Department of Mathematics and Statistics Faculty Publicationshttp://hdl.handle.net/1974/140262019-02-21T03:27:42Z2019-02-21T03:27:42ZOn the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and Queue-Based Channels with MemoryAzar, GhadyAlajaji, Fadyhttp://hdl.handle.net/1974/140272017-03-30T14:24:09Z2016-02-17T00:00:00ZOn the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and Queue-Based Channels with Memory
Azar, Ghady; Alajaji, Fady
We study the optimal maximum likelihood (ML) block decoding of general binary codes sent over two classes of binary additive noise channels with memory. Specifically, we consider the infinite and finite memory Polya contagion and queue-based channel models which were recently shown to approximate well binary modulated correlated fading channels used with hard-decision demodulation. We establish conditions on the codes and channels parameters under which ML and minimum Hamming distance decoding are equivalent. We also present results on the optimality of classical perfect and quasiperfect codes when used over the channels under ML decoding. Finally, we briefly apply these results to the dual problem of syndrome source coding with and without side information.
2016-02-17T00:00:00ZHall conditions for edge-weighted bipartite graphsGregory, Davidhttp://hdl.handle.net/1974/59462017-03-30T14:24:12Z2010-07-28T14:50:18ZHall conditions for edge-weighted bipartite graphs
Gregory, David
A weighted variant of Hall's condition for the existence of matchings is shown to
be equivalent to the existence of a matching in a lexicographic product.
This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable.
Some infinite families of semiregularizable trees are described and all semiregularizable trees on at most 11 vertices are listed.
Matrix analogues of some of the results are mentioned and are shown to imply some of the known characterizations of regularizable graphs.
Notes based on seminar talks given at Queen's University and the Royal Military College, Kingston, 2009-10.
2010-07-28T14:50:18Z