2,206 research outputs found
Error-correction on non-standard communication channels
Many communication systems are poorly modelled by the standard channels assumed in the information theory literature, such as the binary symmetric channel or the additive white Gaussian noise channel. Real systems suffer from additional problems including time-varying noise, cross-talk, synchronization errors and latency constraints. In this thesis, low-density parity-check codes and codes related to them are applied to non-standard channels. First, we look at time-varying noise modelled by a Markov channel. A low-density parity-check code decoder is modified to give an improvement of over 1dB. Secondly, novel codes based on low-density parity-check codes are introduced which produce transmissions with Pr(bit = 1) ≠Pr(bit = 0). These non-linear codes are shown to be good candidates for multi-user channels with crosstalk, such as optical channels. Thirdly, a channel with synchronization errors is modelled by random uncorrelated insertion or deletion events at unknown positions. Marker codes formed from low-density parity-check codewords with regular markers inserted within them are studied. It is shown that a marker code with iterative decoding has performance close to the bounds on the channel capacity, significantly outperforming other known codes. Finally, coding for a system with latency constraints is studied. For example, if a telemetry system involves a slow channel some error correction is often needed quickly whilst the code should be able to correct remaining errors later. A new code is formed from the intersection of a convolutional code with a high rate low-density parity-check code. The convolutional code has good early decoding performance and the high rate low-density parity-check code efficiently cleans up remaining errors after receiving the entire block. Simulations of the block code show a gain of 1.5dB over a standard NASA code
Scalable Neural Network Decoders for Higher Dimensional Quantum Codes
Machine learning has the potential to become an important tool in quantum
error correction as it allows the decoder to adapt to the error distribution of
a quantum chip. An additional motivation for using neural networks is the fact
that they can be evaluated by dedicated hardware which is very fast and
consumes little power. Machine learning has been previously applied to decode
the surface code. However, these approaches are not scalable as the training
has to be redone for every system size which becomes increasingly difficult. In
this work the existence of local decoders for higher dimensional codes leads us
to use a low-depth convolutional neural network to locally assign a likelihood
of error on each qubit. For noiseless syndrome measurements, numerical
simulations show that the decoder has a threshold of around when
applied to the 4D toric code. When the syndrome measurements are noisy, the
decoder performs better for larger code sizes when the error probability is
low. We also give theoretical and numerical analysis to show how a
convolutional neural network is different from the 1-nearest neighbor
algorithm, which is a baseline machine learning method
Duality between Multidimensional Convolutional Codes and Systems
Multidimensional convolutional codes generalize (one dimensional)
convolutional codes and they correspond under a natural duality to
multidimensional systems widely studied in the systems literature.Comment: 16 pages LaTe
Can Punctured Rate-1/2 Turbo Codes Achieve a Lower Error Floor than their Rate-1/3 Parent Codes?
In this paper we concentrate on rate-1/3 systematic parallel concatenated
convolutional codes and their rate-1/2 punctured child codes. Assuming
maximum-likelihood decoding over an additive white Gaussian channel, we
demonstrate that a rate-1/2 non-systematic child code can exhibit a lower error
floor than that of its rate-1/3 parent code, if a particular condition is met.
However, assuming iterative decoding, convergence of the non-systematic code
towards low bit-error rates is problematic. To alleviate this problem, we
propose rate-1/2 partially-systematic codes that can still achieve a lower
error floor than that of their rate-1/3 parent codes. Results obtained from
extrinsic information transfer charts and simulations support our conclusion.Comment: 5 pages, 7 figures, Proceedings of the 2006 IEEE Information Theory
Workshop, Chengdu, China, October 22-26, 200
Minimum Distortion Variance Concatenated Block Codes for Embedded Source Transmission
Some state-of-art multimedia source encoders produce embedded source bit
streams that upon the reliable reception of only a fraction of the total bit
stream, the decoder is able reconstruct the source up to a basic quality.
Reliable reception of later source bits gradually improve the reconstruction
quality. Examples include scalable extensions of H.264/AVC and progressive
image coders such as JPEG2000. To provide an efficient protection for embedded
source bit streams, a concatenated block coding scheme using a minimum mean
distortion criterion was considered in the past. Although, the original design
was shown to achieve better mean distortion characteristics than previous
studies, the proposed coding structure was leading to dramatic quality
fluctuations. In this paper, a modification of the original design is first
presented and then the second order statistics of the distortion is taken into
account in the optimization. More specifically, an extension scheme is proposed
using a minimum distortion variance optimization criterion. This robust system
design is tested for an image transmission scenario. Numerical results show
that the proposed extension achieves significantly lower variance than the
original design, while showing similar mean distortion performance using both
convolutional codes and low density parity check codes.Comment: 6 pages, 4 figures, In Proc. of International Conference on
Computing, Networking and Communications, ICNC 2014, Hawaii, US
Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes
Foliated quantum codes are a resource for fault-tolerant measurement-based
quantum error correction for quantum repeaters and for quantum computation.
They represent a general approach to integrating a range of possible quantum
error correcting codes into larger fault-tolerant networks. Here we present an
efficient heuristic decoding scheme for foliated quantum codes, based on
message passing between primal and dual code 'sheets'. We test this decoder on
two different families of sparse quantum error correcting code: turbo codes and
bicycle codes, and show reasonably high numerical performance thresholds. We
also present a construction schedule for building such code states.Comment: 23 pages, 15 figures, accepted for publication in Phys. Rev.
Spatially Coupled Codes and Optical Fiber Communications: An Ideal Match?
In this paper, we highlight the class of spatially coupled codes and discuss
their applicability to long-haul and submarine optical communication systems.
We first demonstrate how to optimize irregular spatially coupled LDPC codes for
their use in optical communications with limited decoding hardware complexity
and then present simulation results with an FPGA-based decoder where we show
that very low error rates can be achieved and that conventional block-based
LDPC codes can be outperformed. In the second part of the paper, we focus on
the combination of spatially coupled LDPC codes with different demodulators and
detectors, important for future systems with adaptive modulation and for
varying channel characteristics. We demonstrate that SC codes can be employed
as universal, channel-agnostic coding schemes.Comment: Invited paper to be presented in the special session on "Signal
Processing, Coding, and Information Theory for Optical Communications" at
IEEE SPAWC 201
Distributed Matrix-Vector Multiplication: A Convolutional Coding Approach
Distributed computing systems are well-known to suffer from the problem of
slow or failed nodes; these are referred to as stragglers. Straggler mitigation
(for distributed matrix computations) has recently been investigated from the
standpoint of erasure coding in several works. In this work we present a
strategy for distributed matrix-vector multiplication based on convolutional
coding. Our scheme can be decoded using a low-complexity peeling decoder. The
recovery process enjoys excellent numerical stability as compared to
Reed-Solomon coding based approaches (which exhibit significant problems owing
their badly conditioned decoding matrices). Finally, our schemes are better
matched to the practically important case of sparse matrix-vector
multiplication as compared to many previous schemes. Extensive simulation
results corroborate our findings
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