Codes on Graphs and More

Modern communication systems strive to achieve reliable and efficient information transmission and storage with affordable complexity. Hence, efficient low-complexity channel codes providing low probabilities for erroneous receptions are needed. Interpreting codes as graphs and graphs as codes opens new perspectives for constructing such channel codes. Low-density parity-check (LDPC) codes are one of the most recent examples of codes defined on graphs, providing a better bit error probability than other block codes, given the same decoding complexity. After an introduction to coding theory, different graphical representations for channel codes are reviewed. Based on ideas from graph theory, new algorithms are introduced to iteratively search for LDPC block codes with large girth and to determine their minimum distance. In particular, new LDPC block codes of different rates and with girth up to 24 are presented. Woven convolutional codes are introduced as a generalization of graph-based codes and an asymptotic bound on their free distance, namely, the Costello lower bound, is proven. Moreover, promising examples of woven convolutional codes are given, including a rate 5/20 code with overall constraint length 67 and free distance 120. The remaining part of this dissertation focuses on basic properties of convolutional codes. First, a recurrent equation to determine a closed form expression of the exact decoding bit error probability for convolutional codes is presented. The obtained closed form expression is evaluated for various realizations of encoders, including rate 1/2 and 2/3 encoders, of as many as 16 states. Moreover, MacWilliams-type identities are revisited and a recursion for sequences of spectra of truncated as well as tailbitten convolutional codes and their duals is derived. Finally, the dissertation is concluded with exhaustive searches for convolutional codes of various rates with either optimum free distance or optimum distance profile, extending previously published results

Combinatorial Methods in Coding Theory

This thesis is devoted to a range of questions in applied mathematics and signal processing motivated by applications in error correction, compressed sensing, and writing on non-volatile memories. The underlying thread of our results is the use of diverse combinatorial methods originating in coding theory and computer science. The thesis addresses three groups of problems. The first of them is aimed at the construction and analysis of codes for error correction. Here we examine properties of codes that are constructed using random and structured graphs and hypergraphs, with the main purpose of devising new decoding algorithms as well as estimating the distribution of Hamming weights in the resulting codes. Some of the results obtained give the best known estimates of the number of correctable errors for codes whose decoding relies on local operations on the graph. In the second part we address the question of constructing sampling operators for the compressed sensing problem. This topic has been the subject of a large body of works in the literature. We propose general constructions of sampling matrices based on ideas from coding theory that act as near-isometric maps on almost all sparse signal. This matrices can be used for dimensionality reduction and compressed sensing. In the third part we study the problem of reliable storage of information in non-volatile memories such as flash drives. This problem gives rise to a writing scheme that relies on relative magnitudes of neighboring cells, known as rank modulation. We establish the exact asymptotic behavior of the size of codes for rank modulation and suggest a number of new general constructions of such codes based on properties of finite fields as well as combinatorial considerations

Deep filter banks for texture recognition, description, and segmentation

Visual textures have played a key role in image understanding because they convey important semantics of images, and because texture representations that pool local image descriptors in an orderless manner have had a tremendous impact in diverse applications. In this paper we make several contributions to texture understanding. First, instead of focusing on texture instance and material category recognition, we propose a human-interpretable vocabulary of texture attributes to describe common texture patterns, complemented by a new describable texture dataset for benchmarking. Second, we look at the problem of recognizing materials and texture attributes in realistic imaging conditions, including when textures appear in clutter, developing corresponding benchmarks on top of the recently proposed OpenSurfaces dataset. Third, we revisit classic texture representations, including bag-of-visual-words and the Fisher vectors, in the context of deep learning and show that these have excellent efficiency and generalization properties if the convolutional layers of a deep model are used as filter banks. We obtain in this manner state-of-the-art performance in numerous datasets well beyond textures, an efficient method to apply deep features to image regions, as well as benefit in transferring features from one domain to another.Comment: 29 pages; 13 figures; 8 table

Applications of graph-based codes in networks: analysis of capacity and design of improved algorithms

The conception of turbo codes by Berrou et al. has created a renewed interest in modern graph-based codes. Several encouraging results that have come to light since then have fortified the role these codes shall play as potential solutions for present and future communication problems. This work focuses on both practical and theoretical aspects of graph-based codes. The thesis can be broadly categorized into three parts. The first part of the thesis focuses on the design of practical graph-based codes of short lengths. While both low-density parity-check codes and rateless codes have been shown to be asymptotically optimal under the message-passing (MP) decoder, the performance of short-length codes from these families under MP decoding is starkly sub-optimal. This work first addresses the structural characterization of stopping sets to understand this sub-optimality. Using this characterization, a novel improved decoder that offers several orders of magnitude improvement in bit-error rates is introduced. Next, a novel scheme for the design of a good rate-compatible family of punctured codes is proposed. The second part of the thesis aims at establishing these codes as a good tool to develop reliable, energy-efficient and low-latency data dissemination schemes in networks. The problems of broadcasting in wireless multihop networks and that of unicast in delay-tolerant networks are investigated. In both cases, rateless coding is seen to offer an elegant means of achieving the goals of the chosen communication protocols. It was noticed that the ratelessness and the randomness in encoding process make this scheme specifically suited to such network applications. The final part of the thesis investigates an application of a specific class of codes called network codes to finite-buffer wired networks. This part of the work aims at establishing a framework for the theoretical study and understanding of finite-buffer networks. The proposed Markov chain-based method extends existing results to develop an iterative Markov chain-based technique for general acyclic wired networks. The framework not only estimates the capacity of such networks, but also provides a means to monitor network traffic and packet drop rates on various links of the network.Ph.D.Committee Chair: Fekri, Faramarz; Committee Member: Li, Ye; Committee Member: McLaughlin, Steven; Committee Member: Sivakumar, Raghupathy; Committee Member: Tetali, Prasa

The Fold with The Decline of the Empire: Three Essays and a Letter

This thesis implements the principles of Gilles Deleuze’s theory modeled in The Fold [1993] , a framework for presenting multiple perspectives simultaneously. The Deleuzian fold is established as a lens through which to view artists’ approaches to their process of making, with complex linkages referencing aspects of their surroundings, their generation and previous generations. The investigation focuses on the fold concept’s analysis of the production of subjectivity—the process of shifting perspective recursively. The methodology builds on theories and critical literature to: define the fold; give visual context by presenting its role in Cubism; establish the fold’s integral role to the way our brain works—the process that concurrently collects, edits, and stores information as comparisons—that is the fabric of the contemporary arena; present examples of its applications in contemporary artists’ processes and the significance of folding and unfolding within my work. The thesis is structured in two sections: ‘The Fold’ and ‘Artists Background and Imagery’. ‘The Fold’ establishes theory surrounding principles of the Deleuzian fold, the way it coincides with the Cubist movement, and its application in contemporary artists’ processes. ‘Artist’s Background and Imagery’ is structured to present ‘The Fold’ research’s relevance to my background and application in my practice. The multiple perspectives I have lived as son to immigrants—mother a refugee from Baghdad to Israel, father rooted ten generations in Jerusalem—and first in my extended family to attend college, constitutes the borderless, imbricated placement of thought that founds my imagery and institutes my making process. The act of folding is the act of evolving possibilities. The subject of the fold suggests—as the aspiration of a work of art—that witnessing a work of art is witnessing the profound act of life

On Folding: Towards a New Field of Interdisciplinary Research

It is only recently, with the increasing interest in origami and folding in natural sciences and the humanities, that the fold as a new conception in a whole range of disciplines has begun to be conceived in a broader way. Folding as a material and structural process offers a new methodology to think about the close relationship of matter, form and code. It henceforth crosses out old dichotomies, such as the organic and the inorganic or nature and technology, and blurs the boundaries between experimental, conceptual and historical approaches. This anthology aims to unfold this new interdisciplinary field and its disciplinary impact, ranging from materials science, biology, architecture, and mathematics to literature and philosophy

A creative journey developing an integrated high-fashion knitwear development process using computerized seamless v-bed knitting systems

This PhD applied a participatory action research approach to address the organizational problems that compromise the use of computerized seamless V-bed knitwear systems in the high-fashion knitwear sector. The research is a response to a widely acknowledged conflict between high-fashion design processes and processes by which designs are developed on computerized seamless V-bed knitting systems. The social, organizational, and technical aspects of design and manufacturing using computerized seamless V-bed knitting technology in high-fashion knitwear design were analyzed as a socio-technical system (STS). This approach led to a review of the workflows, tasks and roles; identifying and testing new design and manufacturing processes, design methods, and garment solutions; creating a theory model of a new integrated design process; and developing and testing new design processes, design methods, and fashion design education courses that teach these new fashion knitwear approaches.The research was undertaken using a Shima Seiki WholeGarment® system, a current computerized seamless V-bed knitting design and manufacturing technology. The studio workspace, yarn, use of the Shima Seiki system; involvement in fashion projects, and associate supervision were provided by the Department of Agriculture and Food Western Australia (DAFWA).The research demonstrated a high-fashion knitwear designer can undertake all aspects of managing computerized seamless V-bed knitwear design and production to the completion of 1st sample, the first successful sample of a new fabric or garment, was produced using the computer knit data. This finding was developed into a new integrated design process and design methods that remove most of the problems of computerized seamless V-bed knitting systems in high-fashion and offers additional benefits including reduction in time to market and design costs, and increases in the creative solution space for high-fashion knitwear design.The researcher has called this new role, a ‘designer-interpreter’ to denote a professional knitwear designer with additional training in managing computerized seamless knitting machines. Within the context of ‘designer-interpreter’, this research also established the feasibility of a new form of a ‘post-industrial craft-based one-person knitwear production system’

The zone of "becoming": game, text and technicity in videogame narratives

Videogames have emerged as arguably the most prominent form of entertainment in recent years. Their versatility has made them key contributory factors in social, literary, cultural and philosophical discourse; however, critics also tend to see videogames as posing a threat to established cultural parameters. This thesis argues that videogames are firmly grounded in older media and they are important for the development of the notions of textuality, technicity and identity that literary and cultural theories have been debating in recent years. As its point of departure, the thesis takes the contested role of videogames as storytelling media. Challenging the opposition between games and narratives that is posited in earlier research, the framework of the Derridean concept of supplementarity has been adopted to illustrate how the ludic and the narrative inform each other's core, and yet retain their media-specific identities. It is also vital to consider how the technicity and narrative of games inform their perception as texts. Videogames provide a direct illustration of this but they develop on similar principles in earlier media instead of doing something entirely 'new'. The multitelic structure of videogames tends to be looked upon as symptomatic of novelty; in reality, however, they illustrate more clearly the inherent nature of telos in all narrative media