Maximum likelihood sequence estimation from the lattice viewpoint.

Abstract

by Mow Wai Ho.Thesis (M.Phil.)--Chinese University of Hong Kong, 1991.Bibliographies: leaves 98-104.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Channel Model and Other Basic Assumptions --- p.5Chapter 1.2 --- Complexity Measure --- p.8Chapter 1.3 --- Maximum Likelihood Sequence Estimator --- p.9Chapter 1.4 --- The Viterbi Algorithm ´ؤ An Implementation of MLSE --- p.11Chapter 1.5 --- Error Performance of the Viterbi Algorithm --- p.14Chapter 1.6 --- Suboptimal Viterbi-like Algorithms --- p.17Chapter 1.7 --- Trends of Digital Transmission and MLSE --- p.19Chapter 2 --- New Formulation of MLSE --- p.21Chapter 2.1 --- The Truncated Viterbi Algorithm --- p.21Chapter 2.2 --- Choice of Truncation Depth --- p.23Chapter 2.3 --- Decomposition of MLSE --- p.26Chapter 2.4 --- Lattice Interpretation of MLSE --- p.29Chapter 3 --- The Closest Vector Problem --- p.34Chapter 3.1 --- Basic Definitions and Facts About Lattices --- p.37Chapter 3.2 --- Lattice Basis Reduction --- p.40Chapter 3.2.1 --- Weakly Reduced Bases --- p.41Chapter 3.2.2 --- Derivation of the LLL-reduction Algorithm --- p.43Chapter 3.2.3 --- Improved Algorithm for LLL-reduced Bases --- p.52Chapter 3.3 --- Enumeration Algorithm --- p.57Chapter 3.3.1 --- Lattice and Isometric Mapping --- p.58Chapter 3.3.2 --- Enumerating Points in a Parallelepiped --- p.59Chapter 3.3.3 --- Enumerating Points in a Cube --- p.63Chapter 3.3.4 --- Enumerating Points in a Sphere --- p.64Chapter 3.3.5 --- Comparisons of Three Enumeration Algorithms --- p.66Chapter 3.3.6 --- Improved Enumeration Algorithm for the CVP and the SVP --- p.67Chapter 3.4 --- CVP Algorithm Using the Reduce-and-Enumerate Approach --- p.71Chapter 3.5 --- CVP Algorithm with Improved Average-Case Complexity --- p.72Chapter 3.5.1 --- CVP Algorithm for Norms Induced by Orthogonalization --- p.73Chapter 3.5.2 --- Improved CVP Algorithm using Norm Approximation --- p.76Chapter 4 --- MLSE Algorithm --- p.79Chapter 4.1 --- MLSE Algorithm for PAM Systems --- p.79Chapter 4.2 --- MLSE Algorithm for Unimodular Channel --- p.82Chapter 4.3 --- Reducing the Boundary Effect for PAM Systems --- p.83Chapter 4.4 --- Simulation Results and Performance Investigation for Example Channels --- p.86Chapter 4.5 --- MLSE Algorithm for Other Lattice-Type Modulation Systems --- p.91Chapter 4.6 --- Some Potential Applications --- p.92Chapter 4.7 --- Further Research Directions --- p.94Chapter 5 --- Conclusion --- p.96Bibliography --- p.10