Packet Erasure Channels Research Articles

Movable Antenna-Aided Broadcast Packet Erasure Channels: Capacity with Dynamic Position Plan

Movable Antenna-Aided Broadcast Packet Erasure Channels: Capacity with Dynamic Position Plan

On the Required Radio Resources for Ultra-Reliable Communication in Highly Interfered Scenarios

Future wireless systems are expected to support mission-critical services demanding higher and higher reliability. In this letter, we dimension the radio resources needed to achieve a given failure probability target for ultra-reliable wireless systems in high interference conditions, assuming a protocol with frequency hopping combined with packet repetitions. We resort to packet erasure channel models and derive the minimum amount of resource units in the case of receiver with and without collision resolution capability, as well as the number of packet repetitions needed for achieving the failure probability target. Analytical results are numerically validated, and can be used as benchmark for realistic system simulations.

Performance Bounds of Coded Slotted ALOHA Over Erasure Channels

In this paper, we derive an upper bound on load-threshold of coded slotted ALOHA (CSA) for slot erasure channel (SEC) and that for packet erasure channel (PEC), respectively. In SEC, by exploiting the analogy between Gaussian elimination of solving linear equations and the iterative successive interference-cancellation (SIC) decoding procedure of CSA, we derive the upper performance bound for SEC. Subsequently, in PEC, utilizing density evolution to track the average probability of packet-decoded failure within the SIC decoding process, we obtain the upper bound for PEC. Moreover, we propose a numerical search algorithm of these bounds under a given calculating precision. The numerical results indicate that the asymptotic upper limit on load-threshold of CSA over SEC is always less than that over PEC with any given erasure probability and average transmission rate.

Remote monitoring and control of the 2-DoF robotic manipulators over the internet

AbstractThis article is concerned with remote monitoring and control of the 2-degrees of freedom (DoF) robotic manipulators, which have nonlinear dynamics over the packet erasure channel, which is an abstract model for communication over the Internet, WiFi, or Zigbee modules. This type of communication is subject to imperfections, such as random packet dropout and rate distortion. These imperfections cause a significant challenge for monitoring and control of robotic manipulators in the industrial environments because sensitive data, such as sensor data and control commands may not ever reach to their destination resulting in significant performance degradation. Therefore, the effects of these imperfections must be compensated. In this article, we apply two coding and control techniques previously developed for the telepresence ad teleoperation of autonomous vehicles to compensate the effects of the above communication imperfections for remote monitoring and control of the 2-DoF robotic manipulators controlled over the packet erasure channel. To achieve this goal, we design a new linear controller and a new nonlinear controller for the 2-DoF robotic manipulators over the packet erasure channel. The first technique is based on the linearization method and the second technique uses a nonlinear controller. The performances of these two techniques for remote monitoring and control of robotic manipulators are evaluated and compared with each other in this paper. We illustrate their satisfactory performances in the presence of severe communication imperfections.

Federated Learning With Erroneous Communication Links

In this letter, we consider the federated learning (FL) problem in the presence of communication errors. We model the link between the devices and the central node (CN) by a packet erasure channel, where the local parameters from devices are either erased or received correctly by CN with probability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1-\epsilon $ </tex-math></inline-formula> , respectively. We proved that the FL algorithm in the presence of communication errors, where the CN uses the past local update if the fresh one is not received from a device, converges to the same global parameter as that the FL algorithm converges to without any communication error. We provide several simulation results to validate our theoretical analysis. We also show that when the dataset is uniformly distributed among devices, the FL algorithm that only uses fresh updates and discards missing updates might converge faster than the FL algorithm that uses past local updates.

An Explicit Rate-Optimal Streaming Code for Channels With Burst and Arbitrary Erasures

This paper considers the transmission of an infinite sequence of messages (a streaming source) over a packet erasure channel, where every source message must be recovered perfectly at the destination subject to a fixed decoding delay. While the capacity of a channel that introduces only bursts of erasures has been known for more than fifteen years, only recently, the capacity of a channel with either one burst of erasures or multiple arbitrary erasures in any fixed-sized sliding window has been established. However, explicit codes shown to achieve this capacity for any admissible set of parameters require a large field size that scales exponentially with the delay. Recently, it has been shown that there exist codes that achieve the capacity with field size which scales quadratically with the delay. However, explicit constructions were shown only to specific combinations of parameters. This work describes an explicit rate-optimal construction for all admissible channel and delay parameters over a field size that scales quadratically with the delay.

Coded Wireless Distributed Computing With Packet Losses and Retransmissions

In wireless distributed computing systems, mobile devices that are connected wirelessly to the Fog (e.g., small base stations) collaboratively solve a given computational task. Unfortunately, wireless distributed computing systems suffer from packet losses due to severe channel fading. Moreover, a wireless device can drop out of the system when leaving the coverage of a master node in the Fog layer. We model this unreliability between a device and a master node as a packet erasure channel. When a packet fails to be detected at the receiver, the corresponding packet is retransmitted, which would significantly increase the overall run-time to finish the task. We take a coding-theoretic approach to tackle this straggler-like problem in wireless distributed computing. We first investigate the expected latency using an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(n, k)$ </tex-math></inline-formula> maximum-distance separable (MDS) code. We obtain the lower and upper bounds on the latency in closed forms and provide guidelines to design MDS codes depending on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">channel</i> condition characterized by packet erasure probability. Then, we introduce another important performance metric called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">minimum latency</i> , and also provide guidelines on designing optimal codes. Based on optimal codes, we obtain the performance curves of achievable minimum latency and achievable workload as functions of packet erasure probability.

Capacity of Broadcast Packet Erasure Channels With Single-User Delayed CSI

We characterize the capacity region of the two-user broadcast packet erasure channel (PEC) with single-user delayed channel state information (CSI). More precisely, we assume one receiver does not provide its channel state to the other two nodes (the other receiver and the transmitter), while the other receiver reveals its state globally with unit delay. This is a hybrid CSI at the transmitter (CSIT) setting where the transmitter has the delayed CSI of one user but not the other. Previous results developed opportunistic network coding schemes for this setting, which strictly enlarge the achievable rate region compared to the no-CSIT baseline. Characterization of the capacity region with single-user delayed CSI, however, remained open. In this work, we develop an improved achievability strategy and show that the capacity region, surprisingly, matches that of the broadcast PEC with global delayed CSI of both users. The key to such improvement over previous results is a new precoding strategy for the retransmission phase of the opportunistic network coding scheme. It harnesses the single-user delayed CSI in the retransmission phase, so that interference from the feedback receiver can be aligned at the other receiver. Besides the broadcast PEC with two private messages, an extension to a model with an additional common message is also provided and the corresponding capacity region with single-user CSI also matches that with global delayed CSI. Finally, further extensions to three-user cases are also provided.

Optimal Multiplexed Erasure Codes for Streaming Messages With Different Decoding Delays

This paper considers multiplexing two sequences of messages with two different decoding delays over a packet erasure channel. In each time slot, the source constructs a packet based on the current and previous messages and transmits the packet, which may be erased when the packet travels from the source to the destination. The destination must perfectly recover every source message in the first sequence subject to a decoding delay T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> , and every source message in the second sequence subject to a shorter decoding delay T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> ≤ T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> ,. We assume that the channel loss model introduces a burst erasure of a fixed length B on the discrete timeline. Under this channel loss assumption, the capacity region for the case where T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> , ≤ T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> +B was previously solved. In this paper, we fully characterize the capacity region for the remaining case T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> , ) T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> +B. The key step in the achievability proof is achieving the non-trivial corner point of the capacity region through using a multiplexed streaming code constructed by superimposing two single-stream codes. The main idea in the converse proof is obtaining a genie-aided bound when the channel is subject to a periodic erasure pattern where each period consists of a length-B burst erasure followed by a length-T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</sub> noiseless duration.

New coding scheme for the state estimation and reference tracking of nonlinear dynamic systems over the packet erasure channel (IoT): Applications in tele-operation of autonomous vehicles

This paper presents a new technique for the state estimation and reference tracking of nonlinear dynamic systems over the packet erasure channel, which is an abstract model for transmission via the Internet, WiFi wireless network and ZigBee modules. A new encoder and decoder for real time state estimation of nonlinear dynamic systems at the end of communication link when the measurements are sent through the limited capacity erasure channel, are presented. Then, using the available results from control theory, a controller for reference tracking and hence the stability of the system is also designed. That is, for nonlinear systems, almost sure asymptotic state estimation and reference tracking techniques including an encoder, decoder and a controller are presented. The satisfactory performances of the proposed state estimation and control techniques are illustrated via computer simulations by applying the proposed techniques on the unicycle model, which represents the dynamics of autonomous vehicles.

Energy-Aware Scheduling for Broadcast Erasure Channels With Two Energy Harvesting Receivers

A feedback-based coding algorithm is studied for broadcast packet erasure channels (BPECs) with energy harvesting receivers. A probabilistic algorithm is outlined, which is able to achieve the capacity region of two-user BPECs. The probabilistic algorithm is carefully studied from the optimization perspective. In this paper, we take into account the energy levels of receivers. Two new feedback schemes are proposed to reduce the energy consumption of receivers and we explain the advantage of each feedback scheme. We formulate the problem of maximizing the minimum weighted throughput of receivers for each feedback scheme. After several convexifications, we make the formulated optimizations tractable and propose an algorithm to solve the problems globally without compromising optimality. Once optimization problems are solved, we propose an energy-aware scheduling for packet broadcasting. Finally, a packet header design is proposed to enable utilization of the energy-aware scheduling. Simulation results verify that to achieve the optimal throughput, network-coding is necessary.

A New Capacity-Approaching Scheme for General 1-to-K Broadcast Packet Erasure Channels With ACK/NACK

The capacity region of 1-to- K broadcast packet erasure channels with ACK/NACK is well known for some scenarios, e.g., $ {K}\leq 3$ , etc. However, existing achievability schemes either require knowing the target rate $\vec {{R}}$ in advance, and/or have a complicated description of the achievable rate region that is difficult to prove whether it matches the capacity or not. This work proposes a new network coding scheme with the following features: (i) its achievable rate region is identical to the capacity region for all the scenarios in which the capacity is known; (ii) its achievable rate region is much more tractable and has been used to derive new capacity rate vectors; (iii) it employs sequential encoding that naturally handles dynamic packet arrivals; (iv) it automatically adapts to unknown packet arrival rates $\vec {{R}}$ ; (v) it is based on $\mathsf {GF}({q})$ with ${q}\geq {K}$ . In addition to analytically characterizing the achievable rate region of the proposed scheme, numerical simulation has been used to verify its queue length and delay performance.

Tracking Unstable Autoregressive Sources Over Discrete Memoryless Channels

We consider the problem of tracking, in realtime, an unstable autoregressive (AR) source over a discrete memoryless channel (DMC). We present computable achievable bounds on the optimal tracking error for general DMCs, and we particularize these bounds to the binary erasure, packet erasure, and binary symmetric channels. The achievable bounds in this paper are proved using a partially separate source quantization and channel coding architecture. We do not use complete or strict separation in usual Shannon sense: 1) the quantiser’s resolution is optimized against the error-correction capabilities of the channel code and the channel code is optimized against an AR Hamming distortion function matched to the source (a weighted Hamming distortion function that provides unequal error protection to different parts of the AR source). The achievability results for general DMCs are proved by combining the AR Hamming distortion function with new realtime (streaming) versions of the random coding union and dependence testing bounds . When applied to erasure channels, these general bounds combine with simple converses to demonstrate that the channel’s cutoff rate plays an important role in realtime tracking.

Stabilization of Nonlinear Dynamic Systems Over Limited Capacity Communication Channels

This article addresses the stabilization of noiseless nonlinear dynamic systems over limited capacity communication channels. It is shown that the stability of nonlinear dynamic systems over memory-less communication channels implies an inequality condition between the Shannon channel capacity and the summation of the positive equilibrium Lyapunov exponents of the dynamic system or, equivalently, the logarithms of the magnitude of the unstable eigenvalues of system Jacobian. Furthermore, we propose an encoder, decoder, and a controller to prove that scalar nonlinear dynamic systems are stabilizable under the aforementioned inequality condition over the digital noiseless and the packet erasure channels, respectively, in sure and almost sure senses. The performance of the proposed coding scheme is illustrated by computer simulations.

An Explicit Construction of Optimal Streaming Codes for Channels With Burst and Arbitrary Erasures

This paper presents a new construction of error correcting codes which achieves optimal recovery of a streaming source over a packet erasure channel. The channel model considered is the sliding-window erasure model, with burst and arbitrary losses, introduced by Badr et al. We present a simple construction, when the rate of the code is at least 1/2, which achieves optimal error correction in this setup. Our proposed construction is explicit and systematic. It uses off-the-shelf maximum distance separable (MDS) codes and maximum rank distance (MRD) Gabidulin block codes as constituent codes and combines them in a simple manner. This is in contrast to other recent works, where the construction involves a careful design of the generator or parity check matrix from first principles. The field size requirement which depends on the constituent MDS and MRD codes is also analyzed.

A Communication-Aware Mutual Information Measure for Distributed Autonomous Robotic Information Gathering

This letter investigates the computation of information measures for distributed communication-aware information gathering by robotic sensor networks. The mutual information between an unknown target state and measurements received over a lossy network is derived in order to combine sensing and communication into a single objective function that can be optimized by the robot sensor network. Communication is modeled as a packet erasure channel, leading to a formulation of the mutual information that scales exponentially in the number of agents and time horizon. Several approximations to reduce this computational complexity are introduced and evaluated. Further, sample-based methods are introduced in order to derive approximate solutions of the mutual information when the system is nonlinear and uncertainties have non-Gaussian distributions. Finally, the information measure is evaluated through simulation experiments of multiple aerial robots tracking stationary radio emitters.

Optimal Streaming Codes for Channels With Burst and Arbitrary Erasures

This paper considers transmitting a sequence of messages (streaming messages) over a packet erasure channel. In each time slot, the source constructs a packet based on the current and the previous messages and transmits the packet, which may be erased when the packet travels from the source to the destination. Every source message must be recovered perfectly at the destination subject to a fixed decoding delay. We assume that the channel loss model introduces either one burst erasure or multiple arbitrary erasures in any fixed-sized sliding window. Under this channel loss assumption, we fully characterize the maximum achievable rate by constructing streaming codes that achieve the optimal rate. In addition, our construction of optimal streaming codes implies the full characterization of the maximum achievable rate for convolutional codes with any given column distance, column span, and decoding delay. Numerical results demonstrate that the optimal streaming codes outperform existing streaming codes of comparable complexity over some instances of the Gilbert–Elliott channel and the Fritchman channel.

Hybrid Multicast and Device-to-Device Communications Based on Adaptive Random Network Coding

Random network coding (RNC) is an efficient coding scheme to improve the performance of wireless multicast networks, on the premise that a receiver is able to collect a full set of network-coded packets. However, in resource (time, bandwidth, and so on) constrained communications, a receiver may only receive a partial set of network coded packets, leading to poor system performance. On the other hand, device-to-device (D2D) communications utilize user proximity and spatial diversity to improve the communication efficiency. In this paper, we propose a hybrid multicast and D2D transmission scheme based on adaptive RNC (ARNC) to increase network throughput under packet erasure channels. In the proposed scheme, the packet encoding structure is optimized adaptively according to the network status, such that even if only a partial set of the coded packets are received, the user equipments (UEs) can still decode useful information and regenerate new encoded packet for D2D communications. In particular, the multicast mode and D2D mode are switched dynamically during a scheduling session according to the status of each UE. Under this hybrid mode, we can effectively overcome the effect of erasure channel and improve the overall network throughput. By comparing our scheme with other scheduling methods, we provide simulation results to corroborate the effectiveness of the proposed techniques.

Estimation of Nonlinear Dynamic Systems Over Communication Channels

Remote observation of the state trajectory of nonlinear dynamic systems over limited capacity communication channels is studied. It is shown that two extreme cases are possible: Either the system is fully observable or the error in estimation blows up. The key observation is that such behavior is determined by the relationship between the Shannon capacity and the Lyapunov exponents; the well-known characterizing parameters of a communication channel on one side, and a dynamic system from the other side. In particular, it is proved that for nonlinear systems with initial state $x_0$ , the minimum capacity of an additive white Gaussian noise channel required for full observation of the system in the mean square sense is $ \sum _i\kappa _i(x_0)\Delta _i (x_0)$ , where $\Delta _i (x_0)$ s and $\kappa _i(x_0)$ s denote distinct Lyapunov exponents and their multiplicity numbers, respectively. Conversely, if the capacity is less than $E[\sum _i \kappa _i(x_0)\Delta _i (x_0)]$ , then observation is impossible. In order to show the universality of the result, we obtain the same observability conditions for the digital noiseless channel and the packet erasure channel in sure and almost sure senses, respectively.

Capacity Regions of Two-Receiver Broadcast Erasure Channels With Feedback and Memory

The two-receiver broadcast packet erasure channel with feedback and memory is studied. Memory is modeled using a finite-state Markov chain representing a channel state. Two scenarios are considered: 1) when the transmitter has causal knowledge of the channel state (i.e., the state is visible) and 2) when the channel state is unknown at the transmitter, but observations of it are available at the transmitter through feedback (i.e., the state is hidden). In both scenarios, matching outer and inner bounds on the rates of communication are derived and the capacity region is determined. It is shown that similar results carry over to channels with memory and delayed feedback and memoryless compound channels with feedback. When the state is visible, the capacity region has a single-letter characterization and is in terms of a linear program. Two optimal coding schemes are devised that use feedback to keep track of the sent/received packets via a network of queues: a probabilistic scheme and a deterministic backpressure-like algorithm. The former bases its decisions solely on the past channel state information and the latter follows a max-weight queue-based policy. The performance of the algorithms is analyzed using the frameworks of rate stability in networks of queues, max-flow min-cut duality in networks, and finite-horizon Lyapunov drift analysis. When the state is hidden, the capacity region does not have a single-letter characterization and is, in this sense, uncomputable. Approximations of the capacity region are provided and two optimal coding algorithms are outlined. The first algorithm is a probabilistic coding scheme that bases its decisions on the past $L$ acknowledgments and its achievable rate region approaches the capacity region exponentially fast in $L$ . The second algorithm is a backpressure-like algorithm that performs optimally in the long run.