16,455 research outputs found
Coding in the Finite-Blocklength Regime: Bounds based on Laplace Integrals and their Asymptotic Approximations
In this paper we provide new compact integral expressions and associated
simple asymptotic approximations for converse and achievability bounds in the
finite blocklength regime. The chosen converse and random coding union bounds
were taken from the recent work of Polyanskyi-Poor-Verdu, and are investigated
under parallel AWGN channels, the AWGN channels, the BI-AWGN channel, and the
BSC. The technique we use, which is a generalization of some recent results
available from the literature, is to map the probabilities of interest into a
Laplace integral, and then solve (or approximate) the integral by use of a
steepest descent technique. The proposed results are particularly useful for
short packet lengths, where the normal approximation may provide unreliable
results.Comment: 29 pages, 10 figures. Submitted to IEEE Trans. on Information Theory.
Matlab code available from http://dgt.dei.unipd.it section Download->Finite
Blocklength Regim
Multiple Description Vector Quantization with Lattice Codebooks: Design and Analysis
The problem of designing a multiple description vector quantizer with lattice
codebook Lambda is considered. A general solution is given to a labeling
problem which plays a crucial role in the design of such quantizers. Numerical
performance results are obtained for quantizers based on the lattices A_2 and
Z^i, i=1,2,4,8, that make use of this labeling algorithm. The high-rate
squared-error distortions for this family of L-dimensional vector quantizers
are then analyzed for a memoryless source with probability density function p
and differential entropy h(p) < infty. For any a in (0,1) and rate pair (R,R),
it is shown that the two-channel distortion d_0 and the channel 1 (or channel
2) distortions d_s satisfy lim_{R -> infty} d_0 2^(2R(1+a)) = (1/4) G(Lambda)
2^{2h(p)} and lim_{R -> infty} d_s 2^(2R(1-a)) = G(S_L) 2^2h(p), where
G(Lambda) is the normalized second moment of a Voronoi cell of the lattice
Lambda and G(S_L) is the normalized second moment of a sphere in L dimensions.Comment: 46 pages, 14 figure
Delay Performance of MISO Wireless Communications
Ultra-reliable, low latency communications (URLLC) are currently attracting
significant attention due to the emergence of mission-critical applications and
device-centric communication. URLLC will entail a fundamental paradigm shift
from throughput-oriented system design towards holistic designs for guaranteed
and reliable end-to-end latency. A deep understanding of the delay performance
of wireless networks is essential for efficient URLLC systems. In this paper,
we investigate the network layer performance of multiple-input, single-output
(MISO) systems under statistical delay constraints. We provide closed-form
expressions for MISO diversity-oriented service process and derive
probabilistic delay bounds using tools from stochastic network calculus. In
particular, we analyze transmit beamforming with perfect and imperfect channel
knowledge and compare it with orthogonal space-time codes and antenna
selection. The effect of transmit power, number of antennas, and finite
blocklength channel coding on the delay distribution is also investigated. Our
higher layer performance results reveal key insights of MISO channels and
provide useful guidelines for the design of ultra-reliable communication
systems that can guarantee the stringent URLLC latency requirements.Comment: This work has been submitted to the IEEE for possible publication.
Copyright may be transferred without notice, after which this version may no
longer be accessibl
Selective Combining for Hybrid Cooperative Networks
In this study, we consider the selective combining in hybrid cooperative
networks (SCHCNs scheme) with one source node, one destination node and
relay nodes. In the SCHCN scheme, each relay first adaptively chooses between
amplify-and-forward protocol and decode-and-forward protocol on a per frame
basis by examining the error-detecting code result, and () relays will be selected to forward their received signals to the
destination. We first develop a signal-to-noise ratio (SNR) threshold-based
frame error rate (FER) approximation model. Then, the theoretical FER
expressions for the SCHCN scheme are derived by utilizing the proposed SNR
threshold-based FER approximation model. The analytical FER expressions are
validated through simulation results.Comment: 27 pages, 8 figures, IET Communications, 201
Random Subsets of Structured Deterministic Frames have MANOVA Spectra
We draw a random subset of rows from a frame with rows (vectors) and
columns (dimensions), where and are proportional to . For a
variety of important deterministic equiangular tight frames (ETFs) and tight
non-ETF frames, we consider the distribution of singular values of the
-subset matrix. We observe that for large they can be precisely
described by a known probability distribution -- Wachter's MANOVA spectral
distribution, a phenomenon that was previously known only for two types of
random frames. In terms of convergence to this limit, the -subset matrix
from all these frames is shown to be empirically indistinguishable from the
classical MANOVA (Jacobi) random matrix ensemble. Thus empirically the MANOVA
ensemble offers a universal description of the spectra of randomly selected
-subframes, even those taken from deterministic frames. The same
universality phenomena is shown to hold for notable random frames as well. This
description enables exact calculations of properties of solutions for systems
of linear equations based on a random choice of frame vectors out of
possible vectors, and has a variety of implications for erasure coding,
compressed sensing, and sparse recovery. When the aspect ratio is small,
the MANOVA spectrum tends to the well known Marcenko-Pastur distribution of the
singular values of a Gaussian matrix, in agreement with previous work on highly
redundant frames. Our results are empirical, but they are exhaustive, precise
and fully reproducible
Error suppression via complementary gauge choices in Reed-Muller codes
Concatenation of two quantum error correcting codes with complementary sets
of transversal gates can provide a means towards universal fault-tolerant
computation. We first show that it is generally preferable to choose the inner
code with the higher pseudo-threshold in order to achieve lower logical failure
rates. We then explore the threshold properties of a wide range of
concatenation schemes. Notably, we demonstrate that the concatenation of
complementary sets of Reed-Muller codes can increase the code capacity
threshold under depolarizing noise when compared to extensions of previously
proposed concatenation models. We also analyze the properties of logical errors
under circuit level noise, showing that smaller codes perform better for all
sampled physical error rates. Our work provides new insights into the
performance of universal concatenated quantum codes for both code capacity and
circuit level noise.Comment: 11 pages + 4 appendices, 6 figures. In v2, Fig.1 was added to conform
to journal specification
Continuous quantum error correction for non-Markovian decoherence
We study the effect of continuous quantum error correction in the case where
each qubit in a codeword is subject to a general Hamiltonian interaction with
an independent bath. We first consider the scheme in the case of a trivial
single-qubit code, which provides useful insights into the workings of
continuous error correction and the difference between Markovian and
non-Markovian decoherence. We then study the model of a bit-flip code with each
qubit coupled to an independent bath qubit and subject to continuous
correction, and find its solution. We show that for sufficiently large
error-correction rates, the encoded state approximately follows an evolution of
the type of a single decohering qubit, but with an effectively decreased
coupling constant. The factor by which the coupling constant is decreased
scales quadratically with the error-correction rate. This is compared to the
case of Markovian noise, where the decoherence rate is effectively decreased by
a factor which scales only linearly with the rate of error correction. The
quadratic enhancement depends on the existence of a Zeno regime in the
Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze
the range of validity of this result and identify two relevant time scales.
Finally, we extend the result to more general codes and argue that the
performance of continuous error correction will exhibit the same qualitative
characteristics.Comment: 16 pages, 4 figures, minor typos corrected, references update
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