548 research outputs found
Ultra-Reliable Short-Packet Communications: Fundamental Limits and Enabling Technologies
The paradigm shift from 4G to 5G communications, anticipated to enable ultra-reliable low-latency communications (URLLC), will enforce a radical change in the design of wireless communication systems. Unlike in 4G systems, where the main objective is to provide a large transmission rate, in URLLC, as implied by its name, the objective is to enable transmissions with low latency and, simultaneously, very high reliability. Since low latency implies the use of short data packets, the tension between blocklength and reliability is studied in URLLC.Several key enablers for URLLC communications have been designated in the literature. Of special importance are diversity-enabling technologies such as multiantenna systems and feedback protocols. Furthermore, it is not only important to introduce additional diversity by means of the above examples, one must also guarantee that thescarce number of channel uses are used in an optimal way. Therefore, it is imperative to develop design guidelines for how to enable reliable detection of incoming data, how to acquire channel-state information, and how to construct efficient short-packet channel codes. The development of such guidelines is at the heart of this thesis. This thesis focuses on the fundamental performance of URLLC-enabling technologies. Specifically, we provide converse (upper) bounds and achievability (lower) bounds on the maximum coding rate, based on finite-blocklength information theory, for systems that employ the key enablers outlined above. With focus on the wireless channel, modeled via a block-fading assumption, we are able to provide answers to questions like: howto optimally utilize spatial and frequency diversity, how far from optimal short-packet channel codes perform, how multiantenna systems should be designed to serve a given number of users, and how to design feedback schemes when the feedback link is noisy. In particular, this thesis is comprised out of four papers. In Paper A, we study the short-packet performance over the Rician block-fading channel. In particular, we present achievability bounds for pilot-assisted transmission with several different decoders that allow us to quantify the impact, on the achievable performance, of imposed pilots and mismatched decoding. Furthermore, we design short-packet channel codes that perform within 1 dB of our achievability bounds. Paper B studies multiuser massive multiple-input multiple-output systems with short packets. We provide an achievability bound on the average error probability over quasistatic spatially correlated Rayleigh-fading channels. The bound applies to arbitrary multiuser settings, pilot-assisted transmission, and mismatched decoding. This makes it suitable to assess the performance in the uplink/downlink for arbitrary linear signal processing. We show that several lessons learned from infinite-blocklength analyses carry over to the finite-blocklength regime. Furthermore, for the multicell setting with randomly placed users, pilot contamination should be avoided at all cost and minimum mean-squared error signal processing should be used to comply with the stringent requirements of URLLC.In Paper C, we consider sporadic transmissions where the task of the receiver is to both detect and decode an incoming packet. Two novel achievability bounds, and a novel converse bound are presented for joint detection-decoding strategies. It is shown that errors associated with detection deteriorates performance significantly for very short packet sizes. Numerical results also indicate that separate detection-decoding strategies are strictly suboptimal over block-fading channels.Finally, in Paper D, variable-length codes with noisy stop-feedback are studied via a novel achievability bound on the average service time and the average error probability. We use the bound to shed light on the resource allocation problem between the forward and the feedback channel. For URLLC applications, it is shown that enough resources must be assigned to the feedback link such that a NACK-to-ACK error becomes rarer than the target error probability. Furthermore, we illustrate that the variable-length stop-feedback scheme outperforms state-of-the-art fixed-length no-feedback bounds even when the stop-feedback bit is noisy
Reliable Transmission of Short Packets through Queues and Noisy Channels under Latency and Peak-Age Violation Guarantees
This work investigates the probability that the delay and the peak-age of
information exceed a desired threshold in a point-to-point communication system
with short information packets. The packets are generated according to a
stationary memoryless Bernoulli process, placed in a single-server queue and
then transmitted over a wireless channel. A variable-length stop-feedback
coding scheme---a general strategy that encompasses simple automatic repetition
request (ARQ) and more sophisticated hybrid ARQ techniques as special
cases---is used by the transmitter to convey the information packets to the
receiver. By leveraging finite-blocklength results, the delay violation and the
peak-age violation probabilities are characterized without resorting to
approximations based on large-deviation theory as in previous literature.
Numerical results illuminate the dependence of delay and peak-age violation
probability on system parameters such as the frame size and the undetected
error probability, and on the chosen packet-management policy. The guidelines
provided by our analysis are particularly useful for the design of low-latency
ultra-reliable communication systems.Comment: To appear in IEEE journal on selected areas of communication (IEEE
JSAC
Fundamental limits of short-packet wireless communications
Mención Internacional en el título de doctorThis thesis concerns the maximum coding rate at which data can be transmitted
over a noncoherent, single-antenna, Rayleigh block-fading channel using an errorcorrecting
code of a given blocklength with a block-error probability not exceeding
a given value. This is an emerging problem originated by the next generation of
wireless communications, where the understanding of the fundamental limits in the
transmission of short packets is crucial. For this setting, traditional informationtheoretical
metrics of performance that rely on the transmission of long packets, such
as capacity or outage capacity, are not good benchmarks anymore, and the study
of the maximum coding rate as a function of the blocklength is needed. For the
noncoherent Rayleigh block-fading channel model, to study the maximum coding
rate as a function of the blocklength, only nonasymptotic bounds that must be
evaluated numerically were available in the literature. The principal drawback of the
nonasymptotic bounds is their high computational cost, which increases linearly with
the number of blocks (also called throughout this thesis coherence intervals) needed
to transmit a given codeword. By means of different asymptotic expansions in the
number of blocks, this thesis provides an alternative way of studying the maximum
coding rate as a function of the blocklength for the noncoherent, single-antenna,
Rayleigh block-fading channel.
The first approximation on the maximum coding rate derived in this thesis is a
high-SNR normal approximation. This central-limit-theorem-based approximation
becomes accurate as the signal-to-noise ratio (SNR) and the number of coherence
intervals L of size T tend to infinity. We show that the high-SNR normal approximation
is roughly equal to the normal approximation one obtains by transmitting
one pilot symbol per coherence block to estimate the fading coefficient, and by then
transmitting T−1 symbols per coherence block over a coherent fading channel. This
suggests that, at high SNR, one pilot symbol per coherence block suffices to achieve
both the capacity and the channel dispersion. While the approximation was derived
under the assumption that the number of coherence intervals and the SNR tend to
infinity, numerical analyses suggest that it becomes accurate already at SNR values of
15 dB, for 10 coherence intervals or more, and probabilities of error of 10−3 or more. The derived normal approximation is not only useful because it complements
the nonasymptotic bounds available in the literature, but also because it lays the
foundation for analytical studies that analyze the behavior of the maximum coding
rate as a function of system parameters such as SNR, number of coherence intervals,
or blocklength. An example of such a study concerns the optimal design of a simple
slotted-ALOHA protocol, which is also given in this thesis.
Since a big amount of services and applications in the next generation of wireless
communication systems will require to operate at low SNRs and small probabilities
of error (for instance, SNR values of 0 dB and probabilities of error of 10−6), the
second half of this thesis presents saddlepoint approximations of upper and lower
nonasymptotic bounds on the maximum coding rate that are accurate in that regime.
Similar to the normal approximation, these approximations become accurate as the
number of coherence intervals L increases, and they can be calculated efficiently.
Indeed, compared to the nonasymptotic bounds, which require the evaluation of
L-dimensional integrals, the saddlepoint approximations only require the evaluation
of four one-dimensional integrals. Although developed under the assumption of
large L, the saddlepoint approximations are shown to be accurate even for L = 1 and
SNR values of 0 dB or more. The small computational cost of these approximations
can be further avoided by performing high-SNR saddlepoint approximations that
can be evaluated in closed form. These approximations can be applied when some
conditions of convergence are satisfied and are shown to be accurate for 10 dB or
more.
In our analysis, the saddlepoint method is applied to the tail probabilities appearing
in the nonasymptotic bounds. These probabilities often depend on a set
of parameters, such as the SNR. Existing saddlepoint expansions do not consider
such dependencies. Hence, they can only characterize the behavior of the expansion
error in function of the number of coherence intervals L, but not in terms of the
remaining parameters. In contrast, we derive a saddlepoint expansion for random
variables whose distribution depends on an extra parameter, carefully analyze the
error terms, and demonstrate that they are uniform in such an extra parameter. We
then apply the expansion to the Rayleigh block-fading channel and obtain approximations
in which the error terms depend only on the blocklength and are uniform in
the remaining parameters.
Furthermore, the proposed approximations are shown to recover the normal approximation and the reliability function of the channel, thus providing a unifying
tool for the two regimes, which are usually considered separately in the literature.
Specifically, we show that the high-SNR normal approximation can be recovered from
the normal approximation derived from the saddlepoint approximations. By means
of the error exponent analysis that recovers the reliability function of the channel,
we also obtain easier-to-evaluate approximations of the saddlepoint approximations
consisting of the error exponent of the channel multiplied by a subexponential
factor. Numerical evidence suggests that these approximations are as accurate as
the saddlepoint approximations.
Finally, this thesis includes a practical case study where we analyze the benefit of
cooperation in optical wireless communications, a promising technology that can play
an important role in the next generation of wireless communications due to the high
data rates it can achieve. Specifically, a cooperative multipoint transmission and
reception scheme is evaluated for visible light communication (VLC) in an indoor
scenario. The proposed scheme is shown to provide SNR improvements of 3 dB or
more compared to a noncooperative scheme, especially when there is non-line-of-sight
(NLOS) between the access point and the receiver.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Joerg Widmer.- Secretario: Matilde Pilar Sánchez Fernández.- Vocal: Petar Popovsk
Saddlepoint Approximations of Cumulative Distribution Functions of Sums of Random Vectors
In this report, a real-valued function that approximates the cumulative distribution function (CDF) of a finite sum of real-valued independent and identically distributed random vectors is presented. The approximation error is upper bounded and thus, as a byproduct, an upper bound and a lower bound on the CDF are obtained. Finally, it is observed that in the case of lattice and absolutely continuous random variables, the proposed approximation is identical to the saddlepoint approximation of the CDF.Dans ce rapport, une fonction qui approxime la fonction de répartition d'une somme de vecteurs aléatoires indépendants et identiquement distribués est présentée. L'erreur d'approximation est majorée, et par consequent, une borne supérieure et une borne inférieure sur la fonction de répartition sont obtenues. Finalement, pour des vecteurs aléatoires absolument continues ou lattices, l'approximation proposée est identique à l'approximation du point de selle de la fonction de répartition
Using Saddlepoint Approximations and Likelihood-Based Methods to Conduct Statistical Inference for the Mean of the Beta Distribution
The prevalence of conducting statistical inference for the mean of the beta distribution has been rising in various fields of academic research, such as in immunology that analyzes proportions of rare cell population subsets. For our purposes, we will address this statistical inference problem by using likelihood-based applications to hypothesis testing, along with a relatively new statistical method called saddlepoint approximations. Through simulation work, we will compare the performance of these statistical procedures and provide both the statistical and scientific communities with recommendations on best practices
Composite CDMA - A statistical mechanics analysis
Code Division Multiple Access (CDMA) in which the spreading code assignment
to users contains a random element has recently become a cornerstone of CDMA
research. The random element in the construction is particular attractive as it
provides robustness and flexibility in utilising multi-access channels, whilst
not making significant sacrifices in terms of transmission power. Random codes
are generated from some ensemble, here we consider the possibility of combining
two standard paradigms, sparsely and densely spread codes, in a single
composite code ensemble. The composite code analysis includes a replica
symmetric calculation of performance in the large system limit, and
investigation of finite systems through a composite belief propagation
algorithm. A variety of codes are examined with a focus on the high
multi-access interference regime. In both the large size limit and finite
systems we demonstrate scenarios in which the composite code has typical
performance exceeding sparse and dense codes at equivalent signal to noise
ratio.Comment: 23 pages, 11 figures, Sigma Phi 2008 conference submission -
submitted to J.Stat.Mec
Tilted Euler characteristic densities for Central Limit random fields, with application to "bubbles"
Local increases in the mean of a random field are detected (conservatively)
by thresholding a field of test statistics at a level chosen to control the
tail probability or -value of its maximum. This -value is approximated by
the expected Euler characteristic (EC) of the excursion set of the test
statistic field above , denoted . Under isotropy,
one can use the expansion
, where is
an intrinsic volume of the parameter space and is an EC density of the
field. EC densities are available for a number of processes, mainly those
constructed from (multivariate) Gaussian fields via smooth functions. Using
saddlepoint methods, we derive an expansion for for fields which
are only approximately Gaussian, but for which higher-order cumulants are
available. We focus on linear combinations of independent non-Gaussian
fields, whence a Central Limit theorem is in force. The threshold is
allowed to grow with the sample size , in which case our expression has a
smaller relative asymptotic error than the Gaussian EC density. Several
illustrative examples including an application to "bubbles" data accompany the
theory.Comment: Published in at http://dx.doi.org/10.1214/07-AOS549 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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