Mathematics, Department of


First Advisor

Christine A. Kelley

Date of this Version



Beemer, Allison. "Design and analysis of graph-based codes using algebraic lifts and decoding networks," Ph.D. dissertation, University of Nebraska - Lincoln, 2018.


A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfilment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Christine A. Kelley. Lincoln, Nebraska: March, 2018

Copyright (c) 2018 Allison Beemer


Error-correcting codes seek to address the problem of transmitting information efficiently and reliably across noisy channels. Among the most competitive codes developed in the last 70 years are low-density parity-check (LDPC) codes, a class of codes whose structure may be represented by sparse bipartite graphs. In addition to having the potential to be capacity-approaching, LDPC codes offer the significant practical advantage of low-complexity graph-based decoding algorithms. Graphical substructures called trapping sets, absorbing sets, and stopping sets characterize failure of these algorithms at high signal-to-noise ratios. This dissertation focuses on code design for and analysis of iterative graph-based message-passing decoders. The main contributions of this work include the following: the unification of spatially-coupled LDPC (SC-LDPC) code constructions under a single algebraic graph lift framework and the analysis of SC-LDPC code construction techniques from the perspective of removing harmful trapping and absorbing sets; analysis of the stopping and absorbing set parameters of hypergraph codes and finite geometry LDPC (FG-LDPC) codes; the introduction of multidimensional decoding networks that encode the behavior of hard-decision message-passing decoders; and the presentation of a novel Iteration Search Algorithm, a list decoder designed to improve the performance of hard-decision decoders.

Adviser: Christine A. Kelley