196 research outputs found

    CONVERGENCE IMPROVEMENT OF ITERATIVE DECODERS

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    Iterative decoding techniques shaked the waters of the error correction and communications field in general. Their amazing compromise between complexity and performance offered much more freedom in code design and made highly complex codes, that were being considered undecodable until recently, part of almost any communication system. Nevertheless, iterative decoding is a sub-optimum decoding method and as such, it has attracted huge research interest. But the iterative decoder still hides many of its secrets, as it has not been possible yet to fully describe its behaviour and its cost function. This work presents the convergence problem of iterative decoding from various angles and explores methods for reducing any sub-optimalities on its operation. The decoding algorithms for both LDPC and turbo codes were investigated and aspects that contribute to convergence problems were identified. A new algorithm was proposed, capable of providing considerable coding gain in any iterative scheme. Moreover, it was shown that for some codes the proposed algorithm is sufficient to eliminate any sub-optimality and perform maximum likelihood decoding. Its performance and efficiency was compared to that of other convergence improvement schemes. Various conditions that can be considered critical to the outcome of the iterative decoder were also investigated and the decoding algorithm of LDPC codes was followed analytically to verify the experimental results

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

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    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

    Turbo codes: convergence phenomena & non-binary constructions

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    The introduction of turbo codes in 1993 provided a code structure that could approach Shannon limit performance whilst remaining practically decodeable. Much subsequent work has focused on this remarkable structure, attempting to explain its performance and to extend or modify it. This thesis builds on this research providing insights into the convergence behaviour of the iterative decoder for turbo codes and examining the potential of turbo codes constructed from non-binary component codes. The first chapter of this thesis gives a brief history of coding theory, providing context for the work. Chapter two explains in detail both the turbo encoding and decoding structures considered. Chapter three presents new work on convergence phenomena observed in the iterative decoding process. These results emphasise the dynamic nature of the decoder and allow for both a stopping criteria and ARQ scheme to be proposed. Chapters four and five present the work on non-binary turbo codes. First the problem of choosing good component codes is discussed and an achievability bound on the dominant parameter affecting their performance is derived. Searches for good component codes over a number of small rings are then conducted, and simulation results presented. The new results, and suggestions for further work are summarised in the conclusion of Chapter six

    Density Evolution for Asymmetric Memoryless Channels

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    Density evolution is one of the most powerful analytical tools for low-density parity-check (LDPC) codes and graph codes with message passing decoding algorithms. With channel symmetry as one of its fundamental assumptions, density evolution (DE) has been widely and successfully applied to different channels, including binary erasure channels, binary symmetric channels, binary additive white Gaussian noise channels, etc. This paper generalizes density evolution for non-symmetric memoryless channels, which in turn broadens the applications to general memoryless channels, e.g. z-channels, composite white Gaussian noise channels, etc. The central theorem underpinning this generalization is the convergence to perfect projection for any fixed size supporting tree. A new iterative formula of the same complexity is then presented and the necessary theorems for the performance concentration theorems are developed. Several properties of the new density evolution method are explored, including stability results for general asymmetric memoryless channels. Simulations, code optimizations, and possible new applications suggested by this new density evolution method are also provided. This result is also used to prove the typicality of linear LDPC codes among the coset code ensemble when the minimum check node degree is sufficiently large. It is shown that the convergence to perfect projection is essential to the belief propagation algorithm even when only symmetric channels are considered. Hence the proof of the convergence to perfect projection serves also as a completion of the theory of classical density evolution for symmetric memoryless channels.Comment: To appear in the IEEE Transactions on Information Theor

    Low-Complexity Multiple-Component Turbo-Decoding-Aided Hybrid ARQ

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    Optimisation of Iterative Multi-user Receivers using Analytical Tools

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    The objective of this thesis is to develop tools for the analysis and optimization of an iterative receiver. These tools can be applied to most soft-in soft-out (SISO) receiver components. For illustration purposes we consider a multi-user DS-CDMA system with forward error correction that employs iterative multi-user detection based on soft interference cancellation and single user decoding. Optimized power levels combined with adaptive scheduling allows for efficient utilization of receiver resources for heavily loaded systems.¶ Metric transfer analysis has been shown to be an accurate method of predicting the convergence behavior of iterative receivers. EXtrinsic Information (EXIT), fidelity (FT) and variance (VT) transfer analysis are well-known methods, however the relationship between the different approaches has not been explored in detail. We compare the metrics numerically and analytically and derive functions to closely approximate the relationship between them. The result allows for easy translation between EXIT, FT and VT methods. Furthermore, we extend the JJ function, which describes mutual information as a function of variance, to fidelity and symbol error variance, the Rayleigh fading channel model and a channel estimate. ...
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