343,385 research outputs found
Iterative Bounded Distance Decoding of Product Codes with Scaled Reliability
We propose a modified iterative bounded distance decoding of product codes.
The proposed algorithm is based on exchanging hard messages iteratively and
exploiting channel reliabilities to make hard decisions at each iteration.
Performance improvements up to 0.26 dB are achieved
Bias-tailored quantum LDPC codes
Bias-tailoring allows quantum error correction codes to exploit qubit noise
asymmetry. Recently, it was shown that a modified form of the surface code, the
XZZX code, exhibits considerably improved performance under biased noise. In
this work, we demonstrate that quantum low density parity check codes can be
similarly bias-tailored. We introduce a bias-tailored lifted product code
construction that provides the framework to expand bias-tailoring methods
beyond the family of 2D topological codes. We present examples of bias-tailored
lifted product codes based on classical quasi-cyclic codes and numerically
assess their performance using a belief propagation plus ordered statistics
decoder. Our Monte Carlo simulations, performed under asymmetric noise, show
that bias-tailored codes achieve several orders of magnitude improvement in
their error suppression relative to depolarising noise.Comment: 21 Pages, 13 Figures. Comments welcome
Partial Syndrome Measurement for Hypergraph Product Codes
Hypergraph product codes are a promising avenue to achieving fault-tolerant
quantum computation with constant overhead. When embedding these and other
constant-rate qLDPC codes into 2D, a significant number of nonlocal connections
are required, posing difficulties for some quantum computing architectures. In
this work, we introduce a fault-tolerance scheme that aims to alleviate the
effects of implementing this nonlocality by measuring generators acting on
spatially distant qubits less frequently than those which do not. We
investigate the performance of a simplified version of this scheme, where the
measured generators are randomly selected. When applied to hypergraph product
codes and a modified small-set-flip decoding algorithm, we prove that for a
sufficiently high percentage of generators being measured, a threshold still
exists. We also find numerical evidence that the logical error rate is
exponentially suppressed even when a large constant fraction of generators are
not measured.Comment: 10 pages, 4 figure
Degree Optimization and Stability Condition for the Min-Sum Decoder
The min-sum (MS) algorithm is arguably the second most fundamental algorithm
in the realm of message passing due to its optimality (for a tree code) with
respect to the {\em block error} probability \cite{Wiberg}. There also seems to
be a fundamental relationship of MS decoding with the linear programming
decoder \cite{Koetter}. Despite its importance, its fundamental properties have
not nearly been studied as well as those of the sum-product (also known as BP)
algorithm.
We address two questions related to the MS rule. First, we characterize the
stability condition under MS decoding. It turns out to be essentially the same
condition as under BP decoding. Second, we perform a degree distribution
optimization. Contrary to the case of BP decoding, under MS decoding the
thresholds of the best degree distributions for standard irregular LDPC
ensembles are significantly bounded away from the Shannon threshold. More
precisely, on the AWGN channel, for the best codes that we find, the gap to
capacity is 1dB for a rate 0.3 code and it is 0.4dB when the rate is 0.9 (the
gap decreases monotonically as we increase the rate).
We also used the optimization procedure to design codes for modified MS
algorithm where the output of the check node is scaled by a constant
. For , we observed that the gap to capacity was
lesser for the modified MS algorithm when compared with the MS algorithm.
However, it was still quite large, varying from 0.75 dB to 0.2 dB for rates
between 0.3 and 0.9.
We conclude by posing what we consider to be the most important open
questions related to the MS algorithm.Comment: submitted to ITW 0
Development of a Model and Computer Code to Describe Solar Grade Silicon Production Processes
Mathematical models and computer codes based on these models, which allow prediction of the product distribution in chemical reactors for converting gaseous silicon compounds to condensed-phase silicon were developed. The following tasks were accomplished: (1) formulation of a model for silicon vapor separation/collection from the developing turbulent flow stream within reactors of the Westinghouse (2) modification of an available general parabolic code to achieve solutions to the governing partial differential equations (boundary layer type) which describe migration of the vapor to the reactor walls, (3) a parametric study using the boundary layer code to optimize the performance characteristics of the Westinghouse reactor, (4) calculations relating to the collection efficiency of the new AeroChem reactor, and (5) final testing of the modified LAPP code for use as a method of predicting Si(1) droplet sizes in these reactors
Modified algorithm for hard decision decoding of product codes
Product coding produces powerful long codes from short constituent codes. The conventional row-column decoding algorithm of the product code does not exploit its full power of correcting random errors and proposes a modification to the conventional decoding algorithm, which makes it capable of reaching the theoretical error correction capability of the code. In addition to its theoretical significance, the modified algorithm is shown to provide a gain of 0.5 dB over the conventional algorithm for AWGN channels
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