189 research outputs found

    Reliable Transmission of Short Packets through Queues and Noisy Channels under Latency and Peak-Age Violation Guarantees

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    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

    A Simple Derivation of the Refined Sphere Packing Bound Under Certain Symmetry Hypotheses

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    A judicious application of the Berry-Esseen theorem via suitable Augustin information measures is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is Ω(n−0.5(1−Esp′(R)))\mathit{\Omega}\left(n^{-0.5(1-E_{sp}'(R))}\right) for all codes on certain families of channels -- including the Gaussian channels and the non-stationary Renyi symmetric channels -- and for the constant composition codes on stationary memoryless channels. The resulting non-asymptotic bounds have definite approximation error terms. As a preliminary result that might be of interest on its own, the trade-off between type I and type II error probabilities in the hypothesis testing problem with (possibly non-stationary) independent samples is determined up to some multiplicative constants, assuming that the probabilities of both types of error are decaying exponentially with the number of samples, using the Berry-Esseen theorem.Comment: 20 page

    Information-theoretic analysis of a family of additive energy channels

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    This dissertation studies a new family of channel models for non-coherent com- munications, the additive energy channels. By construction, the additive en- ergy channels occupy an intermediate region between two widely used channel models: the discrete-time Gaussian channel, used to represent coherent com- munication systems operating at radio and microwave frequencies, and the discrete-time Poisson channel, which often appears in the analysis of intensity- modulated systems working at optical frequencies. The additive energy chan- nels share with the Gaussian channel the additivity between a useful signal and a noise component. However, the signal and noise components are not complex- valued quadrature amplitudes but, as in the Poisson channel, non-negative real numbers, the energy or squared modulus of the complex amplitude. The additive energy channels come in two variants, depending on whether the channel output is discrete or continuous. In the former case, the energy is a multiple of a fundamental unit, the quantum of energy, whereas in the second the value of the energy can take on any non-negative real number. For con- tinuous output the additive noise has an exponential density, as for the energy of a sample of complex Gaussian noise. For discrete, or quantized, energy the signal component is randomly distributed according to a Poisson distribution whose mean is the signal energy of the corresponding Gaussian channel; part of the total noise at the channel output is thus a signal-dependent, Poisson noise component. Moreover, the additive noise has a geometric distribution, the discrete counterpart of the exponential density. Contrary to the common engineering wisdom that not using the quadrature amplitude incurs in a signi¯cant performance penalty, it is shown in this dis- sertation that the capacity of the additive energy channels essentially coincides with that of a coherent Gaussian model under a broad set of circumstances. Moreover, common modulation and coding techniques for the Gaussian chan- nel often admit a natural extension to the additive energy channels, and their performance frequently parallels those of the Gaussian channel methods. Four information-theoretic quantities, covering both theoretical and practi- cal aspects of the reliable transmission of information, are studied: the channel capacity, the minimum energy per bit, the constrained capacity when a given digital modulation format is used, and the pairwise error probability. Of these quantities, the channel capacity sets a fundamental limit on the transmission capabilities of the channel but is sometimes di±cult to determine. The min- imum energy per bit (or its inverse, the capacity per unit cost), on the other hand, turns out to be easier to determine, and may be used to analyze the performance of systems operating at low levels of signal energy. Closer to a practical ¯gure of merit is the constrained capacity, which estimates the largest amount of information which can be transmitted by using a speci¯c digital modulation format. Its study is complemented by the computation of the pairwise error probability, an e®ective tool to estimate the performance of practical coded communication systems. Regarding the channel capacity, the capacity of the continuous additive energy channel is found to coincide with that of a Gaussian channel with iden- tical signal-to-noise ratio. Also, an upper bound |the tightest known| to the capacity of the discrete-time Poisson channel is derived. The capacity of the quantized additive energy channel is shown to have two distinct functional forms: if additive noise is dominant, the capacity is close to that of the continu- ous channel with the same energy and noise levels; when Poisson noise prevails, the capacity is similar to that of a discrete-time Poisson channel, with no ad- ditive noise. An analogy with radiation channels of an arbitrary frequency, for which the quanta of energy are photons, is presented. Additive noise is found to be dominant when frequency is low and, simultaneously, the signal-to-noise ratio lies below a threshold; the value of this threshold is well approximated by the expected number of quanta of additive noise. As for the minimum energy per nat (1 nat is log2 e bits, or about 1.4427 bits), it equals the average energy of the additive noise component for all the stud- ied channel models. A similar result was previously known to hold for two particular cases, namely the discrete-time Gaussian and Poisson channels. An extension of digital modulation methods from the Gaussian channels to the additive energy channel is presented, and their constrained capacity determined. Special attention is paid to their asymptotic form of the capacity at low and high levels of signal energy. In contrast to the behaviour in the vi Gaussian channel, arbitrary modulation formats do not achieve the minimum energy per bit at low signal energy. Analytic expressions for the constrained capacity at low signal energy levels are provided. In the high-energy limit simple pulse-energy modulations, which achieve a larger constrained capacity than their counterparts for the Gaussian channel, are presented. As a ¯nal element, the error probability of binary channel codes in the ad- ditive energy channels is studied by analyzing the pairwise error probability, the probability of wrong decision between two alternative binary codewords. Saddlepoint approximations to the pairwise error probability are given, both for binary modulation and for bit-interleaved coded modulation, a simple and e±cient method to use binary codes with non-binary modulations. The meth- ods yield new simple approximations to the error probability in the fading Gaussian channel. The error rates in the continuous additive energy channel are close to those of coherent transmission at identical signal-to-noise ratio. Constellations minimizing the pairwise error probability in the additive energy channels are presented, and their form compared to that of the constellations which maximize the constrained capacity at high signal energy levels

    Delay and Peak-Age Violation Probability in Short-Packet Transmissions

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    This paper investigates the distribution of delay and peak age of information in a communication system where packets, generated according to an independent and identically distributed Bernoulli process, are placed in a single-server queue with first-come first-served discipline and transmitted over an additive white Gaussian noise (AWGN) channel. When a packet is correctly decoded, the sender receives an instantaneous error-free positive acknowledgment, upon which it removes the packet from the buffer. In the case of negative acknowledgment, the packet is retransmitted. By leveraging finite-blocklength results for the AWGN channel, we characterize the delay violation and the peak-age violation probability without resorting to approximations based on large deviation theory as in previous literature. Our analysis reveals that there exists an optimum blocklength that minimizes the delay violation and the peak-age violation probabilities. We also show that one can find two blocklength values that result in very similar average delay but significantly different delay violation probabilities. This highlights the importance of focusing on violation probabilities rather than on averages.Comment: 5 pages, 5 figures, accepted for IEEE International Symposium on Information Theory 2018, Edit: corrected peak-age of information formul

    Error Probability Bounds for Gaussian Channels under Maximal and Average Power Constraints

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    This paper studies the performance of block coding on an additive white Gaussian noise channel under different power limitations at the transmitter. Lower bounds are presented for the minimum error probability of codes satisfying maximal and average power constraints. These bounds are tighter than previous results in the finite blocklength regime, and yield a better understanding on the structure of good codes under an average power limitation. Evaluation of these bounds for short and moderate blocklengths is also discussed.Comment: Submitted to the IEEE Transactions on Information Theory. This article was presented in part at the 2019 IEEE International Symposium on Information Theory, Paris, France (ISIT 2019) and at the 2020 International Z\"urich Seminar on Communication and Information, Z\"urich, Switzerland (IZS 2020

    Mismatched decoding: Error exponents, second-order rates and saddlepoint approximations

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    This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error exponents and second-order coding rates matching those of constant-composition random coding, while being directly applicable to channels with infinite or continuous alphabets. The number of auxiliary costs required to match the error exponents and second-order rates of constant-composition coding is studied, and is shown to be at most two. For independent identically distributed random coding, asymptotic estimates of two well-known non-asymptotic bounds are given using saddlepoint approximations. Each expression is shown to characterize the asymptotic behavior of the corresponding random-coding bound at both fixed and varying rates, thus unifying the regimes characterized by error exponents, second-order rates, and moderate deviations. For fixed rates, novel exact asymptotics expressions are obtained to within a multiplicative 1+o(1) term. Using numerical examples, it is shown that the saddlepoint approximations are highly accurate even at short block lengths.This work was supported in part by the European Research Council under Grant 259663, in part by the European Union’s 7th Framework Programme under Grant 303633, and in part by the Spanish Ministry of Economy and Competitiveness under Grants RYC-2011-08150 and TEC2012-38800-C03-03

    Ultra-Reliable Short-Packet Communications: Fundamental Limits and Enabling Technologies

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    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

    Short Packets over Block-Memoryless Fading Channels: Pilot-Assisted or Noncoherent Transmission?

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    We present nonasymptotic upper and lower bounds on the maximum coding rate achievable when transmitting short packets over a Rician memoryless block-fading channel for a given requirement on the packet error probability. We focus on the practically relevant scenario in which there is no \emph{a priori} channel state information available at the transmitter and at the receiver. An upper bound built upon the min-max converse is compared to two lower bounds: the first one relies on a noncoherent transmission strategy in which the fading channel is not estimated explicitly at the receiver; the second one employs pilot-assisted transmission (PAT) followed by maximum-likelihood channel estimation and scaled mismatched nearest-neighbor decoding at the receiver. Our bounds are tight enough to unveil the optimum number of diversity branches that a packet should span so that the energy per bit required to achieve a target packet error probability is minimized, for a given constraint on the code rate and the packet size. Furthermore, the bounds reveal that noncoherent transmission is more energy efficient than PAT, even when the number of pilot symbols and their power is optimized. For example, for the case when a coded packet of 168168 symbols is transmitted using a channel code of rate 0.480.48 bits/channel use, over a block-fading channel with block size equal to 88 symbols, PAT requires an additional 1.21.2 dB of energy per information bit to achieve a packet error probability of 10−310^{-3} compared to a suitably designed noncoherent transmission scheme. Finally, we devise a PAT scheme based on punctured tail-biting quasi-cyclic codes and ordered statistics decoding, whose performance are close (11 dB gap at 10−310^{-3} packet error probability) to the ones predicted by our PAT lower bound. This shows that the PAT lower bound provides useful guidelines on the design of actual PAT schemes.Comment: 30 pages, 5 figures, journa

    Discussion of "Geodesic Monte Carlo on Embedded Manifolds"

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    Contributed discussion and rejoinder to "Geodesic Monte Carlo on Embedded Manifolds" (arXiv:1301.6064)Comment: Discussion of arXiv:1301.6064. To appear in the Scandinavian Journal of Statistics. 18 page
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