3197241
Explicit construction of families of LDPC codes with no 4-cycles
Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m/spl ges/2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2q/sup m/ vertices, which has girth at least 2/spl lceil/m/2/spl rceil/+4. We regard these graphs as Tanner graphs of binary codes LU(m,q). We can determine the dimension and minimum weight of LU(2,q), and show that the weight of its minimum stopping set is at least q+2 for q odd and exactly q+2 for q even. We know that D(2,q) has girth 6 and diameter 4, whereas D(3,q) has girth 8 and diameter 6. We prove that for an odd prime p, LU(3,p) is a [p/sup 3/,k] code with k/spl ges/(p/sup 3/-2p/sup 2/+3p-2)/2. We show that the minimum weight and the weight of the minimum stopping set of LU(3,q) are at least 2q and they are exactly 2q for many LU(3,q) codes. We find some interesting LDPC codes by our partial row construction. We also give simulation results for some of our codes.
16103417
Designs in Additive Codes over GF(4)
The purpose of this paper is to study designs in additive codes over GF(4). There are two types of designs. One is a classical t-design with repeated blocks. In this case we have an analog of the Assmus–Mattson Theorem for additive codes over GF(4). The other is a generalized t-design first introduced by Delsarte [4]. As an example, we consider the dodecacode, which is the unique additive even self-dual (12, 212, 6) code. We show that there exists a 5-(12, 6, 3) design in the dodecacode with either 3 distinct blocks or 3 repeated blocks covering a 5-set. We also find a new simple 3-(11, 5, 4) design in the shortened dodecacode by a computer search. Additionally we show that any extremal additive even self-dual code over GF(4) is homogeneous.
14157019
Projections of Binary Linear Codes onto Larger Fields
We study certain projections of binary linear codes onto larger fields. These projections include the well-known projection of the extended Golay [24,12,8] code onto the hexacode over $\mbox{GF}(4)$ and the projection of the Reed--Muller code R(2,5) onto the unique self-dual [8,4,4] code over $\mbox{GF}(4)$. We give a characterization of these projections, and we construct several binary linear codes which have best known optimal parameters, for instance, [20,11,5], [40,22,8], [48,21,12], and [72,31,16]. We also relate the automorphism group of a quaternary code to that of the corresponding binary code.
1354813
Memory coherence activity prediction in commercial workloads
Recent research indicates that prediction-based coherence optimizations offer substantial performance improvements for scientific applications in distributed shared memory multiprocessors. Important commercial applications also show sensitivity to coherence latency, which will become more acute in the future as technology scales. Therefore it is important to investigate prediction of memory coherence activity in the context of commercial workloads.This paper studies a trace-based Downgrade Predictor (DGP) for predicting last stores to shared cache blocks, and a pattern-based Consumer Set Predictor (CSP) for predicting subsequent readers. We evaluate this class of predictors for the first time on commercial applications and demonstrate that our DGP correctly predicts 47%-76% of last stores. Memory sharing patterns in commercial workloads are inherently non-repetitive; hence CSP cannot attain high coverage. We perform an opportunity study of a DGP enhanced through competitive underlying predictors, and in commercial and scientific applications, demonstrate potential to increase coverage up to 14%.
6225887
Hamiltonian decompositions of random bipartite regular graphs
We prove a complete hamiltonian decomposition theorem for random bipartite regular graphs, thereby verifying a conjecture of Robinson and Wormald. The main step is to prove contiguity (a kind of asymptotic equivalence) of two probabilistic models of 4-regular bipartite graphs; namely, the uniform model, and the model obtained by taking the union of two independent, uniformly chosen bipartite Hamilton cycles, conditioned on forming no multiple edges. The proof uses the small subgraph conditioning method to establish contiguity, while the differential equation method is used to analyse a critical quantity.
3457933
On the Society of Genome: Social Affiliation Network Analysis of Microarray Data
To investigate the structure of the genomic interaction network built from yeast gene-expression compendium dataset of hundreds of systematic perturbations, social affiliation network analysis methodologies were applied through quantifying various density, closeness and centrality measures and exploring core-periphery structures. Genes affected by a larger number of perturbations were found to be involved in responses to various environmental challenges. Deletion of essential genes was suggested to cause larger number of genes to be significantly up or down regulated. We explored the network structure made up of several sub-networks using core-periphery models to find ancient pathways. Glycolysis and TCA cycle have relatively core positions in the energy-related processes of yeast.
2320085
Generating random regular graphs
Random regular graphs play a central role in combinatorics and theoretical computer science. In this paper, we analyze a simple algorithm introduced by Steger and Wormald [9] and prove that it produces an asymptotically uniform random regular graph in a polynomial time. Precisely, for fixed d and n with d=O(n1/3-ε), it is shown that the algorithm generates an asymptotically uniform random d-regular graph on n vertices in time O(nd2). This confirms a conjecture of Wormald. The key ingredient in the proof is a recently developed concentration inequality by the second author.Besides being perhaps the only algorithm which works for relatively large d in practical time, our result also has a significant theoretical value, as it can be used to derive many properties of uniform random regular graphs.
15935373
Random Matchings Which Induce Hamilton Cycles and Hamiltonian Decompositions of Random Regular Graphs
Select four perfect matchings of 2n vertices, independently at random. We find the asymptotic probability that each of the first and second matchings forms a Hamilton cycle with each of the third and fourth. This is generalised to embrace any fixed number of perfect matchings, where a prescribed set of pairs of matchings must each produce Hamilton cycles (with suitable restrictions on the prescribed set of pairs). We also show how the result with four matchings implies that a random d-regular graph for fixed even d?4 asymptotically almost surely decomposes into d/2 Hamilton cycles. This completes a general result on the edge-decomposition of a random regular graph into regular spanning subgraphs of given degrees together with Hamilton cycles and verifies conjectures of Janson and of Robinson and Wormald.