Two-Dimensional Source Coding by Means of Subblock Enumeration

A technique of lossless compression via substring enumeration (CSE) attains compression ratios as well as popular lossless compressors for one-dimensional (1D) sources. The CSE utilizes a probabilistic model built from the circular string of an input source for encoding the source.The CSE is applicable to two-dimensional (2D) sources such as images by dealing with a line of pixels of 2D source as a symbol of an extended alphabet. At the initial step of the CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity increase exponentially when the size of source becomes large. To reduce the time complexity, we propose a new CSE which can encode a 2D source in block-by-block instead of line-by-line. The proposed CSE utilizes the flat torus of an input 2D source as a probabilistic model for encoding the source instead of the circular string of the source. Moreover, we analyze the limit of the average codeword length of the proposed CSE for general sources.Comment: 5 pages, Submitted to ISIT201

A Universal Two-Dimensional Source Coding by Means of Subblock Enumeration

The technique of lossless compression via substring enumeration (CSE) is a kind of enumerative code and uses a probabilistic model built from the circular string of an input source for encoding a one-dimensional (1D) source. CSE is applicable to two-dimensional (2D) sources, such as images, by dealing with a line of pixels of a 2D source as a symbol of an extended alphabet. At the initial step of CSE encoding process, we need to output the number of occurrences of all symbols of the extended alphabet, so that the time complexity increases exponentially when the size of source becomes large. To reduce computational time, we can rearrange pixels of a 2D source into a 1D source string along a space-filling curve like a Hilbert curve. However, information on adjacent cells in a 2D source may be lost in the conversion. To reduce the time complexity and compress a 2D source without converting to a 1D source, we propose a new CSE which can encode a 2D source in a block-by-block fashion instead of in a line-by-line fashion. The proposed algorithm uses the flat torus of an input 2D source as a probabilistic model instead of the circular string of the source. Moreover, we prove the asymptotic optimality of the proposed algorithm for 2D general sources

PERFORMANCE LIMITS FOR ENERGY-CONSTRAINED COMMUNICATION SYSTEMS

Ph.DDOCTOR OF PHILOSOPH

Intelligent Processing in Wireless Communications Using Particle Swarm Based Methods

There are a lot of optimization needs in the research and design of wireless communica- tion systems. Many of these optimization problems are Nondeterministic Polynomial (NP) hard problems and could not be solved well. Many of other non-NP-hard optimization problems are combinatorial and do not have satisfying solutions either. This dissertation presents a series of Particle Swarm Optimization (PSO) based search and optimization algorithms that solve open research and design problems in wireless communications. These problems are either avoided or solved approximately before. PSO is a bottom-up approach for optimization problems. It imposes no conditions on the underlying problem. Its simple formulation makes it easy to implement, apply, extend and hybridize. The algorithm uses simple operators like adders, and multipliers to travel through the search space and the process requires just five simple steps. PSO is also easy to control because it has limited number of parameters and is less sensitive to parameters than other swarm intelligence algorithms. It is not dependent on initial points and converges very fast. Four types of PSO based approaches are proposed targeting four different kinds of problems in wireless communications. First, we use binary PSO and continuous PSO together to find optimal compositions of Gaussian derivative pulses to form several UWB pulses that not only comply with the FCC spectrum mask, but also best exploit the avail- able spectrum and power. Second, three different PSO based algorithms are developed to solve the NLOS/LOS channel differentiation, NLOS range error mitigation and multilateration problems respectively. Third, a PSO based search method is proposed to find optimal orthogonal code sets to reduce the inter carrier interference effects in an frequency redundant OFDM system. Fourth, a PSO based phase optimization technique is proposed in reducing the PAPR of an frequency redundant OFDM system. The PSO based approaches are compared with other canonical solutions for these communication problems and showed superior performance in many aspects. which are confirmed by analysis and simulation results provided respectively. Open questions and future Open questions and future works for the dissertation are proposed to serve as a guide for the future research efforts

Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective

Bibliography: p. 208-225.Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques

Adaptive Discontinuous Galerkin Finite Element Methods for Second and Fourth Order Elliptic Partial Differential Equations

A unified mathematical and computational framework for implementation of an adaptive discontinuous Galerkin (DG) finite element method (FEM) is developed using the symmetric interior penalty formulation to obtain numerical approximations to solutions of second and fourth order elliptic partial differential equations. The DG-FEM formulation implemented allows for h-adaptivity and has the capability to work with linear, quadratic, cubic, and quartic polynomials on triangular elements in two dimensions. Two different formulations of DG are implemented based on how fluxes are represented on interior edges and comparisons are made. Explicit representations of two a posteriori error estimators, a residual based type and a “local” based type, are extended to include both Dirichlet and Neumann type boundary conditions on bounded domains. New list-based approaches to data management in an adaptive computational environment are introduced in an effort to utilize computational resources in an efficient and flexible manner

Tilatiivis toteutus tiedon tiivistämiseen osamerkkijonoja luettelemalla

Häviöttömässä tiedon tiivistämisessä annetusta datasta luodaan tiiviste, joka vie mahdollisimman vähän tilaa suhteessa alkuperäiseen dataan. Tiivisteestä on voitava palauttaa identtinen kopio alkuperäisestä datasta. Tutkielmassa käsitellään häviötöntä tiivistysmenetelmää, joka tutkii tiivistettävää dataa, eli merkkijonoa tai tekstiä, kokonaisuutena, eikä esimerkiksi pieni osa kerrallaan. Menetelmä välittää tiivisteen purkajalle osamerkkijonojen esiintymismääriä tekstissä. Osamerkkijonot käsitellään ennalta tunnetussa järjestyksessä lyhyimmästä pisimpään, jolloin kumpikin osapuoli osaa liittää esiintymismäärän oikeaan osamerkkijonoon. Jotkut esiintymismäärät voivat olla nollia kertomassa, ettei osamerkkijono esiinny tekstissä. Tiivistyvyys saavutetaan huomaamalla, että aiemmin välitetyt osamerkkijonot rajaavat millaisia pidemmät merkkijonot voivat olla. Tällöin osa esiintymismääristä voidaan jättää välittämättä, tai välittämiseen käyttää vähemmän tilaa. Osamerkkijonoja, joiden esiintymismäärä täytyy välittää, karakterisoidaan maksimaalisuuden käsitteen avulla. Maksimaalisten osamerkkijonojen etsiminen ja osamerkkijonojen esiintymismäärien laskeminen paljaasta tekstistä on hidasta. Siksi teksti täytyy tallettaa tietorakenteeseen, joka tukee tarvittuja operaatioita tehden niistä nopeita. Tällaiset tietorakenteet vievät enemmän tilaa kuin paljas teksti. Koska tutkittavassa tiivistysmenetelmässä koko tiivistettävä teksti käsitellään kokonaisuutena, muistinkäytön tehokkuus korostuu. Tutkielmassa toteutetaan tiivistysmenetelmä käyttäen tilatiiviistä tietorakennetta nimeltä kaksisuuntainen BWT-indeksi. Tilatiiviit tietorakenteet vievät vain vähän enemmän tilaa, kuin niihin talletettu data. Tästä huolimatta ne toteuttavat talletettua dataa käsitteleviä operaatioita tehokkaasti. Toteutukselle suoritetut kokeet osoittavat muistinkäytön pysyvän kohtuullisena, jolloin suurempienkin tietomäärien tiivistys on mahdollista