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A Generalized Algebraic Approach to Optimizing SC-LDPC Codes [article]

Allison Beemer, Salman Habib, Christine A. Kelley, Joerg Kliewer
2017 arXiv   pre-print
In this paper, we unify all existing SC-LDPC code construction methods under a new generalized description of SC-LDPC codes based on algebraic lifts of graphs.  ...  That is, σ 1a,x = max(φ 1a,x , θ 1x , θ 3x ), σ 1a,y = max(φ 1a,y , θ 1y , θ 3y ), σ 2a,x = min(φ 2a,x , θ 2x , θ 4x ), σ 2a,y = min(φ 2a,y , θ 2y , θ 4y ).  ...  These points are denoted by σ 1a and σ 2a .  ... 
arXiv:1710.03619v1 fatcat:5qgv6hjwkncyng6iszpzcyr2eu

Algebraic Constructions of Graph-Based Nested Codes from Protographs [article]

Christine A. Kelley, Joerg Kliewer
2010 arXiv   pre-print
Nested codes have been employed in a large number of communication applications as a specific case of superposition codes, for example to implement binning schemes in the presence of noise, in joint network-channel  ...  For j < k, we form the following j × k matrix P with elements from Z * m that has as its (s, t)th element P s,t = b s a t as follows: P =    1 a a 2 . . . a k−1 b ab a 2 b . . . a k−1 b . . . . . .  ...  . , n, exactly c j kj-cycles. 2 Here we distinguish between a k-cycle in a graph which is a closed walk of length k, and a cycle of a permutation which is a closed set of numbers in the cycle representation  ... 
arXiv:1006.2977v1 fatcat:ukszspict5e7dphabivrqkdwqq

Eigenvalue bounds on the pseudocodeword weight of expander codes [article]

Christine A. Kelley, Deepak Sridhara
2007 arXiv   pre-print
Furthermore, Tanner's parity-oriented eigenvalue lower bound on the minimum distance is generalized to yield a new lower bound on the minimum pseudocodeword weight.  ...  We also thank Reviewer 1 for providing the more intuitive definition of a stopping set in a generalized LDPC code.  ...  Acknowledgments We thank Joachim Rosenthal and the reviewers for a careful proof-reading of this paper and their valuable comments. We believe their feedback has greatly improved the paper.  ... 
arXiv:0708.2462v1 fatcat:5r7thuq535cjxnzrjwznougqpe

Geometric WOM codes and coding strategies for multilevel flash memories [article]

Kathryn Haymaker, Christine A. Kelley
2012 arXiv   pre-print
Using ideas from Merkx ('84), we present a construction of WOM codes based on finite Euclidean geometries over F_2.  ...  A brief discussion of the average-write performance of these strategies, as well as concatenation methods for WOM codes is also provided.  ...  The points are the nonzero (m+1)tuples (a 0 , a 1 , . . . , a m ) ∈ F m+1 2 , and a line through two distinct points a 0 and a 1 contains exactly the set of points {a 0 , a 1 , a 0 + a 1 }.  ... 
arXiv:1206.5762v1 fatcat:fmm4tzcwrnd3fn7wxyq4ytzkim

Pseudocodewords of Tanner Graphs

Christine A. Kelley, Deepak Sridhara
2007 IEEE Transactions on Information Theory  
This papers presents a detailed analysis of pseudocodewords of Tanner graphs.  ...  pseudocodewords have components upper bounded by a finite value t that is dependent on the graph structure.  ...  Figure 2 shows a base graph G and a degree four cover of G. A codewordĉ in a lift graphĜ of a Tanner graph G is defined analogously as in Definition 2.1.  ... 
doi:10.1109/tit.2007.907501 fatcat:y76otn7b45hw3a22v3ckfluxzm

Multidimensional Decoding Networks for Trapping Set Analysis [chapter]

Allison Beemer, Christine A. Kelley
2017 Lecture Notes in Computer Science  
We present a novel multidimensional network model as a means to analyze decoder failure and characterize trapping sets of graphbased codes.  ...  We identify a special class of these decoding networks, which we call transitive networks, and show how they may be used to identify trapping sets and inducing sets.  ...  Under Gallager A decoding, representation A does not yield a transitive decoding network.  ... 
doi:10.1007/978-3-319-66278-7_2 fatcat:ofio5c4mxrg3rk47dolmvbpq7y

LDPC codes from voltage graphs

Christine A. Kelley, Judy L. Walker
2008 2008 IEEE International Symposium on Information Theory  
If D(a 1 , a 2 ; b) is a subgraph of a simple bipartite graph with a 1 , a 2 ≥ 1 and b ≥ 0, then a 1 , a 2 ≥ 4 and are even.  ...  Then X, by Theorem 4.5, X has either a subgraph T (a, b, c) with 2a + 2b + 2c ≤ n or a subgraph D(a 1 , a 2 ; b) with 2(a 1 + a 2 ) + 4b ≤ n.  ... 
doi:10.1109/isit.2008.4595095 dblp:conf/isit/KelleyW08 fatcat:fvttiwkphraghnormlagnhhwmq

Pseudocodewords of Tanner graphs [article]

Christine A. Kelley, Deepak Sridhara
2007 arXiv   pre-print
This papers presents a detailed analysis of pseudocodewords of Tanner graphs.  ...  pseudocodewords have components upper bounded by a finite value t that is dependent on the graph structure.  ...  A.  ... 
arXiv:cs/0504013v4 fatcat:gfxhs5yl75akpjqp3ie7s5o5d4

Variations of the McEliece Cryptosystem [article]

Jessalyn Bolkema, Heide Gluesing-Luerssen, Christine A. Kelley, Kristin Lauter, Beth Malmskog, Joachim Rosenthal
2017 arXiv   pre-print
The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process.  ...  These codes are known for their excellent error-correction performance and allow for a relatively low key size in the cryptosystem.  ...  For a vector a = (a 1 , . . . , a m ) ∈ F m denote by C a ∈ F m×m the circulant matrix with i-th row given by the cyclic shift (a i , . . . , a m , a 1 We will use G ′ (D) for the public key.  ... 
arXiv:1612.05085v2 fatcat:iotsnlu6qzdqjpatxcv2vmvrqe

On the independence and domination numbers of replacement product graphs

Jay Cummings, Christine A. Kelley
2016 Involve. A Journal of Mathematics  
The replacement product is a noncommutative graph operation that has been widely applied in many areas. One of its advantages over other graph products is its ability to produce sparse graphs.  ...  Acknowledgements The results in this paper were part of Cummings' undergraduate honors thesis, "On invariants of replacement product graphs", that was conducted under the supervision of Kelley.  ...  Invariants of graphs, including the independence and domination numbers of a graph, have also been widely studied. Many applications in computer science and 182 JAY CUMMINGS AND CHRISTINE A.  ... 
doi:10.2140/involve.2016.9.181 fatcat:yoq4krxo25e3raizb5knk4glaa

Extremal absorbing sets in low-density parity-check codes

Emily McMillon, Allison Beemer, Christine A. Kelley
2021 Advances in Mathematics of Communications  
In this paper, we determine the sizes of absorbing sets that can occur in general and leftregular LDPC code graphs, with emphasis on the range of b for a given a for which an (a, b)-absorbing set may exist  ...  We identify certain cases of extremal absorbing sets that are elementary, a particularly harmful class of absorbing sets, and also introduce the notion of minimal absorbing sets which will help in designing  ...  Acknowledgments We thank the anonymous reviewers for their helpful comments that improved the quality of the paper, including a nicer proof of Theorem 3.2.  ... 
doi:10.3934/amc.2021003 fatcat:5bqyowmvgjalnbc3aprwm4fg4a

Zig-zag and Replacement Product Graphs and LDPC Codes [article]

Christine A. Kelley, Deepak Sridhara, Joachim Rosenthal
2007 arXiv   pre-print
The performance of codes defined from graphs depends on the expansion property of the underlying graph in a crucial way.  ...  A modification of the zig-zag product is also introduced, which can operate on two unbalanced biregular bipartite graphs.  ...  is (a, b)(c, d) = (a + φ b (c), b + d), for a, c ∈ A, b, d ∈ B.  ... 
arXiv:cs/0611155v2 fatcat:3ex3qwbknnhltmvod65dbbtrai

Algebraic constructions of graph-based nested codes from protographs

Christine A. Kelley, Jorg Kliewer
2010 2010 IEEE International Symposium on Information Theory  
Nested codes have been employed in a large number of communication applications as a specific case of superposition codes, for example to implement binning schemes in the presence of noise, in joint network-channel  ...  For j < k, we form the following j × k matrix P with elements from Z * m that has as its (s, t)th element P s,t = b s a t as follows: P =    1 a a 2 . . . a k−1 b ab a 2 b . . . a k−1 b . . . . . .  ...  . , n, exactly c j kj-cycles. 2 Here we distinguish between a k-cycle in a graph which is a closed walk of length k, and a cycle of a permutation which is a closed set of numbers in the cycle representation  ... 
doi:10.1109/isit.2010.5513628 dblp:conf/isit/KelleyK10 fatcat:d4c6h7yibvd2xopihsnpn73n4a

Motives for physical dating violence among college students: A gendered analysis

Erika L. Kelley, Katie M. Edwards, Christina M. Dardis, Christine A. Gidycz
2015 Psychology of Violence  
Method: The sample included 221 college students who reported a history of physical DV perpetration and completed surveys for course credit.  ...  This study explores this gap in the literature with a specific focus on gender, coping, DV perpetration and victimization, and attitudes toward violence.  ...  ) and who participated in a larger mixed-methodological study assessing students' perceptions of abuse in dating relationships (Edwards, Dardis, Kelley, & Gidycz, 2013) .  ... 
doi:10.1037/a0036171 fatcat:mmr5274l5fcqpe3utpjpikm6m4

On codes designed via algebraic lifts of graphs

Christine A. Kelley
2008 2008 46th Annual Allerton Conference on Communication, Control, and Computing  
In particular, we present a construction of LDPC codes by giving an algebraic method of choosing the permutation voltages and illustrate the usefulness of the proposed technique via simulation results.  ...  An (a 1 , a 2 ; b)-dumbbell graph is a connected graph consisting of two disjoint cycles A 1 and A 2 of lengths a 1 ≥ 1 and a 2 ≥ 1, that are connected by a path B of length b ≥ 0.  ...  In [5] , it was shown that if voltages were assigned from an abelian group G to a base graph G, where G contained either a (a, b, c)theta graph or a (a 1 , a 2 ; b)-dumbbell graph as a subgraph, 2 A  ... 
doi:10.1109/allerton.2008.4797704 fatcat:gptjyj4savd3zpsiyzw4pvai5q
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