Iterative Multiuser Detection and Decoding with Spatially Coupled Interleaving

Spatially coupled (SC) interleaving is proposed to improve the performance of iterative multiuser detection and decoding (MUDD) for quasi-static fading multiple-input multiple-output systems. The linear minimum mean-squared error (LMMSE) demodulator is used to reduce the complexity and to avoid error propagation. Furthermore, sliding window MUDD is proposed to circumvent an increase of the decoding latency due to SC interleaving. Theoretical and numerical analyses show that SC interleaving can improve the performance of the iterative LMMSE MUDD for regular low-density parity-check codes.Comment: Long version of a paper submitted to IEEE Wireless Commun. Let

Novel LDPC coding and decoding strategies: design, analysis, and algorithms

In this digital era, modern communication systems play an essential part in nearly every aspect of life, with examples ranging from mobile networks and satellite communications to Internet and data transfer. Unfortunately, all communication systems in a practical setting are noisy, which indicates that we can either improve the physical characteristics of the channel or find a possible systematical solution, i.e. error control coding. The history of error control coding dates back to 1948 when Claude Shannon published his celebrated work “A Mathematical Theory of Communication”, which built a framework for channel coding, source coding and information theory. For the first time, we saw evidence for the existence of channel codes, which enable reliable communication as long as the information rate of the code does not surpass the so-called channel capacity. Nevertheless, in the following 60 years none of the codes have been proven closely to approach the theoretical bound until the arrival of turbo codes and the renaissance of LDPC codes. As a strong contender of turbo codes, the advantages of LDPC codes include parallel implementation of decoding algorithms and, more crucially, graphical construction of codes. However, there are also some drawbacks to LDPC codes, e.g. significant performance degradation due to the presence of short cycles or very high decoding latency. In this thesis, we will focus on the practical realisation of finite-length LDPC codes and devise algorithms to tackle those issues. Firstly, rate-compatible (RC) LDPC codes with short/moderate block lengths are investigated on the basis of optimising the graphical structure of the tanner graph (TG), in order to achieve a variety of code rates (0.1 < R < 0.9) by only using a single encoder-decoder pair. As is widely recognised in the literature, the presence of short cycles considerably reduces the overall performance of LDPC codes which significantly limits their application in communication systems. To reduce the impact of short cycles effectively for different code rates, algorithms for counting short cycles and a graph-related metric called Extrinsic Message Degree (EMD) are applied with the development of the proposed puncturing and extension techniques. A complete set of simulations are carried out to demonstrate that the proposed RC designs can largely minimise the performance loss caused by puncturing or extension. Secondly, at the decoding end, we study novel decoding strategies which compensate for the negative effect of short cycles by reweighting part of the extrinsic messages exchanged between the nodes of a TG. The proposed reweighted belief propagation (BP) algorithms aim to implement efficient decoding, i.e. accurate signal reconstruction and low decoding latency, for LDPC codes via various design methods. A variable factor appearance probability belief propagation (VFAP-BP) algorithm is proposed along with an improved version called a locally-optimized reweighted (LOW)-BP algorithm, both of which can be employed to enhance decoding performance significantly for regular and irregular LDPC codes. More importantly, the optimisation of reweighting parameters only takes place in an offline stage so that no additional computational complexity is required during the real-time decoding process. Lastly, two iterative detection and decoding (IDD) receivers are presented for multiple-input multiple-output (MIMO) systems operating in a spatial multiplexing configuration. QR decomposition (QRD)-type IDD receivers utilise the proposed multiple-feedback (MF)-QRD or variable-M (VM)-QRD detection algorithm with a standard BP decoding algorithm, while knowledge-aided (KA)-type receivers are equipped with a simple soft parallel interference cancellation (PIC) detector and the proposed reweighted BP decoders. In the uncoded scenario, the proposed MF-QRD and VM-QRD algorithms are shown to approach optimal performance, yet require a reduced computational complexity. In the LDPC-coded scenario, simulation results have illustrated that the proposed QRD-type IDD receivers can offer near-optimal performance after a small number of detection/decoding iterations and the proposed KA-type IDD receivers significantly outperform receivers using alternative decoding algorithms, while requiring similar decoding complexity

Approximate inference in massive MIMO scenarios with moment matching techniques

Mención Internacional en el título de doctorThis Thesis explores low-complexity inference probabilistic algorithms in high-dimensional Multiple-Input Multiple-Output (MIMO) systems and high order M-Quadrature Amplitude Modulation (QAM) constellations. Several modern communications systems are using more and more antennas to maximize spectral efficiency, in a new phenomena call Massive MIMO. However, as the number of antennas and/or the order of the constellation grow several technical issues have to be tackled, one of them is that the symbol detection complexity grows fast exponentially with the system dimension. Nowadays the design of massive MIMO low-complexity receivers is one important research line in MIMO because symbol detection can no longer rely on conventional approaches such as Maximum a Posteriori (MAP) due to its exponential computation complexity. This Thesis proposes two main results. On one hand a hard decision low-complexity MIMO detector based on Expectation Propagation (EP) algorithm which allows to iteratively approximate within polynomial cost the posterior distribution of the transmitted symbols. The receiver is named Expectation Propagation Detector (EPD) and its solution evolves from Minimum Mean Square Error (MMSE) solution and keeps per iteration the MMSE complexity which is dominated by a matrix inversion. Hard decision Symbol Error Rate (SER) performance is shown to remarkably improve state-of-the-art solutions of similar complexity. On the other hand, a soft-inference algorithm, more suitable to modern communication systems with channel codification techniques such as Low- Density Parity-Check (LDPC) codes, is also presented. Modern channel decoding techniques need as input Log-Likehood Ratio (LLR) information for each coded bit. In order to obtain that information, firstly a soft bit inference procedure must be performed. In low-dimensional scenarios, this can be done by marginalization over the symbol posterior distribution. However, this is not feasible at high-dimension. While EPD could provide this probabilistic information, it is shown that its probabilistic estimates are in general poor in the low Signal-to-Noise Ratio (SNR) regime. In order to solve this inconvenience a new algorithm based on the Expectation Consistency (EC) algorithm, which generalizes several algorithms such as Belief. Propagation (BP) and EP itself, was proposed. The proposed algorithm called Expectation Consistency Detector (ECD) maps the inference problem as an optimization over a non convex function. This new approach allows to find stationary points and tradeoffs between accuracy and convergence, which leads to robust update rules. At the same complexity cost than EPD, the new proposal achieves a performance closer to channel capacity at moderate SNR. The result reveals that the probabilistic detection accuracy has a relevant impact in the achievable rate of the overall system. Finally, a modified ECD algorithm is presented, with a Turbo receiver structure where the output of the decoder is fed back to ECD, achieving performance gains in all block lengths simulated. The document is structured as follows. In Chapter I an introduction to the MIMO scenario is presented, the advantages and challenges are exposed and the two main scenarios of this Thesis are set forth. Finally, the motivation behind this work, and the contributions are revealed. In Chapters II and III the state of the art and our proposal are presented for Hard Detection, whereas in Chapters IV and V are exposed for Soft Inference Detection. Eventually, a conclusion and future lines can be found in Chapter VI.Esta Tesis aborda algoritmos de baja complejidad para la estimación probabilística en sistemas de Multiple-Input Multiple-Output (MIMO) de grandes dimensiones con constelaciones M-Quadrature Amplitude Modulation (QAM) de alta dimensionalidad. Son diversos los sistemas de comunicaciones que en la actualidad están utilizando más y más antenas para maximizar la eficiencia espectral, en un nuevo fenómeno denominado Massive MIMO. Sin embargo los incrementos en el número de antenas y/o orden de la constelación presentan ciertos desafíos tecnológicos que deben ser considerados. Uno de ellos es la detección de los símbolos transmitidos en el sistema debido a que la complejidad aumenta más rápido que las dimensiones del sistema. Por tanto el diseño receptores para sistemas Massive MIMO de baja complejidad es una de las importantes líneas de investigación en la actualidad en MIMO, debido principalmente a que los métodos tradicionales no se pueden implementar en sistemas con decenas de antenas, cuando lo deseable serían centenas, debido a que su coste es exponencial. Los principales resultados en esta Tesis pueden clasificarse en dos. En primer lugar un receptor MIMO para decisión dura de baja complejidad basado en el algoritmo Expectation Propagation (EP) que permite de manera iterativa, con un coste computacional polinómico por iteración, aproximar la distribución a posteriori de los símbolos transmitidos. El algoritmo, denominado Expectation Propagation Detector (EPD), es inicializado con la solución del algoritmo Minimum Mean Square Error (MMSE) y mantiene el coste de este para todas las iteraciones, dominado por una inversión de matriz. El rendimiento del decisor en probabilidad de error de símbolo muestra ganancias remarcables con respecto a otros métodos en la literatura con una complejidad similar. En segundo lugar, un algoritmo que provee una estimación blanda, información que es más apropiada para los actuales sistemas de comunicaciones que utilizan codificación de canal, como pueden ser códigos Low-Density Parity-Check (LDPC). La información necesaria para estos decodificadores de canal es Log-Likehood Ratio (LLR) para cada uno de los bits codificados. En escenarios de bajas dimensiones se pueden calcular las marginales de la distribución a posteriori, pero en escenarios de grandes dimensiones no es viable, aunque EPD puede proporcionar este tipo de información a la entrada del decodificador, dicha información no es la mejor al estar el algoritmo pensado para detección dura, sobre todo se observa este fenómeno en el rango de baja Signal-to-Noise Ratio (SNR). Para solucionar este problema se propone un nuevo algoritmo basado en Expectation Consistency (EC) que engloba diversos algoritmos como pueden ser Belief Propagation (BP) y el algoritmo EP propuesto con anterioridad. El nuevo algoritmo llamado Expectation Consistency Detector (ECD), trata el problema como una optimización de una función no convexa. Esta aproximación permite encontrar los puntos estacionarios y la relación entre precisión y convergencia, que permitirán reglas de actualización más robustas y eficaces. Con la misma compleja que el algoritmo propuesto inicialmente, ECD permite rendimientos más próximos a la capacidad del canal en regímenes moderados de SNR. Los resultados muestran que la precisión tiene un gran efecto en la tasa que alcanza el sistema. Finalmente una versión modificada de ECD es propuesta en una arquitectura típica de los Turbo receptores, en la que la salida del decodificador es la entrada del receptor, y que permite ganancias en el rendimiento en todas las longitudes de código simuladas. El presente documento está estructurado de la siguiente manera. En el primer Capítulo I, se realiza una introducción a los sistemas MIMO, presentando sus ventajas, desventajas, problemas abiertos. Los modelos que se utilizaran en la tesis y la motivación con la que se inició esta tesis son expuestos en este primer capítulo. En los Capítulos II y III el estado del arte y nuestra propuesta para detección dura son presentados, mientras que en los Capítulos IV y V se presentan para detección suave. Finalmente las conclusiones que pueden obtenerse de esta Tesis y futuras líneas de investigación son expuestas en el Capítulo VI.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Juan José Murillo Fuentes.- Secretario: Gonzalo Vázquez Vilar.- Vocal: María Isabel Valera Martíne