Fountain Codes under Maximum Likelihood Decoding

This dissertation focuses on fountain codes under maximum likelihood (ML) decoding. First LT codes are considered under a practical and widely used ML decoding algorithm known as inactivation decoding. Different analysis techniques are presented to characterize the decoding complexity. Next an upper bound to the probability of decoding failure of Raptor codes under ML decoding is provided. Then, the distance properties of an ensemble of fixed-rate Raptor codes with linear random outer codes are analyzed. Finally, a novel class of fountain codes is presented, which consists of a parallel concatenation of a block code with a linear random fountain code.Comment: PhD Thesi

New Approaches to the Analysis and Design of Reed-Solomon Related Codes

The research that led to this thesis was inspired by Sudan's breakthrough that demonstrated that Reed-Solomon codes can correct more errors than previously thought. This breakthrough can render the current state-of-the-art Reed-Solomon decoders obsolete. Much of the importance of Reed-Solomon codes stems from their ubiquity and utility. This thesis takes a few steps toward a deeper understanding of Reed-Solomon codes as well as toward the design of efficient algorithms for decoding them. After studying the binary images of Reed-Solomon codes, we proceeded to analyze their performance under optimum decoding. Moreover, we investigated the performance of Reed-Solomon codes in network scenarios when the code is shared by many users or applications. We proved that Reed-Solomon codes have many more desirable properties. Algebraic soft decoding of Reed-Solomon codes is a class of algorithms that was stirred by Sudan's breakthrough. We developed a mathematical model for algebraic soft decoding. By designing Reed-Solomon decoding algorithms, we showed that algebraic soft decoding can indeed approach the ultimate performance limits of Reed-Solomon codes. We then shifted our attention to products of Reed-Solomon codes. We analyzed the performance of linear product codes in general and Reed-Solomon product codes in particular. Motivated by these results we designed a number of algorithms, based on Sudan's breakthrough, for decoding Reed-Solomon product codes. Lastly, we tackled the problem of analyzing the performance of sphere decoding of lattice codes and linear codes, e.g., Reed-Solomon codes, with an eye on the tradeoff between performance and complexity.</p

Performance analysis of concatenated coding schemes

Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 1999.Thesis (Master's) -- Bilkent University, 1999.Includes bibliographical references leaves 59-60.Akkor, GünM.S

Techniques for improving the performance of frequency-hopped multiple-access communication systems

Imperial Users onl

Product Code Optimization for Determinate State LDPC Decoding in Robust Image Transmission

We propose a novel scheme for error resilient image transmission. The proposed scheme employs a product coder consisting of LDPC codes and RS codes in order to deal effectively with bit errors. The efficiency of the proposed scheme is based on the exploitation of determinate symbols in Tanner graph decoding of LDPC codes and a novel product code optimization technique based on error estimation. Experimental evaluation demonstrates the superiority of the proposed system in comparison to recent state-of-the art techniques for image transmission

Exposing a waveform interface to the wireless channel for scalable video broadcast

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 157-167).Video broadcast and mobile video challenge the conventional wireless design. In broadcast and mobile scenarios the bit-rate supported by the channel differs across receivers and varies quickly over time. The conventional design however forces the source to pick a single bit-rate and degrades sharply when the channel cannot support it. This thesis presents SoftCast, a clean-slate design for wireless video where the source transmits one video stream that each receiver decodes to a video quality commensurate with its specific instantaneous channel quality. To do so, SoftCast ensures the samples of the digital video signal transmitted on the channel are linearly related to the pixels' luminance. Thus, when channel noise perturbs the transmitted signal samples, the perturbation naturally translates into approximation in the original video pixels. Hence, a receiver with a good channel (low noise) obtains a high fidelity video, and a receiver with a bad channel (high noise) obtains a low fidelity video. SoftCast's linear design in essence resembles the traditional analog approach to communication, which was abandoned in most major communication systems, as it does not enjoy the theoretical opimality of the digital separate design in point-topoint channels nor its effectiveness at compressing the source data. In this thesis, I show that in combination with decorrelating transforms common to modern digital video compression, the analog approach can achieve performance competitive with the prevalent digital design for a wide variety of practical point-to-point scenarios, and outperforms it in the broadcast and mobile scenarios. Since the conventional bit-pipe interface of the wireless physical layer (PHY) forces the separation of source and channel coding, to realize SoftCast, architectural changes to the wireless PHY are necessary. This thesis discusses the design of RawPHY, a reorganization of the PHY which exposes a waveform interface to the channel while shielding the designers of the higher layers from much of the perplexity of the wireless channel. I implement SoftCast and RawPHY using the GNURadio software and the USRP platform. Results from a 20-node testbed show that SoftCast improves the average video quality (i.e., PSNR) across diverse broadcast receivers in our testbed by up to 5.5 dB in comparison to conventional single- or multi-layer video. Even for a single receiver, it eliminates video glitches caused by mobility and increases robustness to packet loss by an order of magnitude.by Szymon Kazimierz Jakubczak.Ph.D

Expander Graphs and Coding Theory

Expander graphs are highly connected sparse graphs which lie at the interface of many different fields of study. For example, they play important roles in prime sieves, cryptography, compressive sensing, metric embedding, and coding theory to name a few. This thesis focuses on the connections between sparse graphs and coding theory. It is a major challenge to explicitly construct sparse graphs with good expansion properties, for example Ramanujan graphs. Nevertheless, explicit constructions do exist, and in this thesis, we survey many of these constructions up to this point including a new construction which slightly improves on an earlier edge expansion bound. The edge expansion of a graph is crucial in applications, and it is well-known that computing the edge expansion of an arbitrary graph is NP-hard. We present a simple algo-rithm for approximating the edge expansion of a graph using linear programming techniques. While Andersen and Lang (2008) proved similar results, our analysis attacks the problem from a different vantage point and was discovered independently. The main contribution in the thesis is a new result in fast decoding for expander codes. Current algorithms in the literature can decode a constant fraction of errors in linear time but require that the underlying graphs have vertex expansion at least 1/2. We present a fast decoding algorithm that can decode a constant fraction of errors in linear time given any vertex expansion (even if it is much smaller than 1/2) by using a stronger local code, and the fraction of errors corrected almost doubles that of Viderman (2013)

Error-Correction Coding and Decoding: Bounds, Codes, Decoders, Analysis and Applications

Coding; Communications; Engineering; Networks; Information Theory; Algorithm