You searched for +publisher:"University of Colorado" +contributor:("Mahesh Varanasi").
Showing records 1 – 4 of
4 total matches.
No search limiters apply to these results.
University of Colorado
1.
Limburg, Steve.
Space-time Codes, Non-associative Division Algebras, and Elliptic Curves.
Degree: PhD, Mathematics, 2012, University of Colorado
URL: https://scholar.colorado.edu/math_gradetds/11 
► Space-time codes are used to reliably send data from multiple transmit antennas and are directly related to non-associative division algebras. While interested in classifying…
(more)
▼ Space-time codes are used to reliably send data from multiple transmit antennas and are directly related to non-associative division algebras. While interested in classifying and building space-time codes, using this relationship this thesis considers the corresponding problem of classifying and building non-associative division algebras. The first four chapters develop the problem and give a classification of 4-dimensional non-associative division algebras. Using the classification in chapter 4, I identify a class with no previously known examples. The rest of the thesis develops the background material necessary to understand two methods to build new non-associative division algebras in the aforementioned class. The thesis ends with the methods to build new non-associative division algebras and two examples using the methods. The intermediary steps used in the construction of the examples use tools from the arithmetic of elliptic curves over number fields, commutative algebra, and algebraic number theory.
Advisors/Committee Members: David Grant, Sebastian Casalaina-Martin, Mahesh Varanasi.
Subjects/Keywords: 4-isogeny; division algebra; elliptic curves; non-associative algebra; space-time codes; Algebra; Mathematics; Systems and Communications
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Limburg, S. (2012). Space-time Codes, Non-associative Division Algebras, and Elliptic Curves. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/11
Chicago Manual of Style (16th Edition):
Limburg, Steve. “Space-time Codes, Non-associative Division Algebras, and Elliptic Curves.” 2012. Doctoral Dissertation, University of Colorado. Accessed January 18, 2021.
https://scholar.colorado.edu/math_gradetds/11.
MLA Handbook (7th Edition):
Limburg, Steve. “Space-time Codes, Non-associative Division Algebras, and Elliptic Curves.” 2012. Web. 18 Jan 2021.
Vancouver:
Limburg S. Space-time Codes, Non-associative Division Algebras, and Elliptic Curves. [Internet] [Doctoral dissertation]. University of Colorado; 2012. [cited 2021 Jan 18].
Available from: https://scholar.colorado.edu/math_gradetds/11.
Council of Science Editors:
Limburg S. Space-time Codes, Non-associative Division Algebras, and Elliptic Curves. [Doctoral Dissertation]. University of Colorado; 2012. Available from: https://scholar.colorado.edu/math_gradetds/11
University of Colorado
2.
Pang, Yimin.
Capacity Approximations of Mimo Interference Channels: Beyond Degrees of Freedom.
Degree: PhD, 2019, University of Colorado
URL: https://scholar.colorado.edu/eeng_gradetds/39
► Spectrum sharing allows the coexistence of heterogeneous wireless networks on the same frequency band. Managing the interference between such networks is critically important to…
(more)
▼ Spectrum sharing allows the coexistence of heterogeneous wireless networks on the same frequency band. Managing the interference between such networks is critically important to ensure high spectrum efficiency, thus motivating the study of multiple-input-multiple-output (MIMO) interference channels (IC) in information theory. This dissertation studies three classes of such interference channels, namely, the MIMO one-to-three IC, the MIMO IC-ZIC, and the MIMO MAC-IC-MAC. The MIMO one-to-three IC is a partially connected three-user IC with multiple antenna terminals, where one transmitter that causes interference is heard at all three receivers, whereas the other two transmitters are heard only by their intended receivers. We present inner and outer bounds on the capacity region of the MIMO one-to-three IC, quantify the gap between the two bounds, and show that the gap is independent of the channel signal-to-noise ratios (SNRs) and interference-to-noise ratios (INRs). In particular, the achievable scheme at the interfering transmitter involves three-level superposition coding with linear precoding based on the generalized singular value decomposition (GSVD) whereas the non-interfering transmitters perform single-user coding with Gaussian codebooks and scaled identity covariances. The outer bound is obtained using genie-aided arguments with various combinations of genie information provided to the receivers. The generalized degrees of freedom (GDoF) region, which can be seen as a high SNR approximation of the capacity region, of the MIMO one-to-three IC is then fully characterized. We study the achievability of the GDoF region and the sum GDoF curve using an analysis tool developed in this dissertation, which we refer to as multidimensional signal-level partitioning. This tool is tailored for demonstrating the achievability of GDoF-tuples of a MIMO network that can be achieved via multi-level superposition coding. The MIMO IC-ZIC is also a partially connected three-user IC consisting of three transmitter-receiver pairs. In the IC-ZIC, the first and second pairs form a two-user IC, the first and third pairs form a one-sided or Z interference channel (ZIC) and the second and third transmitter-receiver pairs taken by themselves are two non-interfering point-to-point links. In this thesis, an explicit inner bound is obtained via a coding scheme is proposed in which the first transmitter employs three-level superposition coding (as in the MIMO one-to-three IC), the second one employs the previously proposed and well-known Karmakar-
Varanasi coding scheme (which achieves a constant-gap-to-capacity region of the two-user MIMO IC), and the third transmitter employs single-user coding with a Gaussian codebook (with scaled identity covariance). An explicit single region outer bound based on genie-aided arguments is then obtained. The gap between the inner and outer bounds is then shown to be within a quantifiable gap to the capacity region and the gap is independent of channel SNRs and INRs. The GDoF region is then…
Advisors/Committee Members: Mahesh Varanasi, Youjian Liu, Fabio Somenzi, Lijun Chen, Sriram Sankaranarayanan.
Subjects/Keywords: generalized degrees of freedom; ic-zic; interference channel; mac-ic-mac; mimo; one-to-three; Electrical and Computer Engineering
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Pang, Y. (2019). Capacity Approximations of Mimo Interference Channels: Beyond Degrees of Freedom. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/eeng_gradetds/39
Chicago Manual of Style (16th Edition):
Pang, Yimin. “Capacity Approximations of Mimo Interference Channels: Beyond Degrees of Freedom.” 2019. Doctoral Dissertation, University of Colorado. Accessed January 18, 2021.
https://scholar.colorado.edu/eeng_gradetds/39.
MLA Handbook (7th Edition):
Pang, Yimin. “Capacity Approximations of Mimo Interference Channels: Beyond Degrees of Freedom.” 2019. Web. 18 Jan 2021.
Vancouver:
Pang Y. Capacity Approximations of Mimo Interference Channels: Beyond Degrees of Freedom. [Internet] [Doctoral dissertation]. University of Colorado; 2019. [cited 2021 Jan 18].
Available from: https://scholar.colorado.edu/eeng_gradetds/39.
Council of Science Editors:
Pang Y. Capacity Approximations of Mimo Interference Channels: Beyond Degrees of Freedom. [Doctoral Dissertation]. University of Colorado; 2019. Available from: https://scholar.colorado.edu/eeng_gradetds/39
University of Colorado
3.
Romero, Henry Paul.
Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach.
Degree: PhD, Applied Mathematics, 2014, University of Colorado
URL: https://scholar.colorado.edu/appm_gradetds/61
► The classical theoretical framework for communication networks is based on the simplifying assumption that each message to be sent is known to a single…
(more)
▼ 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
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
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 18, 2021.
https://scholar.colorado.edu/appm_gradetds/61.
MLA Handbook (7th Edition):
Romero, Henry Paul. “Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach.” 2014. Web. 18 Jan 2021.
Vancouver:
Romero HP. Fundamental Limits of Network Communication with General Message Sets: A Combinatorial Approach. [Internet] [Doctoral dissertation]. University of Colorado; 2014. [cited 2021 Jan 18].
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
University of Colorado
4.
Keyes, David Parker.
Analytic Proofs of Certain MacWilliams Identities.
Degree: PhD, Mathematics, 2011, University of Colorado
URL: https://scholar.colorado.edu/math_gradetds/10
Subjects/Keywords: Codes; MacWilliams Identities; Modular Forms; Theta Functions; Mathematics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Keyes, D. P. (2011). Analytic Proofs of Certain MacWilliams Identities. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/10
Chicago Manual of Style (16th Edition):
Keyes, David Parker. “Analytic Proofs of Certain MacWilliams Identities.” 2011. Doctoral Dissertation, University of Colorado. Accessed January 18, 2021.
https://scholar.colorado.edu/math_gradetds/10.
MLA Handbook (7th Edition):
Keyes, David Parker. “Analytic Proofs of Certain MacWilliams Identities.” 2011. Web. 18 Jan 2021.
Vancouver:
Keyes DP. Analytic Proofs of Certain MacWilliams Identities. [Internet] [Doctoral dissertation]. University of Colorado; 2011. [cited 2021 Jan 18].
Available from: https://scholar.colorado.edu/math_gradetds/10.
Council of Science Editors:
Keyes DP. Analytic Proofs of Certain MacWilliams Identities. [Doctoral Dissertation]. University of Colorado; 2011. Available from: https://scholar.colorado.edu/math_gradetds/10
. 
Open Access Theses and Dissertations