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The diffusion approximation to the equation of transfer (Boltzmann transport equation) is usually applied to media where scattering dominates the interactions. Diffusion approximation helps in significant savings in terms of code complexity and computational time. However, this approximation often has significant error. Error due to the inherent nature of a physics model is called model error. Information about the model error associated with the diffusion approximation is clearly desirable. An indirect measure of model error is a quantity that is related in some way to the error but not equal to the error. In general, indirect measures of error are expected to be less costly than direct measures. Perhaps the most well-known indirect measure of the diffusion model error is the variable-Eddington tensor. This tensor provides a great deal of information about the angular dependence of the angular intensity solution, but it is not always simple to interpret. We define a new indirect measure of the diffusion model error called the diffusion model error source (DME source). When this DME source is added to the diffusion equation, the transport solution for the angular-integrated intensity is obtained. In contrast to the variable-Eddington tensor, our DME source is a scalar that is conceptually easy to interpret. In addition to defining the DME source analytically, we show how to generate this source numerically relative to the Sn radiative transfer equations with linear-discontinuous spatial discretization. This numerical source is computationally tested and shown to reproduce the Sn solution for a number of problems. Our radiative transfer model solves a coupled, time dependent, multi-frequency, 1-D slab equation and material heat transfer equation. We then use diffusion approximation to solve the same problem. The difference due to this approximation can be modelled by a “diffusion source”. The diffusion source is defined as an amount of inhomogeneous source that, when added to a diffusion calculation, gives a solution for the angle-integrated intensity that is equal to the transport solution.

Since the rediscovery, LDPC codes attract a large amount of research efforts. In 1998, nonbinary LDPC codes were firstly investigated and the results shown that they are better than their binary counterparts in performance. Recently, there is always a requirement from the industry to design applied nonbinary LDPC codes. In this dissertation, we firstly propose a novel class of quasi-cyclic (QC) LDPC codes. This class of QC-LDPC codes embraces both linear encoding complexity and excellent compatibility in various degree distributions and nonbinary expansions. We show by simulation results that our proposed QC-LDPC codes perform as well as their comparable counterparts. However, this proposed code structure is more flexible in designing. This feature may show its power when we change the code length and rate adaptively. Further more, we present two algorithms to generate codes with short girth and better girth distribution. The two algorithms are designed based on progressive edge growth (PEG) algorithm and they are specifically designed for quasi-cyclic structure. The simulation results show the improvement they achieved. In this thesis, we also investigate the believe propagation based iterative algorithms for decoding of nonbinary LDPC codes. The algorithms include sum-product (SP) algorithm, SP algorithm using fast Fourier transform, min-sum (MS) algorithm and complexity reduced extended min-sum (EMS) algorithm. In particular, we present the proposed modified min-sum algorithm with threshold filtering which further reduces the computation complexity.

Inaug.-diss.--Rostock.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1966. / Typescript. Vita. Includes bibliographical references (leaves 148-150).

Diss.--Technische Hochschule Dresden. / Bibliography: p. [125].

Thesis (Ph.D.) - University of Queensland, 2004. / Includes bibliographical references.

Inaug.-diss.--Rostock.

Inaug.-dis.--Rostock.

Thesis (Ph. D.)--Saint Louis University, 1932. / Description based on print version record. Includes bibliographical references (p. [179]-181).