Gilbert-Elliott Channel Research Articles

Distributed Channel Access for Control Over Known and Unknown Gilbert–Elliott Channels

Distributed Channel Access for Control Over Known and Unknown Gilbert–Elliott Channels

Age-Optimal Scheduling Over Hybrid Channels

We consider the problem of minimizing the age of information when a source can transmit status updates over two heterogeneous channels. Our work is motivated by recent developments in 5 G mmWave technology, where transmissions may occur over an unreliable but fast (e.g., mmWave) channel or a slow reliable (e.g., sub-6 GHz) channel. The unreliable channel is modeled as a time-correlated Gilbert-Elliot channel at a high rate when the channel is in the “ON” state. The reliable channel provides a deterministic but lower data rate. The scheduling strategy determines the channel to be used for transmission in each time slot, aiming to minimize the time-average age of information (AoI). The optimal scheduling problem is formulated as a Markov Decision Process (MDP), which is challenging to solve because super-modularity does not hold in a part of the state space. We address this challenge and show that a multi-dimensional threshold-type scheduling policy is optimal for minimizing the age. By exploiting the structure of the MDP and analyzing the discrete time Markov chains (DTMCs) of the threshold-type policy, we devise a low-complexity bisection algorithm to compute the optimal thresholds. We compare different scheduling policies using numerical simulations.

Network Coded Constrained Application Protocol With Improved Energy Efficiency for IIoT Networks

Constrained Application Protocol (CoAP) for low-power low-rate data transport in Industrial Internet of Things (IIoT) networks is typically running with two modes, namely, confirmable mode and non-confirmable mode, respectively. Confirmable mode relies on retransmission to ensure a guaranteed Quality of Service (QoS) in terms of packet loss rate at the cost of increased latency and power consumption. Whereas non-confirmable mode consumes less power, it is known to be packet loss prone. To enrich the CoAP transport for IIoT networks, we propose a packet-level Forward Error Correction (FEC) mechanism based on systematic coding with adaptive code rate to provide energy-efficient and reliable packet delivery. We mathematically analyze packet loss and cost of energy consumption of the proposed mechanism and compare it with confirmable CoAP transport scheme in the Gilbert-Elliott channel model. We demonstrate that the proposed mechanism can enhance the performance of non-confirmable CoAP to be comparable to confirmable CoAP in terms of packet loss rate, while outperforming it in energy consumption. The analytical and simulation results verify that the proposed mechanism is suitable for IIoT networks especially in high erasure burstiness scenarios.

Reliable and energy-efficient UAV-assisted air-to-ground transmission: Design, modeling and analysis

In this paper, a novel reliable and energy-efficient transmission scheme is proposed for unmanned aerial vehicle (UAV) assisted air-to-ground (A2G) communication. The scheme is tailored to handle burst errors in transmission caused by network collision, switching or interference. Application Layer Forward Error Correction (AL-FEC) mechanism is proposed to enhance the reliability of the A2G communication. By avoiding retransmissions, energy efficiency can be guaranteed. Based on Gilbert-Elliott channel model, we perform a detailed mathematical analysis on the performance of the proposed AL-FEC scheme. The packet delivery ratio and energy efficiency are studied and validated by comprehensive simulations. An application layer Automatic Repeat reQuest (AL-ARQ) protocol based on selective retransmission is used as a baseline scheme and compared with the proposed scheme. It is shown that the proposed AL-FEC scheme can significantly reduce the energy consumption and ensure the same or even higher application packet delivery ratio compared with the baseline scheme. In addition, the proposed scheme is especially preferable when the channel quality is poor. These specific findings can provide guidance for practical applications relying on UAV-assisted A2G communication, which require reliable and energy-efficient UAV-to-ground transmission in harsh wireless conditions.

Improved filtering of interval type-2 fuzzy systems over Gilbert-Elliott channels

This study is concerned with the filtering problem for networked interval type-2 (IT2) fuzzy systems in the presence of a time-varying saturation function. Different from the existing Bernoulli-type/Gilbert-Elliott packet loss over the unreliable medium, a generalized Gilbert-Elliott model is presented to describe the data transmission follows a two-state nonhomogeneous Markov process, whose transition probabilities are time-varying. For the purpose of mitigating the impacts of abnormal information, a novel filter in the presence of saturation function is constructed, in which the saturation level is dynamically updated along with the estimation errors. On the basis of Lyapunov theory, sufficient conditions for finite-time boundedness of IT2 fuzzy systems are devised. In the end, a simulation example is exploited to show the effectiveness of the above-derived results.

Анализ и оптимизация схем кодирования для каналов с рэлеевскими замираниями

Conventional approach to perform error-correcting decoding in channels with memory is an adoption of interleaving, which increases the receiver complexity and delay. In order to avoid these limitations, approaches for adapting an error-correcting scheme for memory channels may be used. One approach is to use error-correcting codes with modified design and decoding procedure, taking into account the presence of error bursts in the channel. Another approach to adapting the coding scheme for burst error correction is to use product codes with iterative decoding algorithms. Component codes of product codes themselves may not be able to correct error bursts, but a two-dimensional structure of product codes operating as an artificial interleaver and iterative decoding allow for correction of grouping errors. Purpose: The purpose of the study is to analyze the methods of error-correcting code adaptation to burst error correction in channels with memory in order to reduce the probability of error. Results: The study considered methods of error-correcting code scheme adaptation for low-density parity-check codes, polar codes, and product codes for burst error correction in Gilbert-Elliott channel (GE) and correlated Rayleigh fading channel with different correlation coefficients. Degree distribution of low-density parity-check code was optimized for GE channel. The influence of selected parameters of product code component codes on burst error correction in the GE channel was analyzed. The structure of the polar code has been optimized using a genetic algorithm for the correlated Rayleigh channel, which outperforms the 5G polar code design in terms of error probability. Discussion: Existing error-correcting code schemes do not provide theoretically possible limits, so the question remains of developing coding and decoding schemes capable of reaching theoretical limits.

Impact of Channel Memory on the Data Freshness

In this letter, we investigate the impact of channel memory on the average age of information (AoI) for networks with various packet arrival models under the first-come-first-served (FCFS) and the preemptive last-generated-first-served (pLGFS) policies over the Gilbert-Elliott (GE) erasure channel. For networks with Bernoulli and generate-at-will arrival models, the AoI performances under the FCFS and pLGFS policies are derived explicitly as functions of the channel state transition probabilities. For networks with periodic arrival model, we derive the closed-form expression for the average AoI under pLGFS and propose a numerical algorithm for efficient evaluation of the AoI under FCFS. It is revealed that for pLGFS policy, the average AoI increases monotonically with channel memory <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\eta $ </tex-math></inline-formula> at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\frac {\eta }{1-\eta }$ </tex-math></inline-formula> over the symmetric GE channel. For FCFS, the average AoI increases even faster due to the queuing delay, with an additional term related to the packet arrival rate.

Performance Improvement of Polar Codes via UEP Product Coding

Aiming to improve the error correction performance of polar codes, researchers have proposed employing the product coding structure involving RS codes of different rates in the horizontal direction and the short polar codewords along the vertical direction. However, there is no efficient algorithm optimizing the rate allocation of RS codes. In order to address this problem, this paper provides an analytical formulation by maximizing the number of correctly decoded information bits. The proposed rate allocation formulation takes the channel statistics into consideration, and we further find that the number of different RS code rates could be limited to a small value. By doing so, the complexities of both the rate allocation optimization and the iterative product decoding could be reduced. Simulation results demonstrate the superiority of RS-polar product codes with the proposed rate allocation method over both additive white Gaussian noise channels and Gilbert–Elliott channels. When the inner polar codes of rate 1/2 are utilized, the optimized RS-polar product codes of low-to-medium rates significantly outperform the successive cancellation decoding of long polar codes, in the regime of a frame error rate ≥10−3.

On Stability and Performance of the Optimal Linear Filter Over Gilbert–Elliott Channels With Unobservable Packet Losses

On Stability and Performance of the Optimal Linear Filter Over Gilbert–Elliott Channels With Unobservable Packet Losses

Power Allocation for Remote Estimation Over Known and Unknown Gilbert-Elliott Channels

In this paper, we consider the problem of power scheduling of a sensor that transmits over a (possibly) unknown Gilbert-Elliott (GE) channel for remote state estimation. The sensor supports two power modes, namely low power, and high power. The scheduling policy determines when to use low power or high power for data transmission over a fading channel with temporal correlation while satisfying the energy constraints. Although error-free acknowledgement/negative-acknowledgement (ACK/NACK) signals are provided by the remote estimator, they only provide meaningful information about the underlying channel state when low power is utilized. This leads to a partially observable Markov decision process (POMDP) problem and we derive conditions that preserve the optimality of a stationary schedule derived for its fully observable counterpart. However, implementing this schedule requires knowledge of the parameters of the GE model which are not available in practice. To address this, we adopt a Bayesian framework to learn these parameters online and propose an algorithm that is shown to satisfy the energy constraint while achieving near-optimal performance via simulation.

Decoding Polar Codes for a Generalized Gilbert-Elliott Channel With Unknown Parameter

Decoding of polar codes, a class of capacity-achieving channel codes, typically requires the perfect knowledge of channel parameter in advance. This paper aims to investigate how to decode polar codes when channel parameter is unknown. Specifically, we study a generalized Gilbert-Elliott channel model, which assumes that the channel switches between a finite number of states. On the platform of Soft CANcellation (SCAN), which is a low-complexity iterative decoding algorithm of polar codes superior to the widely-used Successive Cancellation (SC) decoder, we propose three adaptive algorithms, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , Sliding-Window SCAN (SWSCAN), Weighted-Window SCAN (W <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> SCAN), and Linear-Weighting SCAN (LWSCAN). These adaptive SCAN decoders are seeded with a coarse estimate of channel state, and after each SCAN iteration, the decoders progressively refine the estimate of channel state. Experimental results demonstrate that the proposed adaptive SCAN decoders outperform the original SCAN decoder and other competitors.

Information Freshness Analysis of Slotted ALOHA in Gilbert-Elliot Channels

This letter analyzes a class of information freshness metrics for large IoT systems in which terminals employ slotted ALOHA to access a common channel. Considering a Gilbert-Elliot channel model, information freshness is evaluated through a penalty function that follows a power law of the time elapsed since the last received update, in contrast with the linear growth of age of information. By means of a signal flow graph analysis of Markov processes, we provide exact closed form expressions for the average penalty and for the peak penalty violation probability.

Recursive Secure Filtering Over Gilbert-Elliott Channels in Sensor Networks: The Distributed Case

This paper is concerned with the recursive secure filtering problem for a class of discrete-time systems subject to unreliable communication due to the security vulnerability of sensor networks. The unreliable communication, caused probably by denial-of-service cyber-attacks, is described by the well-known Gilbert-Elliott model. The addressed nonlinearities are applicable for some of the most investigated stochastic nonlinear models, including the well-known state-dependent multiplicative noises as special cases. The aim of this paper is to design a novel distributed filter that uses the information not only from the individual node itself but also from its neighboring nodes according to the given topology. In order to improve the security of designed filter, a χ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> detector is utilized to detect abnormal innovations. By means of the failure and recovery rates of the Gilbert-Elliott channels, sufficient conditions are established to ensure the existence of an upper bound on the estimation error covariance, and then the desired filter parameters are designed by minimizing the trace of such an upper bound. The asymptotic boundedness of the estimation error covariance is subsequently investigated. Finally, a simulation example on the target tracking problem is employed to verify the effectiveness and the security of the proposed filtering scheme.

A Performance Analysis of Quantum Low-Density Parity-Check Codes for Correcting Correlated Errors

In this paper we analyse the performance of quantum low-density parity-check (LDPC) codes over quantum memory channels for correcting correlated errors, where the quantum LDPC codes we use are the hypergraph product quantum LDPC codes. We generalize the classical Gilbert-Elliot markovian memory channel to the quantum Gilbert-Elliot channel and use it to model the memory effect in quantum memory channels. The simulation results show the memory effects in quantum GE channels has a bad effect to the performance of hypergraph product quantum LDPC codes. Then we propose a concatenation scheme by serially concatenating two hypergraph product quantum LDPC codes and it is shown that the serial concatenation scheme can improve the performance of hypergraph product quantum LDPC codes and lower down the error floor over quantum GE channels.

Optimal PHY Configuration in Wireless Networks

In this work, we study the optimal configuration of the physical layer in wireless networks by means of Semi-Markov Decision Process (SMDP) modeling. In particular, assume the physical layer is characterized by a set of potential operating points, with each point corresponding to a rate and reliability pair; for example, these pairs might be obtained through a now-standard diversity-multiplexing tradeoff characterization. Given the current network state (e.g., buffer occupancies), a Decision Maker (DM) needs to dynamically decide which operating point to use. The SMDP problem formulation allows us to choose from these points. A solution to the SMDP problem is an optimal selection of operating points, which is expressed by a decision rule as a function of the number of packets in the source’s finite queue, the channel state, and the size of the packet to be transmitted. We derive a general solution to the SMDP which covers various model configurations, packet size distributions and channel dynamics. For the specific case of exponential transmission times, we analytically prove the optimal policy has a threshold structure. Numerical results validate this finding, as well as depict muti-threshold policies for time varying channels such as the Gilbert-Elliott channel.

Optimal Mobile Computation Offloading with Hard Deadline Constraints

This paper considers mobile computation offloading where task completion times are subject to hard deadline constraints. Hard deadlines are difficult to meet in conventional computation offloading due to the stochastic nature of the wireless channels involved. Rather than using binary offload decisions, we permit concurrent remote and local job execution when it is needed to ensure task completion deadlines. The paper addresses this problem for homogeneous Markovian wireless channel models. An online energy-optimal computation offloading algorithm, OnOpt, is proposed. Its energy optimality is shown by constructing a time-dilated absorbing Markov process and applying dynamic programming. Closed form results are derived for general Markovian processes, and the Gilbert-Elliott channel model is used to show how the particular structure of the Markov chain can be exploited in computing optimal offload initiation times more efficiently. It is shown that job completion time probabilities can be computed recursively, which leads to a significant reduction in the computational complexity of OnOpt. The performance of the proposed algorithm is compared to three others, namely, Immediate Offloading, Channel Threshold, and Local Execution. Performance results show that the proposed algorithm can significantly improve mobile device energy consumption compared to the other approaches while guaranteeing hard task execution deadlines.

Delivery phase in cache-based wireless networks with modified LT codes

Caching has emerged as an efficient technique to reduce delivery latency and network congestion. The focus of this paper is on content delivery in the caching-based wireless systems. In view of the fact that in such systems, users store fractional of popular contents during off-peak hours, we propose a modified version of the Luby Transform (MLT) encoding for the delivery phase to take the advantage of channel coding. The novelty of our proposed MLT encoding lies in employing the user’s partial information to create an appropriate degree distribution. To evaluate our proposed scheme, this study considers a realistic channel model inspired by the Gilbert-Elliott channel including the erasure mode and a binary symmetric channel model. The effectiveness of our MLT encoding is analyzed by the average degree and the number of encoding symbol. A comprehensive simulation evaluation is performed which shows that MLT encoding outperforms conventional LT coding in terms of the required number of encoding symbols and demonstrates a better performance on the recovered symbols. In particular, the MLT encoding, compared to the conventional LT encoding, reduces the amount of required symbols to recover the original file for at least 20%, when the user stored more than half a file.

Performance‐traffic‐trade‐off of two novel hard decision and two soft decision fusion periodogram‐based algorithms for cooperative spectrum sensing under unreliable reporting channel

Spectrum sensing is one of the most important tasks of cognitive radios (CRs) to detect idle bands for opportunistic access. In centralised cooperative sensing, CRs sense a target band and share sensing information via reporting channel with a fusion centre to decide whether the sensed band is vacant or not. This information can be raw data in soft decision fusion scheme or local decisions on the channel occupation state in hard decision fusion one. A soft decision typically achieves better detection performances, but the hard one intrinsically offers smaller data traffic. This study proposes two periodogram-based hard decision algorithms and makes a detailed performance-traffic-trade-off with two periodogram-based soft-decision algorithms. All the approaches are based on the circular folding cooperative power spectral density split cancellation algorithm. Performance analyses are made under unavoidable errors in the reporting channel. In the first assumption, the simple memoryless binary symmetric channel is adopted. In the second one, the more realist memory Gilbert–Elliott channel is assumed. Results show that the proposed schemes are sensitive to reporting errors, but performance loss can be supplanted with channel encoding, yet keeping the traffic smaller than in the soft decision without channel encoding.

The Role of Information in System Stability with Partially Observable Servers

We present a methodology for analyzing the role of information on system stability. For this we consider a simple discrete-time controlled queueing system, where the controller has a choice of which server to use at each time slot and server performance varies according to a Markov modulated random environment. At the extreme cases of information availability, that is when there is either full information or no information, stability regions and maximally stabilizing policies are trivial. But in the more realistic cases where only the environment state of the selected server is observed, only the service successes are observed or only queue length is observed, finding throughput maximizing control laws is a challenge. To handle these situations, we devise a Partially Observable Markov Decision Process (POMDP) formulation of the problem and illustrate properties of its solution. We further model the system under given decision rules, using Quasi-Birth-and-Death (QBD) structure to find a matrix analytic expression for the stability bound. We use this formulation to illustrate how the stability region grows as the number of controller belief states increases. The example that we consider in this paper is a case of two servers where the environment of each is modulated like a Gilbert-Elliot channel. As simple as this case seems, there appear to be no closed form descriptions of the stability region under the various regimes considered. However, the numerical approximations to the POMDP Bellman equations together with the numerical solutions of the QBDs, both of which are in agreement, hint at a variety of structural results.

Recursive distributed filtering over sensor networks on Gilbert–Elliott channels: A dynamic event-triggered approach

In this paper, the recursive distributed filtering problem is investigated for a class of discrete nonlinear time-varying systems under a dynamic event-triggered mechanism. The system outputs are collected through a sensor network subject to a time-varying topology that is connected via Gilbert–Elliott channels and governed by a set of Markov chains. In order to save communication cost, a dynamic event-triggered strategy is utilized to decide when a particular sensor node should broadcast the corresponding measurement output to its neighbors. For the addressed time-varying systems, our aim is to design a distributed filter for each sensor node such that an upper bound on the filtering error variance is guaranteed and subsequently minimized at each iteration under the dynamic event-triggered transmission protocol. The parameters of the desired filter are obtained recursively by following a certain set of recursions. Finally, an illustrative example is employed to verify the effectiveness of the proposed dynamic event-triggered distributed filtering algorithm.