942,390 research outputs found
Belief Propagation Decoding of Polar Codes on Permuted Factor Graphs
We show that the performance of iterative belief propagation (BP) decoding of
polar codes can be enhanced by decoding over different carefully chosen factor
graph realizations. With a genie-aided stopping condition, it can achieve the
successive cancellation list (SCL) decoding performance which has already been
shown to achieve the maximum likelihood (ML) bound provided that the list size
is sufficiently large. The proposed decoder is based on different realizations
of the polar code factor graph with randomly permuted stages during decoding.
Additionally, a different way of visualizing the polar code factor graph is
presented, facilitating the analysis of the underlying factor graph and the
comparison of different graph permutations. In our proposed decoder, a high
rate Cyclic Redundancy Check (CRC) code is concatenated with a polar code and
used as an iteration stopping criterion (i.e., genie) to even outperform the
SCL decoder of the plain polar code (without the CRC-aid). Although our
permuted factor graph-based decoder does not outperform the SCL-CRC decoder, it
achieves, to the best of our knowledge, the best performance of all iterative
polar decoders presented thus far.Comment: in IEEE Wireless Commun. and Networking Conf. (WCNC), April 201
Learning Laplacian Matrix in Smooth Graph Signal Representations
The construction of a meaningful graph plays a crucial role in the success of
many graph-based representations and algorithms for handling structured data,
especially in the emerging field of graph signal processing. However, a
meaningful graph is not always readily available from the data, nor easy to
define depending on the application domain. In particular, it is often
desirable in graph signal processing applications that a graph is chosen such
that the data admit certain regularity or smoothness on the graph. In this
paper, we address the problem of learning graph Laplacians, which is equivalent
to learning graph topologies, such that the input data form graph signals with
smooth variations on the resulting topology. To this end, we adopt a factor
analysis model for the graph signals and impose a Gaussian probabilistic prior
on the latent variables that control these signals. We show that the Gaussian
prior leads to an efficient representation that favors the smoothness property
of the graph signals. We then propose an algorithm for learning graphs that
enforces such property and is based on minimizing the variations of the signals
on the learned graph. Experiments on both synthetic and real world data
demonstrate that the proposed graph learning framework can efficiently infer
meaningful graph topologies from signal observations under the smoothness
prior
Efficient Implementation of the Plan Graph in STAN
STAN is a Graphplan-based planner, so-called because it uses a variety of
STate ANalysis techniques to enhance its performance. STAN competed in the
AIPS-98 planning competition where it compared well with the other competitors
in terms of speed, finding solutions fastest to many of the problems posed.
Although the domain analysis techniques STAN exploits are an important factor
in its overall performance, we believe that the speed at which STAN solved the
competition problems is largely due to the implementation of its plan graph.
The implementation is based on two insights: that many of the graph
construction operations can be implemented as bit-level logical operations on
bit vectors, and that the graph should not be explicitly constructed beyond the
fix point. This paper describes the implementation of STAN's plan graph and
provides experimental results which demonstrate the circumstances under which
advantages can be obtained from using this implementation
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An effective data placement strategy for XML documents
As XML is increasingly being used in Web applications, new
technologies need to be investigated for processing XML documents with high
performance. Parallelism is a promising solution for structured document
processing and data placement is a major factor for system performance
improvement in parallel processing. This paper describes an effective XML
document data placement strategy. The new strategy is based on a multilevel
graph partitioning algorithm with the consideration of the unique features of
XML documents and query distributions. A new algorithm, which is based on
XML query schemas to derive the weighted graph from the labelled directed
graph presentation of XML documents, is also proposed. Performance analysis
on the algorithm presented in the paper shows that the new data placement
strategy exhibits low workload skew and a high degree of parallelism
Merging Belief Propagation and the Mean Field Approximation: A Free Energy Approach
We present a joint message passing approach that combines belief propagation
and the mean field approximation. Our analysis is based on the region-based
free energy approximation method proposed by Yedidia et al. We show that the
message passing fixed-point equations obtained with this combination correspond
to stationary points of a constrained region-based free energy approximation.
Moreover, we present a convergent implementation of these message passing
fixedpoint equations provided that the underlying factor graph fulfills certain
technical conditions. In addition, we show how to include hard constraints in
the part of the factor graph corresponding to belief propagation. Finally, we
demonstrate an application of our method to iterative channel estimation and
decoding in an orthogonal frequency division multiplexing (OFDM) system
Local And Global Colorability of Graphs
It is shown that for any fixed and , the maximum possible
chromatic number of a graph on vertices in which every subgraph of radius
at most is colorable is (that is, up to a factor poly-logarithmic in ).
The proof is based on a careful analysis of the local and global colorability
of random graphs and implies, in particular, that a random -vertex graph
with the right edge probability has typically a chromatic number as above and
yet most balls of radius in it are -degenerate
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