Finite-Blocklength Bounds on the Maximum Coding Rate of Rician Fading Channels with Applications to Pilot-Assisted Transmission

We present nonasymptotic bounds on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packet error probability. Our bounds, which apply to the scenario where no a priori channel state information is available at the receiver, allow one to quantify the tradeoff between the rate gains resulting from the exploitation of time-frequency diversity and the rate loss resulting from fast channel variations and pilot-symbol overhead

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

Diversity versus Multiplexing at Finite Blocklength

A finite blocklenth analysis of the diversity-multiplexing tradeoff is presented, based on nonasymptotic bounds on the maximum channel coding rate of multiple-antenna block-memoryless Rayleigh-fading channels.The bounds in this paper allow one to numerically assess for which packet size, number of antennas, and degree of channel selectivity, diversity-exploiting schemes are close to optimal, and when instead the available spatial degrees of freedom should be used to provide spatial multiplexing. This finite blocklength view on the diversity-multiplexing tradeoff provides insights on the design of delay-sensitive ultra-reliable communication links.Comment: Proc. IEEE Int. Symp. Wirel. Comm. Syst. (ISWCS), Aug. 2014, to appea

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

Low-Complexity Joint Channel Estimation and List Decoding of Short Codes

A pilot-assisted transmission (PAT) scheme is proposed for short blocklengths, where the pilots are used only to derive an initial channel estimate for the list construction step. The final decision of the message is obtained by applying a non-coherent decoding metric to the codewords composing the list. This allows one to use very few pilots, thus reducing the channel estimation overhead. The method is applied to an ordered statistics decoder for communication over a Rayleigh block-fading channel. Gains of up to $1.2$ dB as compared to traditional PAT schemes are demonstrated for short codes with QPSK signaling. The approach can be generalized to other list decoders, e.g., to list decoding of polar codes.Comment: Accepted at the 12th International ITG Conference on Systems, Communications and Coding (SCC 2019), Rostock, German

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

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 $168$ symbols is transmitted using a channel code of rate $0.48$ bits/channel use, over a block-fading channel with block size equal to $8$ symbols, PAT requires an additional $1.2$ dB of energy per information bit to achieve a packet error probability of $10^{-3}$ 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 ($1$ dB gap at $10^{-3}$ 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

Short-Packet Transmission over a Bidirectional Massive MIMO link

We consider the transmission of short packets over a bidirectional communication link where multiple devices, e.g., sensors and actuators, exchange small-data payloads with a base station equipped with a large antenna array. Using results from finite-blocklength information theory, we characterize the minimum SNR required to achieve a target error probability for a fixed packet length and a fixed payload size. Our nonasymptotic analysis, which applies to the scenario in which the bidirectional communication is device-initiated, and also to the more challenging case when it is base-station initiated, provides guidelines on the design of massive multiple-input multiple-output links that need to support sporadic ultra-reliable low-latency transmissions. Specifically, it allows us to determine the optimal amount of resources that need to be dedicated to the acquisition of channel state information.Comment: 5 pages, presented at Asiloma

Low-latency Ultra Reliable 5G Communications: Finite-Blocklength Bounds and Coding Schemes

Future autonomous systems require wireless connectivity able to support extremely stringent requirements on both latency and reliability. In this paper, we leverage recent developments in the field of finite-blocklength information theory to illustrate how to optimally design wireless systems in the presence of such stringent constraints. Focusing on a multi-antenna Rayleigh block-fading channel, we obtain bounds on the maximum number of bits that can be transmitted within given bandwidth, latency, and reliability constraints, using an orthogonal frequency-division multiplexing system similar to LTE. These bounds unveil the fundamental interplay between latency, bandwidth, rate, and reliability. Furthermore, they suggest how to optimally use the available spatial and frequency diversity. Finally, we use our bounds to benchmark the performance of an actual coding scheme involving the transmission of short packets

URLLC with Massive MIMO: Analysis and Design at Finite Blocklength

The fast adoption of Massive MIMO for high-throughput communications was enabled by many research contributions mostly relying on infinite-blocklength information-theoretic bounds. This makes it hard to assess the suitability of Massive MIMO for ultra-reliable low-latency communications (URLLC) operating with short blocklength codes. This paper provides a rigorous framework for the characterization and numerical evaluation (using the saddlepoint approximation) of the error probability achievable in the uplink and downlink of Massive MIMO at finite blocklength. The framework encompasses imperfect channel state information, pilot contamination, spatially correlated channels, and arbitrary linear spatial processing. In line with previous results based on infinite-blocklength bounds, we prove that, with minimum mean-square error (MMSE) processing and spatially correlated channels, the error probability at finite blocklength goes to zero as the number $M$ of antennas grows to infinity, even under pilot contamination. On the other hand, numerical results for a practical URLLC network setup involving a base station with $M=100$ antennas, show that a target error probability of $10^{-5}$ can be achieved with MMSE processing, uniformly over each cell, only if orthogonal pilot sequences are assigned to all the users in the network. Maximum ratio processing does not suffice.Comment: 30 pages, 5 figure

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