2,967 research outputs found
DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models
The work identifies the first general, explicit, and non-random MIMO
encoder-decoder structures that guarantee optimality with respect to the
diversity-multiplexing tradeoff (DMT), without employing a computationally
expensive maximum-likelihood (ML) receiver. Specifically, the work establishes
the DMT optimality of a class of regularized lattice decoders, and more
importantly the DMT optimality of their lattice-reduction (LR)-aided linear
counterparts. The results hold for all channel statistics, for all channel
dimensions, and most interestingly, irrespective of the particular lattice-code
applied. As a special case, it is established that the LLL-based LR-aided
linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal
decoding of any lattice code at a worst-case complexity that grows at most
linearly in the data rate. This represents a fundamental reduction in the
decoding complexity when compared to ML decoding whose complexity is generally
exponential in rate.
The results' generality lends them applicable to a plethora of pertinent
communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI,
cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality
of the LR-aided linear decoder is guaranteed. The adopted approach yields
insight, and motivates further study, into joint transceiver designs with an
improved SNR gap to ML decoding.Comment: 16 pages, 1 figure (3 subfigures), submitted to the IEEE Transactions
on Information Theor
The Devil is in the Decoder: Classification, Regression and GANs
Many machine vision applications, such as semantic segmentation and depth
prediction, require predictions for every pixel of the input image. Models for
such problems usually consist of encoders which decrease spatial resolution
while learning a high-dimensional representation, followed by decoders who
recover the original input resolution and result in low-dimensional
predictions. While encoders have been studied rigorously, relatively few
studies address the decoder side. This paper presents an extensive comparison
of a variety of decoders for a variety of pixel-wise tasks ranging from
classification, regression to synthesis. Our contributions are: (1) Decoders
matter: we observe significant variance in results between different types of
decoders on various problems. (2) We introduce new residual-like connections
for decoders. (3) We introduce a novel decoder: bilinear additive upsampling.
(4) We explore prediction artifacts
Asymptotics of Fingerprinting and Group Testing: Tight Bounds from Channel Capacities
In this work we consider the large-coalition asymptotics of various
fingerprinting and group testing games, and derive explicit expressions for the
capacities for each of these models. We do this both for simple decoders (fast
but suboptimal) and for joint decoders (slow but optimal).
For fingerprinting, we show that if the pirate strategy is known, the
capacity often decreases linearly with the number of colluders, instead of
quadratically as in the uninformed fingerprinting game. For many attacks the
joint capacity is further shown to be strictly higher than the simple capacity.
For group testing, we improve upon known results about the joint capacities,
and derive new explicit asymptotics for the simple capacities. These show that
existing simple group testing algorithms are suboptimal, and that simple
decoders cannot asymptotically be as efficient as joint decoders. For the
traditional group testing model, we show that the gap between the simple and
joint capacities is a factor 1.44 for large numbers of defectives.Comment: 14 pages, 6 figure
Advantages of versatile neural-network decoding for topological codes
Finding optimal correction of errors in generic stabilizer codes is a
computationally hard problem, even for simple noise models. While this task can
be simplified for codes with some structure, such as topological stabilizer
codes, developing good and efficient decoders still remains a challenge. In our
work, we systematically study a very versatile class of decoders based on
feedforward neural networks. To demonstrate adaptability, we apply neural
decoders to the triangular color and toric codes under various noise models
with realistic features, such as spatially-correlated errors. We report that
neural decoders provide significant improvement over leading efficient decoders
in terms of the error-correction threshold. Using neural networks simplifies
the process of designing well-performing decoders, and does not require prior
knowledge of the underlying noise model.Comment: 11 pages, 6 figures, 2 table
Enhanced Feedback Iterative Decoding of Sparse Quantum Codes
Decoding sparse quantum codes can be accomplished by syndrome-based decoding
using a belief propagation (BP) algorithm.We significantly improve this
decoding scheme by developing a new feedback adjustment strategy for the
standard BP algorithm. In our feedback procedure, we exploit much of the
information from stabilizers, not just the syndrome but also the values of the
frustrated checks on individual qubits of the code and the channel model.
Furthermore we show that our decoding algorithm is superior to belief
propagation algorithms using only the syndrome in the feedback procedure for
all cases of the depolarizing channel. Our algorithm does not increase the
measurement overhead compared to the previous method, as the extra information
comes for free from the requisite stabilizer measurements.Comment: 10 pages, 11 figures, Second version, To be appeared in IEEE
Transactions on Information Theor
2-D Compass Codes
The compass model on a square lattice provides a natural template for
building subsystem stabilizer codes. The surface code and the Bacon-Shor code
represent two extremes of possible codes depending on how many gauge qubits are
fixed. We explore threshold behavior in this broad class of local codes by
trading locality for asymmetry and gauge degrees of freedom for stabilizer
syndrome information. We analyze these codes with asymmetric and spatially
inhomogeneous Pauli noise in the code capacity and phenomenological models. In
these idealized settings, we observe considerably higher thresholds against
asymmetric noise. At the circuit level, these codes inherit the bare-ancilla
fault-tolerance of the Bacon-Shor code.Comment: 10 pages, 7 figures, added discussion on fault-toleranc
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