63,757 research outputs found
Characterization and Efficient Search of Non-Elementary Trapping Sets of LDPC Codes with Applications to Stopping Sets
In this paper, we propose a characterization for non-elementary trapping sets
(NETSs) of low-density parity-check (LDPC) codes. The characterization is based
on viewing a NETS as a hierarchy of embedded graphs starting from an ETS. The
characterization corresponds to an efficient search algorithm that under
certain conditions is exhaustive. As an application of the proposed
characterization/search, we obtain lower and upper bounds on the stopping
distance of LDPC codes.
We examine a large number of regular and irregular LDPC codes, and
demonstrate the efficiency and versatility of our technique in finding lower
and upper bounds on, and in many cases the exact value of, . Finding
, or establishing search-based lower or upper bounds, for many of the
examined codes are out of the reach of any existing algorithm
Classification of generalized Hadamard matrices H(6,3) and quaternary Hermitian self-dual codes of length 18
All generalized Hadamard matrices of order 18 over a group of order 3,
H(6,3), are enumerated in two different ways: once, as class regular symmetric
(6,3)-nets, or symmetric transversal designs on 54 points and 54 blocks with a
group of order 3 acting semi-regularly on points and blocks, and secondly, as
collections of full weight vectors in quaternary Hermitian self-dual codes of
length 18. The second enumeration is based on the classification of Hermitian
self-dual [18,9] codes over GF(4), completed in this paper. It is shown that up
to monomial equivalence, there are 85 generalized Hadamard matrices H(6,3), and
245 inequivalent Hermitian self-dual codes of length 18 over GF(4).Comment: 17 pages. Minor revisio
Clifford Gates by Code Deformation
Topological subsystem color codes add to the advantages of topological codes
an important feature: error tracking only involves measuring 2-local operators
in a two dimensional setting. Unfortunately, known methods to compute with them
were highly unpractical. We give a mechanism to implement all Clifford gates by
code deformation in a planar setting. In particular, we use twist braiding and
express its effects in terms of certain colored Majorana operators.Comment: Extended version with more detail
Learning Spatiotemporal Features for Infrared Action Recognition with 3D Convolutional Neural Networks
Infrared (IR) imaging has the potential to enable more robust action
recognition systems compared to visible spectrum cameras due to lower
sensitivity to lighting conditions and appearance variability. While the action
recognition task on videos collected from visible spectrum imaging has received
much attention, action recognition in IR videos is significantly less explored.
Our objective is to exploit imaging data in this modality for the action
recognition task. In this work, we propose a novel two-stream 3D convolutional
neural network (CNN) architecture by introducing the discriminative code layer
and the corresponding discriminative code loss function. The proposed network
processes IR image and the IR-based optical flow field sequences. We pretrain
the 3D CNN model on the visible spectrum Sports-1M action dataset and finetune
it on the Infrared Action Recognition (InfAR) dataset. To our best knowledge,
this is the first application of the 3D CNN to action recognition in the IR
domain. We conduct an elaborate analysis of different fusion schemes (weighted
average, single and double-layer neural nets) applied to different 3D CNN
outputs. Experimental results demonstrate that our approach can achieve
state-of-the-art average precision (AP) performances on the InfAR dataset: (1)
the proposed two-stream 3D CNN achieves the best reported 77.5% AP, and (2) our
3D CNN model applied to the optical flow fields achieves the best reported
single stream 75.42% AP
From Cages to Trapping Sets and Codewords: A Technique to Derive Tight Upper Bounds on the Minimum Size of Trapping Sets and Minimum Distance of LDPC Codes
Cages, defined as regular graphs with minimum number of nodes for a given
girth, are well-studied in graph theory. Trapping sets are graphical structures
responsible for error floor of low-density parity-check (LDPC) codes, and are
well investigated in coding theory. In this paper, we make connections between
cages and trapping sets. In particular, starting from a cage (or a modified
cage), we construct a trapping set in multiple steps. Based on the connection
between cages and trapping sets, we then use the available results in graph
theory on cages and derive tight upper bounds on the size of the smallest
trapping sets for variable-regular LDPC codes with a given variable degree and
girth. The derived upper bounds in many cases meet the best known lower bounds
and thus provide the actual size of the smallest trapping sets. Considering
that non-zero codewords are a special case of trapping sets, we also derive
tight upper bounds on the minimum weight of such codewords, i.e., the minimum
distance, of variable-regular LDPC codes as a function of variable degree and
girth
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