A large number of streaming applications use reliable transport protocols such as TCP to deliver content over the Internet. However, head-of-line blocking due to packet loss recovery can often result in unwanted behavior and poor application layer performance. Transport layer coding can help mitigate this issue by helping to recover from lost packets without waiting for retransmissions. We consider the use of an on-line network code that inserts coded packets at strategic locations within the underlying packet stream. If retransmissions are necessary, additional coding packets are transmitted to ensure the receiver's ability to decode. An analysis of this scheme is provided that helps determine both the expected in-order packet delivery delay and its variance. Numerical results are then used to determine when and how many coded packets should be inserted into the packet stream, in addition to determining the trade-offs between reducing the in-order delay and the achievable rate. The analytical results are finally compared with experimental results to provide insight into how to minimize the delay of existing transport layer protocols.
On the other hand, a large body of research investigating the delay of coding in different settings has taken place. In general, most of these works can be summarized by Figure . The coding delay of chunked and overlapping chunked codes ( @cite_5 ) (shown in Figure (a)), network coding in time-division duplexing (TDD) channels ( @cite_17 @cite_10 @cite_0 ), and network coding in line networks where coding also occurs at intermediate nodes ( @cite_7 ) is well understood. In addition, a non-asymptotic analysis of the delay distributions of random linear network coding (RLNC) ( @cite_20 ) and various multicast scenarios ( @cite_4 @cite_13 @cite_9 ) using a variant of the scheme in Figure (b) have also been investigated. Furthermore, the research that looks at the in-order packet delay is provided in @cite_19 and @cite_23 for uncoded systems, while @cite_14 , @cite_3 , and @cite_1 considers the in-order packet delay for non-systematic coding schemes similar to the one shown in Figure (b). However, these non-systematic schemes may not be the optimum strategy in networks or communication channels with a long @math .
@cite_13 @cite_14 @cite_4 @cite_7 @cite_9 @cite_1 @cite_3 @cite_0 @cite_19 @cite_23 @cite_5 @cite_10 @cite_20 @cite_17
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This paper analyzes the gains in delay performance resulting from network coding. We consider a model of file transmission to multiple receivers from a single base station. Using this model, we show that gains in delay performance from network coding with or without channel side information can be substantial compared to conventional scheduling methods for downlink transmission. 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 problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of µ messages to several receivers over separate erasure channels. The sender can broadcast a single message or a combination (encoding) of messages at each timestep. Receivers provide feedback as to whether the transmission was received. If at some time step a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the successive refinement of an image encoded using multiple description coding. Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. It allows Θ(µ) benefits as compared to previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay than online algorithms without feedback. Our main complexity results are that the offline minimization problem is NP-hard when the sender only schedules single messages and that the general problem remains NP-hard even when coding is allowed. However we show that coding does offer delay and complexity gains over scheduling. We also discuss online heuristics and evaluate their performance through simulations. 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. 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. 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. 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. A new random linear network coding scheme for reliable communications for time division duplexing channels is proposed. The setup assumes a packet erasure channel and that nodes cannot transmit and receive information simultaneously. The sender transmits coded data packets back-to-back before stopping to wait for the receiver to acknowledge (ACK) the number of degrees of freedom, if any, that are required to decode correctly the information. We provide an analysis of this problem to show that there is an optimal number of coded data packets, in terms of mean completion time, to be sent before stopping to listen. This number depends on the latency, probabilities of packet erasure and ACK erasure, and the number of degrees of freedom that the receiver requires to decode the data. This scheme is optimal in terms of the mean time to complete the transmission of a fixed number of data packets. We show that its performance is very close to that of a full duplex system, while transmitting a different number of coded packets can cause large degradation in performance, especially if latency is high. Also, we study the throughput performance of our scheme and compare it to existing half-duplex Go-back-N and Selective Repeat ARQ schemes. Numerical results, obtained for different latencies, show that our scheme has similar performance to the Selective Repeat in most cases and considerable performance gain when latency and packet error probability is high. Protocols such as TCP require packets to be accepted (i.e., delivered to the receiving application) in the order they are transmitted at the sender. Packets are sometimes mis-ordered in the network. In order to deliver the arrived packets to the application in sequence, the receiver's transport layer needs to temporarily buffer out-of-order packets and resequence them as more packets arrive. Even when the application can consume the packets infinitely fast, the packets may still be delayed for resequencing. In this paper, we model packet mis-ordering by adding an IID random propagation delay to each packet and analyze the required buffer size for packet resequencing and the resequencing delay for an average packet. We demonstrate that these two quantities can be significant and show how they scale with the network bandwidth. We consider streaming over a blockage channel with long feedback delay, as arises in, e.g., real-time satellite communication from a comm-on-the-move (COTM) terminal. For this problem, we introduce a definition of delay that captures the real-time nature of the problem, which we show grows at least as fast as O(log(k)) for memoryless channels, where k corresponds to the number of packets in the transmission. Moreover, a tradeoff exists between this delay and a natural notion of throughput we introduce to capture the bandwidth requirements of the communication. We develop and analyze an efficient "multi-burst" transmission (MBT) protocol for achieving good delay-throughput tradeoffs within this framework, which we show to be robust and near-optimal within the class of retransmission protocols with fixed schedules. The MBT protocol can be augmented with coding for additional performance gains. Simulations validate the new protocols, including when peak bandwidth and delay constraints are imposed. We study an online random linear network coding approach for time division duplexing (TDD) channels under Poisson arrivals. We model the system as a bulk-service queue with variable bulk size and with feedback, i.e., when a set of packets are serviced at a given time, they might be reintroduced to the queue to form part of the next service batch. We show that there is an optimal number of coded data packets that the sender should transmit back-to-back before stopping to wait for an acknowledgement from the receiver. This number depends on the latency, probability of packet erasure, degrees of freedom at the receiver, the size of the coding window, and the arrival rate of the Poisson process. Random network coding is performed across a moving window of packets that depends on the packets in the queue, design constraints on the window size, and the feedback sent from the receiver. We study the mean time between generating a packet at the source and it being seen", but not necessarily decoded, at the receiver. We also analyze the mean time between a decoding event and the next, defined as the decoding of all the packets that have been previously seen" and those packets involved in the current window of packets. Inherently, a decoding event implies an in-order decoding of a batch of data packets. We present numerical results illustrating the trade-off between mean delay and mean time between decoding events. 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. We study random linear network coding for broadcasting in time division duplexing channels. We assume a packet erasure channel with nodes that cannot transmit and receive information simultaneously. The sender transmits coded data packets back-to-back before stopping to wait for the receivers to acknowledge the number of degrees of freedom, if any, that are required to decode correctly the information. We study the mean time to complete the transmission of a block of packets to all receivers. We also present a bound on the number of stops to wait for acknowledgement in order to complete transmission with probability at least 1 − e, for any e ≫ 0. We present analysis and numerical results showing that our scheme outperforms optimal scheduling policies for broadcast, in terms of the mean completion time. We provide a simple heuristic to compute the number of coded packets to be sent before stopping that achieves close to optimal performance with the advantage of a considerable reduction in the search time.