在“On Coding for Reliable Communication over Packet Networks”（Lun，Medard和Effros，Proc.42nd Annu. Allerton Conf.Communication，Control，and Computing，2004），提出了一种用于有损有线或无线分组网络上的单播或多播的容量实现编码方案。我们扩展该文件的结果在两个方面：首先，我们扩展的网络模型，允许接收到的数据包的链路上到达根据任何过程的平均速率，而不是假设的泊松流量与i.i.d.以前的损失。第二，在具有i.i.d.损失，我们得出错误指数，量化的速率，错误的概率随编码延迟衰减。
英文摘要：
In "On Coding for Reliable Communication over Packet Networks" (Lun, Medard, and Effros, Proc. 42nd Annu. Allerton Conf. Communication, Control, and Computing, 2004), a capacity-achieving coding scheme for unicast or multicast over lossy wireline or wireless packet networks is presented. We extend that paper's results in two ways: First, we extend the network model to allow packets received on a link to arrive according to any process with an average rate, as opposed to the assumption of Poisson traffic with i.i.d. losses that was previously made. Second, in the case of Poisson traffic with i.i.d. losses, we derive error exponents that quantify the rate at which the probability of error decays with coding delay.
Network Coding is a packet encoding technique which has recently been shown to improve network performance (by reducing delays and increasing throughput) in broadcast and multicast communications. The cost for such an improvement comes in the form of increased decoding complexity (and thus delay) at the receivers end. Before delivering the file to higher layers, the receiver should first decode those packets. In our work we consider the broadcast transmission of a large file to N wireless users. The file is segmented into a number of blocks (each containing K packets - the Coding Window Size).…
Batched network coding (BNC) is a low-complexity solution to network transmission in multi-hop packet networks with packet loss. BNC encodes the source data into batches of packets. As a network coding scheme, the intermediate nodes perform recoding on the received packets belonging to the same batch instead of just forwarding them. A recoding scheme that may generate more recoded packets for batches of a higher rank is also called adaptive recoding. Meanwhile, in order to combat burst packet loss, the transmission of a block of batches can be interleaved. Stream interleaving studied in litera…
Fly-PRAC: Packet Recovery for Random Linear Network Coding
Technische Universität Dresden (TUD)（德累斯顿工业大学）；Cluster of Excellence “Centre for Tactile Internet with Human-in-the-Loop” (CeTI) of TUD（德累斯顿工业大学触觉互联网与人机交互卓越集群）；Aalborg University（奥尔堡大学）
This paper investigates the information freshness of two-way relay networks (TWRN) operated with physical-layer network coding (PNC). Information freshness is quantified by age of information (AoI), defined as the time elapsed since the generation time of the latest received information update. PNC reduces communication latency of TWRNs by turning superimposed electromagnetic waves into network-coded messages so that end users can send update packets to each other via the relay more frequently. Although sending update packets more frequently is potential to reduce AoI, how to deal with packet …
This paper considers a multi-source multi-relay network, in which relay nodes employ a coding scheme based on random linear network coding on source packets and generate coded packets. If a destination node collects enough coded packets, it can recover the packets of all source nodes. The links between source-to-relay nodes and relay-to-destination nodes are modeled as packet erasure channels. Improved bounds on the probability of decoding failure are presented, which are markedly close to simulation results and notably better than previous bounds. Examples demonstrate the tightness and useful…
We consider a wireless communication network with an adaptive scheme to select the number of packets to be admitted and encoded for each transmission, and characterize the information timeliness. For a network of erasure channels and discrete time, we provide closed form expressions for the Average and Peak Age of Information (AoI) as functions of admission control and adaptive coding parameters, the feedback delay, and the maximum feasible end-to-end rate that depends on channel conditions and network topology. These new results guide the system design for robust improvements of the AoI when …
We consider a problem in which a source is encoded into N packets, an unknown number of which are subject to adversarial errors en route to the decoder. We seek code designs for which the decoder is guaranteed to be able to reproduce the source subject to a certain distortion constraint when there are no packets errors, subject to a less stringent distortion constraint when there is one error, etc. Focusing on the special case of the erasure distortion measure, we introduce a code design based on the polytope codes of Kosut, Tong, and Tse. The resulting designs are also applied to a separate p…
In this paper, we propose PopNetCod, a popularity-based caching policy for network coding enabled Named Data Networking. PopNetCod is a distributed caching policy, in which each router measures the local popularity of the content objects by analyzing the requests that it receives. It then uses this information to decide which Data packets to cache or evict from its content store. Since network coding is used, partial caching of content objects is supported, which facilitates the management of the content store. The routers decide the Data packets that they cache or evict in an online manner wh…
We analyze a wireless line network employing wireless network coding. The two end nodes exchange their packets through relays. While a packet at a relay might not find its coding pair upon arrival, a transmission cost can be reduced by waiting for coding with a packet from the other side. To strike a balance between the reduced transmission cost and the cost incurred by the delay, a scheduling algorithm determining either to transmit an uncoded packet or to wait for coding is needed. Because of highly uncertain traffic injections, scheduling with no assumption of the traffic is critical. This …
In modern implementations of Cloud Radio Access Network (C-RAN), the fronthaul transport network will often be packet-based and it will have a multi-hop architecture built with general-purpose switches using network function virtualization (NFV) and software-defined networking (SDN). This paper studies the joint design of uplink radio and fronthaul transmission strategies for a C-RAN with a packet-based fronthaul network. To make an efficient use of multiple routes that carry fronthaul packets from remote radio heads (RRHs) to cloud, as an alternative to more conventional packet-based multirou…
The perceived quality of real-time media delivered over IP networks depends on both the rate and burstiness of packet loss. In this paper, we develop a new mathematical model for the residual burstiness of loss under erasure coding. We derive the expected number of consecutive losses in a burst as a function of erasure coding parameters and the network loss probability assuming a Bernoulli model for network losses.
The optimization of joint source and channel coding for a sequence of numerous progressive packets is a challenging problem. Further, the problem becomes more complicated if the space-time coding is also involved with the optimization in a multiple-input multiple-output (MIMO) system. This is because the number of ways of jointly assigning channels codes and space-time codes to progressive packets is much larger than that of solely assigning channel codes to the packets. We are unaware of any feasible and complete solution for such optimization of joint source, channel, and space-time coding o…
Batched network coding is a variation of random linear network coding which has low computational and storage costs. In order to adapt to random fluctuations in the number of erasures in individual batches, it is not optimal to recode and transmit the same number of packets for all batches. Different distributed optimization models, which are called adaptive recoding schemes, were formulated for this purpose. The key component of these optimization problems is the expected value of the rank distribution of a batch at the next network node, which is also known as the expected rank. In this pape…
Characterization of the delay profile of systems employing random linear network coding is important for the reliable provision of broadcast services. Previous studies focused on network coding over large finite fields or developed Markov chains to model the delay distribution but did not look at the effect of transmission deadlines on the delay. In this work, we consider generations of source packets that are encoded and transmitted over the erasure broadcast channel. The transmission of packets associated to a generation is taken to be deadline-constrained, that is, the transmitter drops a g…
A message composed of packets is transmitted using erasure and channel coding over a fading channel with no feedback. For this scenario, the paper explores the trade-off between the redundancies allocated to the packet-level erasure code and the channel code, along with an objective of a low probability of failure to recover the message. To this end, we consider a fading model that we term proportional-diversity block fading (PD block fading). For a fixed overall code rate and transmit power, we formulate an optimization problem to numerically find the optimal channel-coding rate (and thus the…
We study network coding gaps for the problem of makespan minimization of multiple unicasts. In this problem distinct packets at different nodes in a network need to be delivered to a destination specific to each packet, as fast as possible. The network coding gap specifies how much coding packets together in a network can help compared to the more natural approach of routing. While makespan minimization using routing has been intensely studied for the multiple unicasts problem, no bounds on network coding gaps for this problem are known. We develop new techniques which allow us to upper bound …
Network switches and routers need to serve packet writes and reads at rates that challenge the most advanced memory technologies. As a result, scaling the switching rates is commonly done by parallelizing the packet I/Os using multiple memory units. For improved read rates, packets can be coded upon write, thus giving more flexibility at read time to achieve higher utilization of the memory units. This paper presents a detailed study of coded network switches, and in particular how to design them to maximize the throughput advantages over standard uncoded switches. Toward that objective the pa…
This paper investigates coherent detection for physical-layer network coding (PNC) with short packet transmissions in a two-way relay channel (TWRC). PNC turns superimposed EM waves into network-coded messages to improve throughput in a relay system. To achieve this, accurate channel information at the relay is a necessity. Much prior work applies preambles to estimate the channel. For long packets, the preamble overhead is low because of the large data payload. For short packets, that is not the case. To avoid excessive overhead, we consider a set-up in which short packets do not have preambl…
The groupcast index coding (GIC) problem is a generalization of the index coding problem, where one packet can be demanded by multiple users. In this paper, we propose a new coding scheme called independent user partition multicast (IUPM) for the GIC problem. The novelty of this scheme compared to the user partition multicast (UPM) (Shanmugam \textit{et al.}, 2015) is in removing redundancies in the UPM solution by eliminating the linearly dependent coded packets. We also prove that the UPM scheme subsumes the packet partition multicast (PPM) scheme (Tehrani \textit{et al.}, 2012). Hence, the …
This paper considers a source, which employs random linear coding (RLC) to encode a message, a legitimate destination, which can recover the message if it gathers a sufficient number of coded packets, and an eavesdropper. The probability of the eavesdropper accumulating enough coded packets to recover the message, known as the intercept probability, has been studied in the literature. In our work, the eavesdropper does not abandon its efforts to obtain the source message if RLC decoding has been unsuccessful; instead, it employs partial packet recovery (PPR) offline in an effort to repair erro…
The conversational quality of voice over IP (VoIP) depends on packet-loss rates, burstiness of packet loss, and delays (or latencies). The benefits for conversational voice quality of erasure coding attributable to its reduction in packet loss rates are widely appreciated. When block erasure coding is used, our analysis shows how those benefits are reduced or even eliminated by increases in delays and in a measure of burstiness of packet loss. We nevertheless show that the net effect of those three factors is still positive over a wide range of network loss rates provided that block sizes are …
