27,340 research outputs found
Quantum Error Correction - Decoders
Error correction is used to correct any errors that may arise when sending any message, as errors are prone to appear due to noise. For classical codes, there are many decoders used, for example, belief propagation. Unfortunately, these classical decoders are less efficient for quantum codes. A proposed remedy to improve the decoders efficiency is to use a neural network for decoding. In this thesis, we will implement belief propagation on the toric code and check its efficiency. We will see that for few errors, belief propagation works, but it fails for other cases. We also introduce the modifications needed for neural belief propagation, a modification of the original algorithm that integrates a neural network on the algorithm structure
Multilevel Decoders Surpassing Belief Propagation on the Binary Symmetric Channel
In this paper, we propose a new class of quantized message-passing decoders
for LDPC codes over the BSC. The messages take values (or levels) from a finite
set. The update rules do not mimic belief propagation but instead are derived
using the knowledge of trapping sets. We show that the update rules can be
derived to correct certain error patterns that are uncorrectable by algorithms
such as BP and min-sum. In some cases even with a small message set, these
decoders can guarantee correction of a higher number of errors than BP and
min-sum. We provide particularly good 3-bit decoders for 3-left-regular LDPC
codes. They significantly outperform the BP and min-sum decoders, but more
importantly, they achieve this at only a fraction of the complexity of the BP
and min-sum decoders.Comment: 5 pages, in Proc. of 2010 IEEE International Symposium on Information
Theory (ISIT
Distributed Local Linear Parameter Estimation using Gaussian SPAWN
We consider the problem of estimating local sensor parameters, where the
local parameters and sensor observations are related through linear stochastic
models. Sensors exchange messages and cooperate with each other to estimate
their own local parameters iteratively. We study the Gaussian Sum-Product
Algorithm over a Wireless Network (gSPAWN) procedure, which is based on belief
propagation, but uses fixed size broadcast messages at each sensor instead.
Compared with the popular diffusion strategies for performing network parameter
estimation, whose communication cost at each sensor increases with increasing
network density, the gSPAWN algorithm allows sensors to broadcast a message
whose size does not depend on the network size or density, making it more
suitable for applications in wireless sensor networks. We show that the gSPAWN
algorithm converges in mean and has mean-square stability under some technical
sufficient conditions, and we describe an application of the gSPAWN algorithm
to a network localization problem in non-line-of-sight environments. Numerical
results suggest that gSPAWN converges much faster in general than the diffusion
method, and has lower communication costs, with comparable root mean square
errors
An Adaptive Entanglement Distillation Scheme Using Quantum Low Density Parity Check Codes
Quantum low density parity check (QLDPC) codes are useful primitives for
quantum information processing because they can be encoded and decoded
efficiently. Besides, the error correcting capability of a few QLDPC codes
exceeds the quantum Gilbert-Varshamov bound. Here, we report a numerical
performance analysis of an adaptive entanglement distillation scheme using
QLDPC codes. In particular, we find that the expected yield of our adaptive
distillation scheme to combat depolarization errors exceed that of Leung and
Shor whenever the error probability is less than about 0.07 or greater than
about 0.28. This finding illustrates the effectiveness of using QLDPC codes in
entanglement distillation.Comment: 12 pages, 6 figure
Cooperative and Distributed Localization for Wireless Sensor Networks in Multipath Environments
We consider the problem of sensor localization in a wireless network in a
multipath environment, where time and angle of arrival information are
available at each sensor. We propose a distributed algorithm based on belief
propagation, which allows sensors to cooperatively self-localize with respect
to one single anchor in a multihop network. The algorithm has low overhead and
is scalable. Simulations show that although the network is loopy, the proposed
algorithm converges, and achieves good localization accuracy
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