University of Colorado
Romero, Henry Paul.
Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach.
Degree: PhD, Applied Mathematics, 2014, University of Colorado
The classical theoretical framework for communication networks is based on the simplifying assumption that each message to be sent is known to a single transmitter and intended for a single receiver. Modern communication protocols reflect this framework by treating the physical layer as a network of individual links. However, this wireline view of wireless communications fails to account for the heterogeneous nature of network demands, consisting of both unicast and multicast services, and can fail to leverage the inherent broadcast advantage of the wireless medium.
This thesis extends the classical framework of a private-message interface to the physical layer to one with both private and common messages. A key difficulty, in both the description and analysis of a communication model with general messages sets, is that there are combinatorially many message possibilities. With order-theoretic language and tools from combinatorial optimization and graphical models, we develop a general framework for characterizing the fundamental limits of information transfer over large many-to-one (multiple access) and one-to-many (broadcast) communication channels with general message sets. In particular, achievable regions are proposed for arbitrary such channels. For the multiple-access channel, the achievable region is optimal, and the order-theoretic perspective both unifies and extends previous results. For the broadcast channel, the region is specialized to an inner bound to the Degree of Freedom region, a setting where it is provably optimal in select cases.
This thesis provides fresh insights into the long-standing random coding technique of superposition coding to arrive at these results. Governing constraints on reliable communication through superposition coding are shown to be polymatroidal over a lattice of subsets that may not be the boolean lattice of all subsets. Permissible input distributions for superposition coding are concisely characterized through directed graphical models of conditional dependencies. The two-user interference channel is also addressed, where the state-of-the art is extended from the case with two private messages to one with an additional common message.
Advisors/Committee Members: Mahesh Varanasi, Juan Restrepo, Vanja Dukic, Jem N. Corcoran, Clifford T. Mullis.
Subjects/Keywords: Information Theory; DM Multiple Access Channel; MIMO Multiple Access Channel; Broadcast Channel; Inteference Channel; Computer Sciences; Electrical and Computer Engineering; Mathematics
to Zotero / EndNote / Reference
APA (6th Edition):
Romero, H. P. (2014). Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/appm_gradetds/61
Chicago Manual of Style (16th Edition):
Romero, Henry Paul. “Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach.” 2014. Doctoral Dissertation, University of Colorado. Accessed January 24, 2021.
MLA Handbook (7th Edition):
Romero, Henry Paul. “Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach.” 2014. Web. 24 Jan 2021.
Romero HP. Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach. [Internet] [Doctoral dissertation]. University of Colorado; 2014. [cited 2021 Jan 24].
Available from: https://scholar.colorado.edu/appm_gradetds/61.
Council of Science Editors:
Romero HP. Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach. [Doctoral Dissertation]. University of Colorado; 2014. Available from: https://scholar.colorado.edu/appm_gradetds/61