Year: 2024
Type: dissertation
Abstract: Iterative algorithms are becoming more common in modern systems. This ranges from algorithms for communicationsystems receivers, machine learning, group testing, and various computation problems. The success of thesealgorithms lies in the ability to simplify computation by breaking down the system into components and exchangingmessages on graphs. The graph has the components as nodes and connections between them as edges. This separationis needed since attempting to solve the problem without dividing it into parts results into an optimal solution,the joint maximum a posterior (MAP) solution, but the computational complexity is prohibitive.With the systems divided into separate parts it often seems reasonable to use the best component for each partto achieve good performance. This, however, results into degraded performance compared to the optimal overallsolution. To get improved performance the components have to exchange information iteratively in a number ofcycles a process known as belief propagation (BP). This principle has been applied with much success in variousareas such as the design of turbo codes and low density parity-check (LDPC) codes for reliable communication.Other examples include iterative receivers for cancelling intersymbol interference (ISI) and better performance ofmodulation and coding in coded modulation.Choosing component codes for communication systems with iterative systems is often a process which involvescompromises. For example, if one chooses a strong code to work with a particular detector, the resulting performancein the waterfall region becomes poor but the error floor is improved whereas choosing a weak code results in improvedwaterfall region but poor error floor. One can also optimize the code, for example, by tuning the degree distributionof LDPC codes to achieve good performance but the optimization introduces weak components that compromise theerror floor. Furthermore, the optimization can work well for a given set of channel conditions, but the optimizedcode may not work well if the conditions are changed.These problems are a result of the fact that we have limitations from two aspects. First, we are limited by thecomponent (e.g. codes or detectors) choice which sets the limit on the MAP threshold. A strong code will thenhave a good MAP threshold and good error floor wheres a weak code will have a bad MAP threshold and bad errorfloor. It is important to note that the MAP threshold is the best we can do with the choice of the components butit can still be away from the ultimate information theoretical limit of the system (this corresponds to the capacityin communication systems for example). A second limitation comes from the decoding algorithm. The BP algorithmis not globally optimal for most graph used, thus setting a limit which is termed the BP threshold. A strong codehas then a bad BP threshold whereas a weak code has a better BP threshold.This thesis focuses on improving the performance of iterative algorithms by tackling the limitations highlighted.We propose improved algorithms and, more importantly, we apply the concept of spatial coupling to improve theperformance and robustness of the systems. We do this in two parts.In the first part we apply the concept on channels with ISI showing that we can obtain robust performance withchanging channel conditions and changing detector type. We propose three schemes of coupling and compute theBP and MAP thresholds as well as perform finite length simulations.In the second part, we investigate non-adaptive quantitative group testing using sparse graphs. We proposeimprovements of the algorithms and show that with spatial coupling we can obtain improved and robust performance.
Author: Mashauri, Mgeni Makambi
Institution: Lund University
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7037596800
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