18,467 research outputs found
Quasi-Cyclic Asymptotically Regular LDPC Codes
Families of "asymptotically regular" LDPC block code ensembles can be formed
by terminating (J,K)-regular protograph-based LDPC convolutional codes. By
varying the termination length, we obtain a large selection of LDPC block code
ensembles with varying code rates, minimum distance that grows linearly with
block length, and capacity approaching iterative decoding thresholds, despite
the fact that the terminated ensembles are almost regular. In this paper, we
investigate the properties of the quasi-cyclic (QC) members of such an
ensemble. We show that an upper bound on the minimum Hamming distance of
members of the QC sub-ensemble can be improved by careful choice of the
component protographs used in the code construction. Further, we show that the
upper bound on the minimum distance can be improved by using arrays of
circulants in a graph cover of the protograph.Comment: To be presented at the 2010 IEEE Information Theory Workshop, Dublin,
Irelan
The Trapping Redundancy of Linear Block Codes
We generalize the notion of the stopping redundancy in order to study the
smallest size of a trapping set in Tanner graphs of linear block codes. In this
context, we introduce the notion of the trapping redundancy of a code, which
quantifies the relationship between the number of redundant rows in any
parity-check matrix of a given code and the size of its smallest trapping set.
Trapping sets with certain parameter sizes are known to cause error-floors in
the performance curves of iterative belief propagation decoders, and it is
therefore important to identify decoding matrices that avoid such sets. Bounds
on the trapping redundancy are obtained using probabilistic and constructive
methods, and the analysis covers both general and elementary trapping sets.
Numerical values for these bounds are computed for the [2640,1320] Margulis
code and the class of projective geometry codes, and compared with some new
code-specific trapping set size estimates.Comment: 12 pages, 4 tables, 1 figure, accepted for publication in IEEE
Transactions on Information Theor
Algorithmic patterns for -matrices on many-core processors
In this work, we consider the reformulation of hierarchical ()
matrix algorithms for many-core processors with a model implementation on
graphics processing units (GPUs). matrices approximate specific
dense matrices, e.g., from discretized integral equations or kernel ridge
regression, leading to log-linear time complexity in dense matrix-vector
products. The parallelization of matrix operations on many-core
processors is difficult due to the complex nature of the underlying algorithms.
While previous algorithmic advances for many-core hardware focused on
accelerating existing matrix CPU implementations by many-core
processors, we here aim at totally relying on that processor type. As main
contribution, we introduce the necessary parallel algorithmic patterns allowing
to map the full matrix construction and the fast matrix-vector
product to many-core hardware. Here, crucial ingredients are space filling
curves, parallel tree traversal and batching of linear algebra operations. The
resulting model GPU implementation hmglib is the, to the best of the authors
knowledge, first entirely GPU-based Open Source matrix library of
this kind. We conclude this work by an in-depth performance analysis and a
comparative performance study against a standard matrix library,
highlighting profound speedups of our many-core parallel approach
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