Delay and coding in multiple-user communications

2009 Information Theory and Applications Workshop, 2009

In networks with large latency, feedback about received packets may lag considerably the transmission of the original packets, limiting the feedback's usefulness. Moreover, time duplex constraints may entail that receiving feedback may be costly. In this work, we consider tailoring feedback and coding jointly in such settings to reduce the expected delay for successful in order reception of packets. We find that, in certain applications, judicious choices provide results that are close to those that would be obtained with a full-duplex system.

2014

Network coding is a technique that proposes a different approach for the protocol design in data communication networks. Thus, the nodes in the network are allowed not only to store and forward data packets, but also to process and mix different packets in a single coded packet. By using this technique, the throughput and robustness of the network can be significantly improved. However, the transmission delay of network coding is still not well understood. In real-time communication systems with stringent delay constraints, understanding the transmission delay distribution is at the core of implementing network coding in practical scenarios. Moreover, the benefits of network coding for broadcast scenarios have been proven, but the use of this technique in data gathering applications is limited. Unlike broadcast applications, where the main objective is to minimize the transmission delay, in data gathering applications the challenge is to reduce the data collection time, called the c...

2016 IEEE International Symposium on Information Theory (ISIT), 2016

The burst rank loss channel is an extension of the burst erasure channel where the channel matrix between the sender and receiver becomes rank-deficient for a certain period of consecutive time-slots. We study streaming communication over the burst rank loss channel, propose a new class of codes, ROBIN codes, and establish their optimality. Our construction uses the Maximum Rank Distance (MRD) and Maximum Sum Rank (MSR) codes from previous works as constituent codes, and combines them in a layered fashion. Our results generalize previous work on both the single-link and multiple-parallel-link streaming setups over burst erasure channels. We perform simulations over statistical network models to show that ROBIN codes attain low packet loss rates in comparison to existing codes. I. INTRODUCTION Streaming communication is characterized by two factors: causality and delay. Source packets arrive sequentially at a transmitter, which generates channel packets causally. The receiver collecting the transmitted packets must reconstruct the source within a decoding deadline, using only what it has observed up to that point. A receiving user is interested in sequential playback, meaning if a packet has not been recovered within the deadline, the decoder considers it lost and moves to the next packet. Error correcting codes capable of low delay decoding have previously been designed in the context of a single-link erasure channel connecting the transmitter and receiver [1]-[5]. In Internet communication, packet erasures primarily occur in bursts [6], and consequently the works of [1], [3]-[5] focus primarily on low-delay recovery from a burst of consecutive erasures. Alternatively, [2], [3], [5] also consider arbitrary loss patterns and guarantee low-delay recovery when there are fewer than the maximum tolerable number of erasures in a window. The above mentioned works consider the case of a single communication link between the sender and receiver. As communication methods increase in sophistication, it is natural to consider streaming over a network where there are multiple links and paths connecting the source and destination nodes [7], [8]. The simplest extension of a single-link setting is the case when there are multiple parallel links. This extension has been previously studied for streaming in [7, Chapter 8], [9]. In the network setting. multiple parallel links correspond to separate paths chosen by a naive routing algorithm. Link failures in the network then lead to packet erasures over the associated path. It was shown that joint coding across packets transmitted over different paths, can outperform separate coding applied to individual paths only. An alternative to path routing is generationbased linear network coding, where the received packets are a linear transformation of the transmitted packets [10]-[12]. Links failures in the network now can potentially reduce the channel rank [13]. Rank metric codes such as Gabidulin codes can be used as end-to-end codes for protecting packets in such rank-deficient channels [14]-[17]. In this work, we extend streaming under the burst packet loss model, see e.g., [18], to a rank-deficient matrix channel. In the context of network coding, the rank is equal to the min-cut of the network, decreasing to a minimum tolerable rank when links fail in a burst [10], [13], [19]. For such a burst rank loss model, we design an end-to-end code with a layered structure and establish its optimality. Our approach generalizes the prior work in [7, Chapter 8], which addressed a network with naive routing and permitted at most one link to fail during a burst. While there, the problem simplified to multiple parallel links with one behaving as a periodic burst erasure channel, we permit both multiple bursts and linear transformations of the channel packets that can ensue as a result of network coding. Furthermore, their code construction involved diagonally interleaving

Networks, 1999

We examine the problem of transmitting in minimum time a given amount of data between a source and a destination in a network with finite channel capacities and nonzero propagation delays. In the absence of delays, the problem has been shown to be solvable in polynomial time. In this paper, we show that the general problem is NP-complete. In addition, we examine transmissions along a single path, called the quickest path, and present algorithms for general and special classes of networks that improve upon previous approaches. The first dynamic algorithm for the quickest path problem is also given.

IEEE INFOCOM 2009 - The 28th Conference on Computer Communications, 2009

Motivated by streaming applications with stringent delay constraints, we consider the design of online network coding algorithms with timely delivery guarantees. Assuming that the sender is providing the same data to multiple receivers over independent packet erasure channels, we focus on the case of perfect feedback and heterogeneous erasure probabilities. Based on a general analytical framework for evaluating the decoding delay, we show that existing ARQ schemes fail to ensure that receivers with weak channels are able to recover from packet losses within reasonable time. To overcome this problem, we redefine the encoding rules in order to break the chains of linear combinations that cannot be decoded after one of the packets is lost. Our results show that sending uncoded packets at key times ensures that all the receivers are able to meet specific delay requirements with very high probability.

In this paper, 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 in an unreliable single-hop broadcast network setting. Our model consists of a source transmitting packets of a single flow to a set of N receivers over independent erasure channels. The source performs random linear network coding (RLNC) over K (coding window size) packets and broadcasts them to the receivers. 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 . By appealing to the Central Limit Theorem, we approximate the Negative Binomial random variable arising in our analysis by a Gaussian random variable. We then obtain tight upper and lower bounds on the mean decoding delay and throughput in terms of K and 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. Our numerical investigations show that the bounds obtained using the Gaussian approximation also apply to the real system performance, thus illustrating the accuracy of the analysis.

IEEE/ACM Transactions on Networking

In this paper, we introduce construction techniques for network coding in bidirectional networks with arbitrary transmission delays. These coding schemes reduce the number of transmissions and achieve the optimal rate region in the corresponding broadcast model for both multiple unicast and multicast cases with up to three users, under the equal rate constraint. The coding schemes are presented in two phases; first, coding schemes for line, star and line-star topologies with arbitrary transmission delays are provided and second, any general topology with multiple bidirectional unicast and multicast sessions is shown to be decomposable into these canonical topologies to reduce the number of transmissions. As a result, the coding schemes developed for the line, star, and line-star topologies serve as building blocks for the construction of more general coding schemes for all networks. The proposed schemes are proved to be real time in the sense that they achieve the minimum decoding delay. With a negligible size header, these coding schemes are shown to be applicable to unsynchronized networks, i.e., networks with arbitrary transmission delays. Finally, we demonstrate the applicability of these schemes by extensive simulations. The implementation of such coding schemes on a wireless network with arbitrary transmission delays can improve performance and power efficiency.

2012

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.

Here, we characterize the throughput of a broad cast network with receivers using rate less codes with block size. We characterize the system throughput asymptotically. Specifically, we explicitly show how the throughput behaves for different values of the coding block size as a function. We are able to provide a lower bound on the maximum achievable throughput. Using simulations, we show the tightness of the bound with respect to system parameters and find that its performance is significantly better than the previously known lower bounds. The packets are not decidable if any deviation is occurred.

Computer Communications, 2012

Despite the substantial research efforts on network coding, its real-world implementation is mainly over wireless networks or peer-to-peer networks. The deployment of network coding in the Internet core still largely lags behind. Among the many challenges, one difficulty is the selection of routers to perform network coding, which relies on the understanding of the queueing behavior of network coding. Unfortunately, the intricate queueing behavior of network coding, even for a single node case, is still unclear. In this paper, we build a generic queueing model to answer many fundamental questions, including for example, under what condition is the system stable? How many packets could be possibly coded when multiple stochastic traffic flows pass through a coding node? What is the quantitative relationship among the traffic arrival rate, the service rate, and the coding opportunities under a general network configuration? Based on our analytical results, we propose a self-adjustable delay-based coding mechanism for better congestion control. Our work provides network researchers and engineers with insights on the queueing behavior of network coding, which are helpful in future applications of network coding in the Internet core.

Computer Networks, 2013

This paper investigates the interaction between network coding and link-layer transmission rate diversity in multi-hop wireless networks. By appropriately mixing data packets at intermediate nodes, network coding allows a single multicast flow to achieve higher throughput to a set of receivers. Broadcast applications can also exploit link-layer rate diversity, whereby individual nodes can transmit at faster rates at the expense of corresponding smaller coverage area. We first demonstrate how combining rate-diversity with network coding can provide a larger capacity for data dissemination of a single multicast flow, and how consideration of rate diversity is critical for maximizing system throughput. Next we address the following question: given a specific topology of wireless nodes, what is the maximum rate that can be supported by the resultant network exploiting both network coding and multi-rate? We present a linear programming model to compute the maximal throughput that a multicast application can achieve with network coding in a rate-diverse wireless network. We also present analytical results where we observe noticeably better throughput than traditional routing. This suggests there is opportunity for achieving higher throughput by combining network coding and multi-rate diversity.

2009 IEEE International Symposium on Information Theory, 2009

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 N P-hard when the sender only schedules single messages and that the general problem remains N P-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.

2007

An asymptotic analysis for the delay-throughput of a single-hop wireless network with K links, operating in bandwidth W , is considered. The links are assumed to be partitioned into M clusters, each operating in a subchannel with bandwidth W M. The analysis relies basically on the distributed on-off power allocation strategy proposed in [1] and [2]. Our analysis consists of two parts. The first part deals with the throughput of the network in terms of M and under the shadowing effect with probability α. Assuming the Rayleigh fading channel model, it is proved that the maximum achievable throughput of the network for every value of 1 ≤ M ≤ K and 0 ≤ α ≤ 1 is obtained at M = 1. In the second part, we present the delay characteristics of the underlying network. It is proved that for M ∼ o(K) and 0 < α ≤ 1, where α is fixed, the delay threshold that makes the dropping probability of the link tend to zero, while achieving the maximum throughput, scales as ω(n log 2 n), where n = K M. We also present the similar arguments for the minimum delays in each cluster and the whole network. An asymptotic analysis shows that the delay improves without any significant impact on the the throughput.

2011

We resolve the question of optimality for a wellstudied packetized implementation of random linear network coding, called PNC. In PNC, in contrast to the classical memoryless setting, nodes store received information in memory to later produce coded packets that reflect this information. PNC is known to achieve order optimal stopping times for the manyto-all multicast problem in many settings.

2012

The problem of designing efficient feedback-based scheduling policies for chunked codes (CC) over packet networks with delay and loss is considered. For networks with feedback, two scheduling policies, referred to as random push (RP) and local-rarest-first (LRF), already exist. We propose a new scheduling policy, referred to as minimum-distance-first (MDF), based on the expected number of innovative successful packet transmissions at each node of the network prior to the "next" transmission time, given the feedback information from the downstream node(s) about the received packets. Unlike the existing policies, the MDF policy incorporates loss and delay models of the link in the selection process of the chunk to be transmitted. Our simulations show that MDF significantly reduces the expected time required for all the chunks (or equivalently, all the message packets) to be decodable compared to the existing scheduling policies for line networks with feedback. The improvements are particularly profound (up to about 46% for the tested cases) for smaller chunks and larger networks which are of more practical interest. The improvement in the performance of the proposed scheduling policy comes at the cost of more computations, and a slight increase in the amount of feedback. We also propose a low-complexity version of MDF with a rather small loss in the performance, referred to as minimumcurrent-metric-first (MCMF). The MCMF policy is based on the expected number of innovative packet transmissions prior to the "current" transmission time, as opposed to the next transmission time, used in MDF. Our simulations (over line networks) demonstrate that MCMF is always superior to RP and LRF policies, and the superiority becomes more pronounced for smaller chunks and larger networks.