11,700 research outputs found
Low-Density Parity-Check Codes From Transversal Designs With Improved Stopping Set Distributions
This paper examines the construction of low-density parity-check (LDPC) codes
from transversal designs based on sets of mutually orthogonal Latin squares
(MOLS). By transferring the concept of configurations in combinatorial designs
to the level of Latin squares, we thoroughly investigate the occurrence and
avoidance of stopping sets for the arising codes. Stopping sets are known to
determine the decoding performance over the binary erasure channel and should
be avoided for small sizes. Based on large sets of simple-structured MOLS, we
derive powerful constraints for the choice of suitable subsets, leading to
improved stopping set distributions for the corresponding codes. We focus on
LDPC codes with column weight 4, but the results are also applicable for the
construction of codes with higher column weights. Finally, we show that a
subclass of the presented codes has quasi-cyclic structure which allows
low-complexity encoding.Comment: 11 pages; to appear in "IEEE Transactions on Communications
Algorithmic and enumerative aspects of the Moser-Tardos distribution
Moser & Tardos have developed a powerful algorithmic approach (henceforth
"MT") to the Lovasz Local Lemma (LLL); the basic operation done in MT and its
variants is a search for "bad" events in a current configuration. In the
initial stage of MT, the variables are set independently. We examine the
distributions on these variables which arise during intermediate stages of MT.
We show that these configurations have a more or less "random" form, building
further on the "MT-distribution" concept of Haeupler et al. in understanding
the (intermediate and) output distribution of MT. This has a variety of
algorithmic applications; the most important is that bad events can be found
relatively quickly, improving upon MT across the complexity spectrum: it makes
some polynomial-time algorithms sub-linear (e.g., for Latin transversals, which
are of basic combinatorial interest), gives lower-degree polynomial run-times
in some settings, transforms certain super-polynomial-time algorithms into
polynomial-time ones, and leads to Las Vegas algorithms for some coloring
problems for which only Monte Carlo algorithms were known.
We show that in certain conditions when the LLL condition is violated, a
variant of the MT algorithm can still produce a distribution which avoids most
of the bad events. We show in some cases this MT variant can run faster than
the original MT algorithm itself, and develop the first-known criterion for the
case of the asymmetric LLL. This can be used to find partial Latin transversals
-- improving upon earlier bounds of Stein (1975) -- among other applications.
We furthermore give applications in enumeration, showing that most applications
(where we aim for all or most of the bad events to be avoided) have many more
solutions than known before by proving that the MT-distribution has "large"
min-entropy and hence that its support-size is large
Decomposition Based Search - A theoretical and experimental evaluation
In this paper we present and evaluate a search strategy called Decomposition
Based Search (DBS) which is based on two steps: subproblem generation and
subproblem solution. The generation of subproblems is done through value
ranking and domain splitting. Subdomains are explored so as to generate,
according to the heuristic chosen, promising subproblems first.
We show that two well known search strategies, Limited Discrepancy Search
(LDS) and Iterative Broadening (IB), can be seen as special cases of DBS. First
we present a tuning of DBS that visits the same search nodes as IB, but avoids
restarts. Then we compare both theoretically and computationally DBS and LDS
using the same heuristic. We prove that DBS has a higher probability of being
successful than LDS on a comparable number of nodes, under realistic
assumptions. Experiments on a constraint satisfaction problem and an
optimization problem show that DBS is indeed very effective if compared to LDS.Comment: 16 pages, 8 figures. LIA Technical Report LIA00203, University of
Bologna, 200
Absorbing Set Analysis and Design of LDPC Codes from Transversal Designs over the AWGN Channel
In this paper we construct low-density parity-check (LDPC) codes from
transversal designs with low error-floors over the additive white Gaussian
noise (AWGN) channel. The constructed codes are based on transversal designs
that arise from sets of mutually orthogonal Latin squares (MOLS) with cyclic
structure. For lowering the error-floors, our approach is twofold: First, we
give an exhaustive classification of so-called absorbing sets that may occur in
the factor graphs of the given codes. These purely combinatorial substructures
are known to be the main cause of decoding errors in the error-floor region
over the AWGN channel by decoding with the standard sum-product algorithm
(SPA). Second, based on this classification, we exploit the specific structure
of the presented codes to eliminate the most harmful absorbing sets and derive
powerful constraints for the proper choice of code parameters in order to
obtain codes with an optimized error-floor performance.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1306.511
Rainbow matchings in properly-coloured multigraphs
Aharoni and Berger conjectured that in any bipartite multigraph that is
properly edge-coloured by colours with at least edges of each
colour there must be a matching that uses each colour exactly once. In this
paper we consider the same question without the bipartiteness assumption. We
show that in any multigraph with edge multiplicities that is properly
edge-coloured by colours with at least edges of each colour
there must be a matching of size that uses each colour at most once.Comment: 7 page
Collaborative video searching on a tabletop
Almost all system and application design for multimedia systems is based around a single user working in isolation to perform some task yet much of the work for which we use computers to help us, is based on working collaboratively with colleagues. Groupware systems do support user collaboration but typically this is supported through software and users still physically work independently. Tabletop systems, such as the DiamondTouch from MERL, are interface devices which support direct user collaboration on a tabletop. When a tabletop is used as the interface for a multimedia system, such as a video search system, then this kind of direct collaboration raises many questions for system design. In this paper we present a tabletop system for supporting a pair of users in a video search task and we evaluate the system not only in terms of search performance but also in terms of userâuser interaction and how different user personalities within each pair of searchers impacts search performance and user interaction. Incorporating the user into the system evaluation as we have done here reveals several interesting results and has important ramifications for the design of a multimedia search system
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