Peak-Age Violation Guarantees for the Transmission of Short Packets over Fading Channels

We investigate the probability that the peak age of information in a point-to-point communication system operating over a multiantenna wireless fading channel exceeds a predetermined value. The packets are scheduled according to a last-come first-serve policy with preemption in service, and are transmitted over the channel using a simple automatic repetition request protocol. We consider quadrature phase shift keying modulation, pilot-assisted transmission, maximum-likelihood channel estimation, and mismatched scaled nearest-neighbor decoding. Our analysis, which exploits nonasymptotic tools in information theory, allows one to determine, for a given information packet size, the physical layer parameters such as the SNR, the number of transmit and receive antennas, the amount of frequency diversity to exploit, and the number of pilot symbols, to ensure that the system operates below a target peak-age violation probability.Comment: 6 pages, 6 figures. To be presented at Infocom 201

Low-Latency Short-Packet Transmissions: Fixed Length or HARQ?

We study short-packet communications, subject to latency and reliability constraints, under the premises of limited frequency diversity and no time diversity. The question addressed is whether, and when, hybrid automatic repeat request (HARQ) outperforms fixed-blocklength schemes with no feedback (FBL-NF) in such a setting. We derive an achievability bound for HARQ, under the assumption of a limited number of transmissions. The bound relies on pilot-assisted transmission to estimate the fading channel and scaled nearest-neighbor decoding at the receiver. We compare our achievability bound for HARQ to stateof-the-art achievability bounds for FBL-NF communications and show that for a given latency, reliability, number of information bits, and number of diversity branches, HARQ may significantly outperform FBL-NF. For example, for an average latency of 1 ms, a target error probability of 10^-3, 30 information bits, and 3 diversity branches, the gain in energy per bit is about 4 dB.Comment: 6 pages, 5 figures, accepted to GLOBECOM 201

Capacity bounds for MIMO microwave backhaul links affected by phase noise

We present bounds and a closed-form high-SNR expression for the capacity of multiple-antenna systems affected by Wiener phase noise. Our results are developed for the scenario where a single oscillator drives all the radio-frequency circuitries at each transceiver (common oscillator setup), the input signal is subject to a peak-power constraint, and the channel matrix is deterministic. This scenario is relevant for line-of-sight multiple-antenna microwave backhaul links with sufficiently small antenna spacing at the transceivers. For the 2 by 2 multiple-antenna case, for a Wiener phase-noise process with standard deviation equal to 6 degrees, and at the medium/high SNR values at which microwave backhaul links operate, the upper bound reported in the paper exhibits a 3 dB gap from a lower bound obtained using 64-QAM. Furthermore, in this SNR regime the closed-form high-SNR expression is shown to be accurate.Comment: 10 pages, 2 figures, to appear in IEEE Transactions on Communication

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

Peak-Age Violation Guarantees for the Transmission of Short Packets over Fading Channels

We investigate the probability that the peak age of information in a point-to-point communication system operating over a multiantenna wireless fading channel exceeds a predetermined value. The packets are scheduled according to a last-come first-serve policy with preemption in service, and are transmitted over the channel using a simple automatic repetition request protocol. We consider quadrature phase shift keying modulation, pilot-assisted transmission, maximum-likelihood channel estimation, and mismatched scaled nearest-neighbor decoding. Our analysis, which exploits nonasymptotic tools in information theory, allows one to determine, for a given information packet size, the physical layer parameters such as the SNR, the number of transmit and receive antennas, the amount of frequency diversity to exploit, and the number of pilot symbols, to ensure that the system operates below a target peak-age violation probability

Short-packet Transmission via Variable-Length Codes in the Presence of Noisy Stop Feedback

We present an upper bound on the error probability achievable using variable-length stop feedback codes, for a fixed size of the information payload and a given constraint on the maximum latency and the average service time. Differently from the bound proposed in Polyanskiy et al. (2011), which pertains to the scenario in which the stop signal is sent over a noiseless feedback channel, our bound applies to the practically relevant setup in which the feedback link is noisy. By numerically evaluating our bound, we illustrate that, for fixed latency and reliability constraints, noise in the feedback link can cause a significant increase in the minimum average service time, to the extent that fixed-length codes without feedback may be preferable in some scenarios.Comment: Submitted to a Transactions on Wireless Communication

Nonasymptotic coding-rate bounds for binary erasure channels with feedback

We present nonasymptotic achievability and converse bounds on the maximum coding rate (for a fixed average error probability and a fixed average blocklength) of variable-length full-feedback (VLF) and variable-length stop-feedback (VLSF) codes operating over a binary erasure channel (BEC). For the VLF setup, the achievability bound relies on a scheme that maps each message onto a variable-length Huffman codeword and then repeats each bit of the codeword until it is received correctly. The converse bound is inspired by the meta-converse framework by Polyanskiy, Poor, and Verdú (2010) and relies on binary sequential hypothesis testing. For the case of zero error probability, our achievability and converse bounds match. For the VLSF case, we provide achievability bounds that exploit the following feature of BEC: the decoder can assess the correctness of its estimate by verifying whether the chosen codeword is the only one that is compatible with the erasure pattern. One of these bounds is obtained by analyzing the performance of a variable-length extension of random linear fountain codes. The gap between the VLSF achievability and the VLF converse bound, when number of messages is small, is significant: 23% for 8 messages on a BEC with erasure probability 0.5. The absence of a tight VLSF converse bound does not allow us to assess whether this gap is fundamental

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

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

Shannon Capacity of LOS MIMO Channels with Uniform Circular Arrays

The Shannon capacity for the line-of-sight (LOS) multiple-input multiple-output (MIMO) channel between two perfectly aligned uniform circular arrays (UCAs) is derived from the first principles in a tutorial fashion. It is well known that harmonically related complex exponentials (also known in the literature as orbital angular momentum (OAM) modes) are eigenmodes for the spatially continuous channel. We show that the corresponding eigenvalues can be expressed as Bessel functions of the first kind. We also show that the spatially discrete channel between two UCAs with the same finite number of Hertzian dipole antennas on both sides has eigenmodes that are spatially sampled continuous OAM modes, and discrete eigenvalues that are aliased versions of the continuous eigenvalues. Through numerical solution of Maxwell\u27s equations, we verify that the discrete eigenvalues for UCAs with realistic dipole antennas are the same as with the Hertzian dipoles for the studied geometries (1~km hop distance, UCA radius 1 and 2 m, carrier frequency 70 GHz) as long as antenna spacing is not very dense

Shannon Capacity of LOS MIMO Channels with Uniform Circular Arrays

The Shannon capacity for the line-of-sight (LOS) multiple-input multiple-output (MIMO) channel between two perfectly aligned uniform circular arrays (UCAs) is derived from the first principles in a tutorial fashion. It is well known that harmonically related complex exponentials (also known in the literature as orbital angular momentum (OAM) modes) are eigenmodes for the spatially continuous channel. We show that the corresponding eigenvalues can be expressed as Bessel functions of the first kind. We also show that the spatially discrete channel between two UCAs with the same finite number of Hertzian dipole antennas on both sides has eigenmodes that are spatially sampled continuous OAM modes, and discrete eigenvalues that are aliased versions of the continuous eigenvalues. Through numerical solution of Maxwell\u27s equations, we verify that the discrete eigenvalues for UCAs with realistic dipole antennas are the same as with the Hertzian dipoles for the studied geometries (1~km hop distance, UCA radius 1 and 2 m, carrier frequency 70 GHz) as long as antenna spacing is not very dense