decision-directed phase-locked loop (PLL). They are adequate only when the operating signal-to-noise ratio (SNR) is sufficiently high, but recent advances in error-control coding have made it possible to communicate reliably at very low SNR, where conventional techniques fail. This thesis develops new techniques for timing recovery that are capable of working at low SNR. We propose a new timing recovery scheme based on per-survivor processing (PSP), which jointly performs timing recovery and equalization, by embedding a separate PLL into each survivor of a Viterbi algorithm. The proposed scheme is shown to perform better than conventional scheme, especially when the SNR is low and the timing error is large. An important advantage of this technique is its amenability to real-time implementation. We also propose a new iterative timing recovery scheme that exploits the presence of the error-control code; in doing so, it can perform even better than the PSP scheme described above, but at the expense of increased complexity and the requirement of batch processing. This scheme is realized by embedding the timing recovery process into a trellis-based soft-output equalizer using PSP. Then, this module iteratively exchanges soft information with the error-control decoder, as in conventional turbo equalization. The resulting system jointly performs the functions of timing recovery, equalization, and decoding. The proposed iterative timing recovery scheme is shown to perform better than previously reported iterative timing recovery schemes, especially when the timing error is severe. Finally, performance analysis of iterative timing recovery schemes is difficult because of their high complexity. We propose to use the extrinsic information transfer (EXIT) chart as a tool to predict and compare their performances, considering that the bit-error rate computation takes a significant amount of simulation time. Experimental results indicate that the system performance predicted by the EXIT chart coincides with that obtained by simulating data transmission over a complete iterative receiver, especially when the coded block length is large.

International Telemetering Conference Proceedings / October 18-21, 2004 / Town & Country Resort, San Diego, California / This paper presents a joint source-channel decoding scheme based on a JPEG2000 source coder and an LDPC channel coder. At the encoder, JPEG2000 is used to perform source coding with certain error resilience (ER) modes, and LDPC codes are used to perform channel coding. At the decoder, after one iteration of LDPC decoding, the output codestream is then decoded by JPEG2000. With the error resilience mode switches on, the source decoder detects the position of the first error within each codeblock of the JPEG2000 codestream. This information is fed back to the channel decoder, and incorporated into the calculation of likelihood values of variable nodes for the next iteration of LDPC decoding. Our results indicate that the proposed method has significant gains over conventional separate channel and source decoding.

ITC/USA 2007 Conference Proceedings / The Forty-Third Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2007 / Riviera Hotel & Convention Center, Las Vegas, Nevada / An acoustic modem employing direct-sequence spread-spectrum (DSSS) signaling is considered with LDPC coding. The underwater acoustic channel is tracked using a Kalman filter which requires accurate data decisions. To improve KF performance and reduce the overall error rate, joint iterative LDPC decoding and channel estimation is proposed based on a factor graph and sum-product algorithm approximation. In this scheme, the decoder posterior log likelihood ratios (LLRs) provide data decisions for the KF. Decoder extrinsic LLRs are similarly incorporated into the detector LLRs to yield improved priors for decoding. Error rate simulations of the overall modem are provided for a shallow-water channel model with Ricean/Rayleigh fading.

International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Low-Density Parity-Check (LDPC) codes are powerful codes capable of nearly achieving the Shannon channel capacity. This paper presents a tutorial introduction to LDPC codes, with a detailed description of the decoding algorithm. The algorithm propagates information about bit and check probabilities through a tree obtained from the Tanner graph for the code. This paper may be useful as a supplement in a course on error-control coding or digital communication.

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy