We propose a novel causal coding scheme with forward error correction (FEC) for a point-to-point communication link with delayed feedback. The proposed model can learn the erasure pattern in the channel, and adaptively adjust its transmission and FEC rate based on the burstiness of the channel and the feedback. We investigate the throughput, and the in-order delivery delay of the adaptive causal coding algorithm, and contrast its performance with the one of the selective repeat (SR) ARQ. We demonstrate via an experimental study of the protocol that our model can double the throughput gains, and triple the gain in terms of mean in-order delivery delay when the channel is bursty, while keeping the difference between the maximum and mean in-order delivery delay is much smaller than SR ARQ. Closing the delay gap along with boosting the throughput is very promising for enabling ultra-reliable low-latency communications applications. We validate the performance of data delivery under the traces of Intel.
Using FEC, in order delivery delay over packet erasure channels can be reduced @cite_23 , and the performance of SR ARQ protocols @cite_6 can be boosted. Delay bounds for convolutional codes have been provided in @cite_3 , @cite_0 . Packet dropping to reduce playback delay of streaming over an erasure channel is investigated in @cite_16 , @cite_11 , @cite_26 . Delay-optimal codes without feedback for burst erasure channels, and the decoding delay of codes for more general erasure models have been analyzed in @cite_15 . Transmission with delay constraints have been considered in @cite_12 by combining the PHY and NET layer aspects, where bit level FEC is performed at the PHY layer, and Random Linear Network Coding (RLNC) is performed at the NET layer. To prevent packet loss in the presence of interference and large RTT, a network coded TCP solution has been proposed in @cite_19 . In Fig. , we refer to two of the coding approaches that are the closest to ours.
@cite_26 @cite_3 @cite_6 @cite_0 @cite_19 @cite_23 @cite_15 @cite_16 @cite_12 @cite_11
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We investigate the performance of delay constrained data transmission over wireless networks without end-to-end feedback. Forward error-correction coding (FEC) is performed at the bit level to combat channel distortions and random linear network coding (RLNC) is performed at the packet level to recover from packet erasures. We focus on the scenario where RLNC re-encoding is performed at intermediate nodes and we assume that any packet that contains bit errors after FEC decoding can be detected and erased. To facilitate explicit characterization of data transmission over network-coded wireless systems, we propose a generic two-layer abstraction of a network that models both bit symbol-level operations at the lower layer (termed PHY-layer) over several heterogeneous links and packet-level operations at the upper layer (termed NET-layer). Based on this model, we propose a network reduction method to characterize the throughput-reliability function of the end-to-end transmission. Our approach not only reveals an explicit tradeoff between data delivery rate and reliability, but also provides an intuitive visualization of the bottlenecks within the underlying network. We illustrate our approach via a point-to-point link and a relay network and highlight the advantages of this method over capacity-based approaches. We consider use of FEC to reduce in-order delivery delay over packet erasure channels. We propose a class of streaming codes that is capacity achieving and provides a superior throughput-delay trade-off compared to block codes by introducing flexibility in where and when redundancy is placed. This flexibility results in significantly lower in-order delay for a given throughput for a wide range of network scenarios. Furthermore, a major contribution of this paper is the combination of queuing and coding theory to analyze the code's performance. Finally, we present simulation and experimental results illustrating the code's benefits. In an unreliable single-hop broadcast network setting, we investigate the throughput and decoding-delay performance of random linear network coding as a function of the coding window size and the network size. Our model consists of a source transmitting packets of a single flow to a set of n users over independent time-correlated erasure channels. The source performs random linear network coding (RLNC) over k (coding window size) packets and broadcasts them to the users. We note that the broadcast throughput of RLNC must vanish with increasing n, for any fixed k. Hence, in contrast to other works in the literature, we investigate how the coding window size k must scale for increasing n. Our analysis reveals that the coding window size of Θ(ln(n)) represents a phase transition rate, below which the throughput converges to zero, and above which, it converges to the broadcast capacity. Further, we characterize the asymptotic distribution of decoding delay and provide approximate expressions for the mean and variance of decoding delay for the scaling regime of k=ω(ln(n)). These asymptotic expressions reveal the impact of channel correlations on the throughput and delay performance of RLNC. We also show that how our analysis can be extended to other rateless block coding schemes such as the LT codes. Finally, we comment on the extension of our results to the cases of dependent channels across users and asymmetric channel model. In an unreliable single-hop broadcast network setting, we investigate the throughput and decoding-delay performance of random linear network coding as a function of the coding window size and the network size. Our model consists of a source transmitting packets of a single flow to a set of @math users over independent erasure channels. The source performs random linear network coding (RLNC) over @math (coding window size) packets and broadcasts them to the users. We note that the broadcast throughput of RLNC must vanish with increasing @math , for any fixed @math Hence, in contrast to other works in the literature, we investigate how the coding window size @math must scale for increasing @math . Our analysis reveals that the coding window size of @math represents a phase transition rate, below which the throughput converges to zero, and above which it converges to the broadcast capacity. Further, we characterize the asymptotic distribution of decoding delay and provide approximate expressions for the mean and variance of decoding delay for the scaling regime of @math These asymptotic expressions reveal the impact of channel correlations on the throughput and delay performance of RLNC. We also show how our analysis can be extended to other rateless block coding schemes such as the LT codes. Finally, we comment on the extension of our results to the cases of dependent channels across users and asymmetric channel model. We propose a new feedback-based adaptive coding scheme for a packet erasure broadcast channel. The main performance metric of interest is the delay. We consider two types of delay - decoding delay and delivery delay. Decoding delay is the time difference between the instant when the packet is decoded at an arbitrary receiver and the instant when it arrived at the sender. Delivery delay also includes the period when a decoded packet waits in a resequencing buffer at the receiver until all previous packets have also been decoded. This notion of delay is motivated by applications that accept packets only in order. Our coding scheme has the innovation guarantee property and is hence throughput optimal. It also allows efficient queue management. It uses the simple strategy of mixing only the oldest undecoded packet of each receiver, and therefore extends to any number of receivers. We conjecture that this scheme achieves the asymptotically optimal delivery (and hence decoding) delay. The asymptotic behavior is studied in the limit as the load factor of the system approaches capacity. This conjecture is verified through simulations. Understanding the delay behavior of network coding with a fixed number of receivers, small field sizes and a limited number of encoded symbols is a key step towards its applicability in real-time communication systems with stringent delay constraints. Previous results are typically asymptotic in nature and focus mainly on the average delay performance. Seeking to characterize the complete delay distribution of random linear network coding, we present a brute-force methodology that is feasible for up to four receivers, limited field and generation sizes. The key idea is to fix the pattern of packet erasures and to try out all possible encodings for various system and channel parameters. Our findings, which are valid for both decoding delay and ordered-delivery delay, can be used to optimize network coding protocols with respect not only to their average but also to their worst-case performance. We consider the throughput-delay tradeoff in network coded transmission over erasure broadcast channels. Interested in minimizing decoding delay, we formulate the problem of instantly decodable network coding as an integer linear program and propose algorithms to solve it heuristically. In particular, we investigate channels with memory and propose algorithms that can exploit channel erasure dependence to increase throughput and decrease delay. With increasing dependence on wireless networks as an integral part of the communication infrastructure, it is critical that data link and transport layer protocols perform reasonably under potentially severe lossy conditions. A key strategy is to use hybrid ARQ (HARQ) with erasure codes (a.k.a. forward error correction or FEC) sent both proactively and reactively in response to feedback about dynamic loss statistics. A challenge is to design HARQ to satisfy multiple objectives such as high goodput, low latency and negligible residual loss rate. In this paper, we analyze the performance benefits and trade-offs of these reliability strategies (hybrid ARQ+FEC). We derive expressions for the expected good-put (and overhead in terms of FEC wastage), latency, and residual loss for a given raw erasure loss process (e.g. uniform and bursty loss models). We show how the analysis can be used to explain and provide specialized design guidance for link-layer HARQ that is subject to tight delay constraints and a recently designed transport layer HARQ scheme (called loss-tolerant TCP). We validate our analysis by comparing the predictions with values obtained from simulations performed on the link and transport layer HARQ strategies with ns-2. We believe that such an analysis could also have value for other adaptive protocols using network coding and incremental redundancy techniques. This paper introduces a robust point-to-point transmission scheme: Tetrys, that relies on a novel on-the-fly erasure coding concept which reduces the delay for recovering lost data at the receiver side. In current erasure coding schemes, the packets that are not rebuilt at the receiver side are either lost or delayed by at least one RTT before transmission to the application. The present contribution aims at demonstrating that Tetrys coding scheme can fill the gap between real-time applications requirements and full reliability. Indeed, we show that in several cases, Tetrys can recover lost packets below one RTT over lossy and best-effort networks. We also show that Tetrys allows to enable full reliability without delay compromise and as a result: significantly improves the performance of time constrained applications. For instance, our evaluations present that video-conferencing applications obtain a PSNR gain up to 7 dB compared to classic block-based erasure codes. We analyze a simple network where a source and a receiver are connected by a line of erasure channels of different reliabilities. Recent prior work has shown that random linear network coding can achieve the min-cut capacity and therefore the asymptotic rate is determined by the worst link of the line network. In this paper we investigate the delay for transmitting a batch of packets, which is a function of all the erasure probabilities and the number of packets in the batch. We show a monotonicity result on the delay function and derive simple expressions which characterize the expected delay behavior of line networks. Further, we use a martingale bounded differences argument to show that the actual delay is tightly concentrated around its expectation. Throughput and per-packet delay can present strong trade-offs that are important in the cases of delay sensitive applications.We investigate such trade-offs using a random linear network coding scheme for one or more receivers in single hop wireless packet erasure broadcast channels. We capture the delay sensitivities across different types of network applications using a class of delay metrics based on the norms of packet arrival times. With these delay metrics, we establish a unified framework to characterize the rate and delay requirements of applications and optimize system parameters. In the single receiver case, we demonstrate the trade-off between average packet delay, which we view as the inverse of throughput, and maximum ordered inter-arrival delay for various system parameters. For a single broadcast channel with multiple receivers having different delay constraints and feedback delays, we jointly optimize the coding parameters and time-division scheduling parameters at the transmitters. We formulate the optimization problem as a Generalized Geometric Program (GGP). This approach allows the transmitters to adjust adaptively the coding and scheduling parameters for efficient allocation of network resources under varying delay constraints. In the case where the receivers are served by multiple non-interfering wireless broadcast channels, the same optimization problem is formulated as a Signomial Program, which is NP-hard in general. We provide approximation methods using successive formulation of geometric programs and show the convergence of approximations. Future 5G systems will need to support ultra-reliable low-latency communications scenarios. From a latency-reliability viewpoint, it is inefficient to rely on average utility-based system design. Therefore, we introduce the notion of guaranteeable delay which is the average delay plus three standard deviations of the mean. We investigate the trade-off between guaranteeable delay and throughput for the point-to-point wireless erasure links with unreliable and delayed feedback, by bringing together signal flow techniques to the area of coding. We use tiny codes, i.e., sliding window by coding with just 2 packets, and design three variations of selective-repeat ARQ protocols, by building on the baseline scheme, i.e., uncoded ARQ, developed by Ausavapattanakun and Nosratinia: (i) Hybrid ARQ with soft combining at the receiver; (ii) cumulative feedback-based ARQ without rate adaptation; and (iii) coded ARQ with rate adaptation based on the cumulative feedback. Contrasting the performance of these protocols with uncoded ARQ, we demonstrate that the HARQ performs only slightly better, the cumulative feedback-based ARQ does not provide significant throughput while it has a better average delay, and the Coded ARQ can provide gains up to about 40 in terms of throughput. The Coded ARQ also provides delay guarantees, and is robust to various challenges such as imperfect and delayed feedback, burst erasures, and round-trip time fluctuations. This feature may be preferable for meeting the strict end-to-end latency and reliability requirements of the future use cases of ultra-reliable low-latency communications in 5G, such as mission-critical communications and industrial control for critical control messaging. We consider the delay of network coding compared to routing with retransmissions in packet erasure networks with probabilistic erasures. We investigate the sublinear term in the block delay required for unicasting n packets and show that there is an unbounded gap between network coding and routing. In particular, we show that delay benefit of network coding scales at least as √n. Our analysis of the delay function for the routing strategy involves a major technical challenge of computing the expectation of the maximum of two negative binomial random variables. Previous characterizations of this expectation are approximate; we derive an exact characterization and analyze its scaling behavior, which may be of independent interest. We also use a martingale bounded differences argument to show that the actual coding delay is concentrated around its expectation. Throughput and per-packet delay can present strong trade-offs that are important in the cases of delay sensitive applications. We investigate such trade-offs using a random linear network coding scheme for one or more receivers in single hop wireless packet erasure broadcast channels. We capture the delay sensitivities across different types of network applications using a class of delay metrics based on the norms of packet arrival times. With these delay metrics, we establish a unified framework to characterize the rate and delay requirements of applications and to optimize system parameters. In the single receiver case, we demonstrate the trade-off between average packet delay, which we view as the inverse of throughput, and maximum inorder inter-arrival delay for various system parameters. For a single broadcast channel with multiple receivers having different delay constraints and feedback delays, we jointly optimize the coding parameters and time-division scheduling parameters at the transmitter. We formulate the optimization problem as a Generalized Geometric Program (GGP). This approach allows the transmitter to adjust adaptively the coding and scheduling parameters for efficient allocation of network resources under varying delay constraints. In the case where the receivers are served by multiple non-interfering wireless broadcast channels, the same optimization problem is formulated as a Signomial Program, which is NP-hard in general. We provide approximation methods using successive formulation of geometric programs and show the convergence of approximations. In this work we address the stability and delay performance of a multicast erasure channel with random arrivals at the source node. We consider both a standard retransmission (ARQ) scheme as well as random linear coding. Our results show that while random linear coding may outperform re-transmissions for heavy traffic, the delay incurred by the use of random linear codes is significantly higher when the source is lightly loaded Current approaches to the practical implementation of network coding are batch-based, and often do not use feedback, except possibly to signal completion of a file download. In this paper, the various benefits of using feedback in a network coded system are studied. It is shown that network coding can be performed in a completely online manner, without the need for batches or generations, and that such online operation does not affect the throughput. Although these ideas are presented in a single-hop packet erasure broadcast setting, they naturally extend to more general lossy networks which employ network coding in the presence of feedback. The impact of feedback on queue size at the sender and decoding delay at the receivers is studied. Strategies for adaptive coding based on feedback are presented, with the goal of minimizing the queue size and delay. The asymptotic behavior of these metrics is characterized, in the limit of the traffic load approaching capacity. Different notions of decoding delay are considered, including an order-sensitive notion which assumes that packets are useful only when delivered in order. Our work may be viewed as a natural extension of Automatic Repeat reQuest (ARQ) schemes to coded networks. We present an expression for the delay distribution of Random Linear Network Coding over an erasure channel with a given loss probability. In contrast with previous contributions, our analysis is non- asymptotic in the sense that it is valid for any field size and any number of symbols. The results confirm that GF(16) already offers near-optimal decoding delay, whereas smaller field sizes (e.g. requiring only XOR operations) induce heavy tails in the delay distribution. A comparison with Automatic Repeat reQuest (ARQ) techniques (with perfect feedback) is also included. The severe nature of underwater channel poses a great challenge for prolonging underwater acoustic sensor networks (UASNs) lifetime and achieving a reliable communication performance. Traditional approaches to improve the reliability such as automatic repeat request (ARQ) negatively affect the network lifetime (NL) due to energy dissipation caused by ARQ retransmission. A forward error correction (FEC) technique called fountain codes (FCs) can solve the energy efficiency problem of ARQ by transmitting both the original packet and some redundant packets to ensure a targeted reliability with few or no retransmissions. In this paper, we investigate performances of both traditional ARQ- and FC-based FEC methods in terms of NL, end-to-end delay, energy consumption, and frame error rate (FER) for UASNs. In this context, we abstract energy dissipation characteristics of conventional ARQ- and FC-based FEC method at the link-layer. We propose an integer linear programming (ILP) framework that maximizes the NL, which is operated on top of developed link-layer energy consumption models. Our results reveal that FC-based FEC methods can prolong the NL at a minimum of 16 while end-to-end delay, energy consumption, and FER can be reduced at least by 11 , 14 , and 9 as compared to classical ARQ, respectively. For a packet erasure broadcast channel with three receivers, we propose a new coding algorithm that makes use of feedback to dynamically adapt the code. Our algorithm is throughput optimal, and we conjecture that it also achieves an asymptotically optimal average decoding delay at the receivers. We consider heavy traffic asymptotics, where the load factor rho approaches 1 from below with either the arrival rate (lambda) or the channel parameter (mu) being fixed at a number less than 1. We verify through simulations that our algorithm achieves an asymptotically optimal decoding delay of O (1 1-rho). In this paper, we consider the problem of min- imizing the multicast decoding delay of generalized instantly decodable network coding (G-IDNC) over persistent forward and feedback erasure channels with feedback intermittence. In such an environment, the sender does not always receive acknowledgement from the receivers after each transmission. Moreover, both the forward and feedback channels are subject to persistent erasures, which can be modelled by a two state (good and bad states) Markov chain known as Gilbert-Elliott channel (GEC). Due to such feedback imperfections, the sender is unable to determine subsequent instantly decodable packets combination for all receivers. Given this harsh channel and feedback model, we first derive expressions for the probability distributions of decoding delay increments and then employ these expressions in formulating the minimum decoding problem in such environment as a maximum weight clique problem in the G-IDNC graph. We also show that the problem formulations in simpler channel and feedback models are special cases of our generalized formulation. Since this problem is NP-hard, we design a greedy algorithm to solve it and compare it to blind approaches proposed in literature. Through extensive simulations, our adaptive algorithm is shown to outperform the blind approaches in all situations and to achieve significant improvement in the decoding delay, especially when the channel is highly persistent. Index Terms—Multicast Channels, Persistent Erasure Chan- nels, G-IDNC, Decoding Delay, Lossy Intermittent Feedback, Maximum Weight Clique Problem.