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 (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=(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.