Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Articles (17)
- L(2 (5)
- 1)-labeling (3)
- 1)-coloring (2)
- 1)-labeling; L(2 (2)
-
- Channel assignment (2)
- Complex orthogonal designs (2)
- Generalized Petersen graph (2)
- Multiple-input multiple-output (MIMO) (2)
- Quaternions (2)
- 1)-coloring; Distance two labeling; Graph labeling; Channel assignment; Generalized Petersen graph (1)
- 1)-coloring; Matched sum (1)
- Amicable orthogonal designs (AOD) (1)
- Block codes (1)
- Circulant matrix (1)
- Complex orthogonal space–time block codes (CO STBCs) (1)
- Conference Proceedings (1)
- Decoding delay (1)
- Decoupled decoding (1)
- Dimension (1)
- Distance two labeling (1)
- Diversity (1)
- Dynamic monopoly; Dynamo; Feedback vertex set; Hexagonal grid; Majority conversion process; Target set selection (1)
- Error-control codes (1)
- Frequency allocation (1)
- Generalized complex orthogonal design (GCOD) (1)
- Graph labeling (1)
- Graph theory (1)
- Hadamard matrix (1)
- Hole index (1)
Articles 1 - 18 of 18
Full-Text Articles in Entire DC Network
The Minimum Span Of L(2,1)-Labelings Of Certain Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Matthew Tesch, Denise Troxell, Cody Wheeland
The Minimum Span Of L(2,1)-Labelings Of Certain Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Matthew Tesch, Denise Troxell, Cody Wheeland
Sarah Spence Adams
In the classical channel assignment problem, transmitters that are sufficiently close together are assigned transmission frequencies that differ by prescribed amounts, with the goal of minimizing the span of frequencies required. This problem can be modeled through the use of an L(2,1)-labeling, which is a function f from the vertex set of a graph G to the non-negative integers such that |f(x)–f(y)|≥ 2 if xand y are adjacent vertices and |f(x)–f(y)|≥1 if xand y are at distance two. The goal is to …
On An Orthogonal Space-Time-Polarization Block Code, Beata Wysocki, Tadeusz Wysocki, Sarah Adams
On An Orthogonal Space-Time-Polarization Block Code, Beata Wysocki, Tadeusz Wysocki, Sarah Adams
Sarah Spence Adams
Over the past several years, diversity methods such as space, time, and polarization diversity have been successfully implemented in wireless communications systems. Orthogonal space-time block codes efficiently combine space and time diversity, and they have been studied in detail. Polarization diversity has also been studied, however it is usually considered in a simple concatenation with other coding methods. In this paper, an efficient method for incorporating polarization diversity with space and time diversity is studied. The simple yet highly efficient technique is based on extending orthogonal space-time block codes into the quaternion domain and utilizing a description of the dual-polarized …
Novel Constructions Of Improved Square Complex Orthogonal Designs For Eight Transmit Antennas, Le Chung Tran, Tadeusz Wysocki, Jennifer Seberry, Alfred Mertins, Sarah Adams
Novel Constructions Of Improved Square Complex Orthogonal Designs For Eight Transmit Antennas, Le Chung Tran, Tadeusz Wysocki, Jennifer Seberry, Alfred Mertins, Sarah Adams
Sarah Spence Adams
Constructions of square, maximum rate complex orthogonal space-time block codes (CO STBCs) are well known, however codes constructed via the known methods include numerous zeros, which impede their practical implementation. By modifying the Williamson and Wallis-Whiteman arrays to apply to complex matrices, we propose two methods of construction of square, order-4n CO STBCs from square, order-n codes which satisfy certain properties. Applying the proposed methods, we construct square, maximum rate, order-8 CO STBCs with no zeros, such that the transmitted symbols are equally dispersed through transmit antennas. Those codes, referred to as the improved square CO STBCs, have the advantages …
Multilevel And Multidimensional Hadamard Matrices, Sarah Adams, Matthew Crawford, Caitlin Greeley, Bryce Lee, Mathav Murugan
Multilevel And Multidimensional Hadamard Matrices, Sarah Adams, Matthew Crawford, Caitlin Greeley, Bryce Lee, Mathav Murugan
Sarah Spence Adams
Multilevel Hadamard matrices (MHMs), whose entries are integers as opposed to the traditional restriction to {±1}, were introduced by Trinh, Fan, and Gabidulin in 2006 as a way to construct multilevel zero-correlation zone sequences, which have been studied for use in approximately synchronized code division multiple access systems. We answer the open question concerning the maximum number of distinct elements permissible in an order n MHM by proving the existence of an order n MHM with n elements of distinct absolute value for all n. We also define multidimensional MHMs and prove an analogous existence result.
An Extension Of The Channel-Assignment Problem: L(2, 1)-Labelings Of Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Denise Troxell
An Extension Of The Channel-Assignment Problem: L(2, 1)-Labelings Of Generalized Petersen Graphs, Sarah Adams, Jonathan Cass, Denise Troxell
Sarah Spence Adams
The channel-assignment problem involves assigning frequencies represented by nonnegative integers to radio transmitters such that transmitters in close proximity receive frequencies that are sufficiently far apart to avoid interference. In one of its variations, the problem is commonly quantified as follows: transmitters separated bythe smallest unit distance must be assigned frequencies that are at least two apart and transmitters separated by twice the smallest unit distance must be assigned frequencies that are at least one apart. Naturally, thischannel-assignment problem can be modeled with vertex labelings of graphs. An L(2, 1)-labeling of a graph G is a function f from the …
Identifying High-Dimension Subspace Subcodes Of Reed-Solomon Codes, Sarah Adams
Identifying High-Dimension Subspace Subcodes Of Reed-Solomon Codes, Sarah Adams
Sarah Spence Adams
Subspace subcodes of Reed-Solomon (SSRS) codes were introduced by Hattori, McEliece, Solomo, and Lin in the mid-1990s. These authors found a complicated dimension formula and a simple, tight lower bound on thedimension of SSRS codes over F2m. We prove a conjecture of Hattori concerning how to identify subspaces that can be used to build SSRS codes whose dimension exceeds this lower bound.
Quaternion Orthogonal Designs From Complex Companion Designs, Sarah Adams, Jennifer Seberry, Nathaniel Karst, Jonathan Pollack, Tadeusz Wysocki
Quaternion Orthogonal Designs From Complex Companion Designs, Sarah Adams, Jennifer Seberry, Nathaniel Karst, Jonathan Pollack, Tadeusz Wysocki
Sarah Spence Adams
The success of applying generalized complex orthogonal designs as space–time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space–time-polarization block codes. This paper offers techniques for constructing quaternion orthogonal designs via combinations of specially chosen complex orthogonal designs. One technique is used to build quaternion orthogonal designs on complex variables for any even number of columns. A second related technique is applied to maximum rate complex orthogonal designs to generate an infinite family of quaternion orthogonal designs on complex variables such that the resulting designs have no zero entries. This second technique is …
The Final Case Of The Decoding Delay Problem For Maximum Rate Complex Orthogonal Designs, Sarah Adams, Nathaniel Karst, Mathav Murugan
The Final Case Of The Decoding Delay Problem For Maximum Rate Complex Orthogonal Designs, Sarah Adams, Nathaniel Karst, Mathav Murugan
Sarah Spence Adams
Complex orthogonal space-time block codes (COSTBCs) based on generalized complex orthogonal designs (CODs) have been successfully implemented in wireless systems with multiple transmit antennas and single or multiple receive antennas. It has been shown that for a maximum rate COD with 2m-1 or 2m columns, a lower bound on decoding delay is (m-1 2m) and this delay is achievable when the number of columns is congruent to 0, 1 , or 3 modulo 4. In this paper, the final case is addressed, and it is shown that when the number of columns is congruent to 2 modulo 4, the lower …
On The Hole Index Of L(2,1)-Labelings Of R-Regular Graphs, Sarah Adams, Matthew Tesch, Denise Troxell, Bradford Westgate, Cody Wheeland
On The Hole Index Of L(2,1)-Labelings Of R-Regular Graphs, Sarah Adams, Matthew Tesch, Denise Troxell, Bradford Westgate, Cody Wheeland
Sarah Spence Adams
An L(2,1)-labeling of a graph G is an assignment of nonnegative integers to the vertices of G so that adjacent vertices get labels at least distance two apart and vertices at distance two get distinct labels. A hole is an unused integer within the range of integers used by the labeling. The lambda number of a graphG, denoted λ(G), is the minimum span taken over all L(2,1)-labelings of G. The hole index of a graph G, denoted ρ(G), is the minimum number of holes taken over all L(2,1)-labelings with span exactly λ(G). Georges and Mauro [On the structure of graphs …
The Minimum Decoding Delay Of Maximum Rate Complex Orthogonal Space–Time Block Codes, Sarah Adams, Nathaniel Karst, Jonathan Pollack
The Minimum Decoding Delay Of Maximum Rate Complex Orthogonal Space–Time Block Codes, Sarah Adams, Nathaniel Karst, Jonathan Pollack
Sarah Spence Adams
The growing demand for efficient wireless transmissions over fading channels motivated the development ofspace-time block codes. Space-time block codes built from generalized complex orthogonal designs are particularly attractive because the orthogonality permits a simple decoupled maximum-likelihood decodingalgorithm while achieving full transmit diversity. The two main research problems for these complex orthogonalspace-time block codes (COSTBCs) have been to determine for any number of antennas the maximum rate andthe minimum decoding delay for a maximum rate code. The maximum rate for COSTBCs was determined by Liang in 2003. This paper addresses the second fundamental problem by providing a tight lower bound on …
On The Issue Of Decoupled Decoding Of Codes Derived From Quaternion Orthogonal Designs, Tadeusz Wysocki, Beata Wysocki, Sarah Spence Adams
On The Issue Of Decoupled Decoding Of Codes Derived From Quaternion Orthogonal Designs, Tadeusz Wysocki, Beata Wysocki, Sarah Spence Adams
Sarah Spence Adams
Quaternion orthogonal designs (QODs) have been previously introduced as a basis for orthogonal space-time polarization block codes (OSTPBCs). This note will serve to correct statements concerning the optimality of a decoupled maximum-likelihood (ML) decoding algorithm. It will be shown that when compared to coupled decoding, the decoupled decoding is only optimal in certain cases. This raises several open problems concerning the decoding of OSTPBCs.
Modeling The Spread Of Fault In Majority-Based Network Systems: Dynamic Monopolies In Triangular Grids, Sarah Spence Adams, Paul Booth, Denise Troxell, Luke Zinnen
Modeling The Spread Of Fault In Majority-Based Network Systems: Dynamic Monopolies In Triangular Grids, Sarah Spence Adams, Paul Booth, Denise Troxell, Luke Zinnen
Sarah Spence Adams
In a graph theoretical model of the spread of fault in distributed computing and communication networks, each element in the network is represented by a vertex of a graph where edges connect pairs of communicating elements, and each colored vertex corresponds to a faulty element at discrete time periods. Majority-based systems have been used to model the spread of fault to a certain vertex by checking for faults within a majority of its neighbors. Our focus is on irreversible majority processes wherein a vertex becomes permanently colored in a certain time period if at least half of its neighbors were …
Labeling Matched Sums With A Condition At Distance Two, Sarah Spence Adams, Denise Troxell
Labeling Matched Sums With A Condition At Distance Two, Sarah Spence Adams, Denise Troxell
Sarah Spence Adams
An L(2,1)-labeling of a graph G is a function f:V(G)→{0,1,…,k} such that |f(x)−f(y)|≥2 if x and y are adjacent vertices, and |f(x)−f(y)|≥1 if x and y are at distance 2. Such labelings were introduced as a way of modeling the assignment of frequencies to transmitters operating in close proximity within a communications network. The lambda number of G is the minimum k over all L(2,1)-labelings of G. This paper considers the lambda number of the matched sum of two same-order disjoint graphs, wherein the graphs have been connected by a perfect matching between the two vertex sets. Matched sums have …
Dynamic Monopolies And Feedback Vertex Sets In Hexagonal Grids, Sarah Spence Adams, Denise Troxell, S. Luke Zinnen
Dynamic Monopolies And Feedback Vertex Sets In Hexagonal Grids, Sarah Spence Adams, Denise Troxell, S. Luke Zinnen
Sarah Spence Adams
In a majority conversion process, the vertices of a graph can be in one of the two states, colored or uncolored, and these states are dynamically updated so that a vertex becomes colored at a certain time period if at least half of its neighbors were in the colored state in the previous time period. A dynamic monopoly is a set of vertices in a graph that when initially colored will eventually cause all vertices in the graph to become colored. This paper establishes a connection between dynamic monopolies and the well-known feedback vertex sets which are sets of vertices …
A Construction Technique For Generalized Complex Orthogonal Designs And Applications To Wireless Communications, Jennifer Seberry, Sarah Spence Adams, Tadeusz Wysocki
A Construction Technique For Generalized Complex Orthogonal Designs And Applications To Wireless Communications, Jennifer Seberry, Sarah Spence Adams, Tadeusz Wysocki
Sarah Spence Adams
We introduce a construction technique for generalized complex linear processing orthogonal designs, which are p × n matrices X satisfying XHX = fI, where f is a complex quadratic form, I is the identity matrix, and Xhas complex entries. These matrices generalize the familiar notions of orthogonal designs and generalized complex orthogonal designs. We explain the application of these matrices to space–time block coding for multiple-antenna wireless communications. In particular, we discuss the practical strengths of the space–time block codes constructed via our proposed technique.
Exact Lambda-Numbers Of Generalized Petersen Graphs Of Certain Higher-Orders And On Mobius Strips, Sarah Spence Adams, Paul Booth, Harold Jaffe, Denise Troxell, Luke Zinnen
Exact Lambda-Numbers Of Generalized Petersen Graphs Of Certain Higher-Orders And On Mobius Strips, Sarah Spence Adams, Paul Booth, Harold Jaffe, Denise Troxell, Luke Zinnen
Sarah Spence Adams
An L(2,1)-labeling of a graph G is an assignment f of nonnegative integers to the vertices of G such that if vertices x and y are adjacent, |f(x)−f(y)|≥2, and if x and y are at distance two, |f(x)−f(y)|≥1. The λ-number of Gis the minimum span over all L(2,1)-labelings of G. A generalized Petersen graph (GPG) of order n consists of two disjoint copies of cycles on n vertices together with a perfect matching between the two vertex sets. By …
Correction To “The Theory Of Quaternion Orthogonal Designs”, Tadeusz Wysocki, Beata Wysocki, Sarah Spence Adams
Correction To “The Theory Of Quaternion Orthogonal Designs”, Tadeusz Wysocki, Beata Wysocki, Sarah Spence Adams
Sarah Spence Adams
Seberry et al. claimed that even though the dual-polarized transmission channel cannot be considered as described by means of a single quaternionic gain, the maximum-likelihood (ML) decoding rule can be decoupled for orthogonal space–time-polarization block codes (OSTPBCs) derived from quaternion orthogonal designs (QODs) [1, Sec. IV]. Regretfully, a correction is necessary, and we will show that decoupled decoding using the method presented therein is only optimal for codes derived from certain QODs, not from arbitrary QODs as previously suggested.
Balancing The R With The E In Reu Programs, Sarah Spence Adams, Rick Gillman, Darren Narayan
Balancing The R With The E In Reu Programs, Sarah Spence Adams, Rick Gillman, Darren Narayan
Sarah Spence Adams
Externally or internally funded Research Experience for Undergraduates (REU) programs offer students the opportunity to work with faculty on unsolved problems and can serve as a highlight of their undergraduate career. The overall goal of these formative programs is that students and faculty have an enjoyable experience as they investigate the horizon of knowledge. However, there is a question on how much a program should focus on research and how much emphasis should be placed on the experience. In the end, both aspects should be given considerable weight.