759 research outputs found
ARQ for Network Coding
A new coding and queue management algorithm is proposed for communication
networks that employ linear network coding. The algorithm has the feature that
the encoding process is truly online, as opposed to a block-by-block approach.
The setup assumes a packet erasure broadcast channel with stochastic arrivals
and full feedback, but the proposed scheme is potentially applicable to more
general lossy networks with link-by-link feedback. The algorithm guarantees
that the physical queue size at the sender tracks the backlog in degrees of
freedom (also called the virtual queue size). The new notion of a node "seeing"
a packet is introduced. In terms of this idea, our algorithm may be viewed as a
natural extension of ARQ schemes to coded networks. Our approach, known as the
drop-when-seen algorithm, is compared with a baseline queuing approach called
drop-when-decoded. It is shown that the expected queue size for our approach is
as opposed to for the baseline
approach, where is the load factor.Comment: Submitted to the 2008 IEEE International Symposium on Information
Theory (ISIT 2008
Performance Modelling and Optimisation of Multi-hop Networks
A major challenge in the design of large-scale networks is to predict and optimise the
total time and energy consumption required to deliver a packet from a source node to a
destination node. Examples of such complex networks include wireless ad hoc and sensor
networks which need to deal with the effects of node mobility, routing inaccuracies, higher
packet loss rates, limited or time-varying effective bandwidth, energy constraints, and the
computational limitations of the nodes. They also include more reliable communication
environments, such as wired networks, that are susceptible to random failures, security
threats and malicious behaviours which compromise their quality of service (QoS) guarantees.
In such networks, packets traverse a number of hops that cannot be determined
in advance and encounter non-homogeneous network conditions that have been largely
ignored in the literature. This thesis examines analytical properties of packet travel in
large networks and investigates the implications of some packet coding techniques on both
QoS and resource utilisation.
Specifically, we use a mixed jump and diffusion model to represent packet traversal
through large networks. The model accounts for network non-homogeneity regarding
routing and the loss rate that a packet experiences as it passes successive segments of a
source to destination route. A mixed analytical-numerical method is developed to compute
the average packet travel time and the energy it consumes. The model is able to capture
the effects of increased loss rate in areas remote from the source and destination, variable
rate of advancement towards destination over the route, as well as of defending against
malicious packets within a certain distance from the destination. We then consider sending
multiple coded packets that follow independent paths to the destination node so as to
mitigate the effects of losses and routing inaccuracies. We study a homogeneous medium
and obtain the time-dependent properties of the packet’s travel process, allowing us to
compare the merits and limitations of coding, both in terms of delivery times and energy
efficiency. Finally, we propose models that can assist in the analysis and optimisation
of the performance of inter-flow network coding (NC). We analyse two queueing models
for a router that carries out NC, in addition to its standard packet routing function. The
approach is extended to the study of multiple hops, which leads to an optimisation problem
that characterises the optimal time that packets should be held back in a router, waiting
for coding opportunities to arise, so that the total packet end-to-end delay is minimised
Random Linear Network Coding For Time Division Duplexing: When To Stop Talking And Start Listening
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.Comment: 9 pages, 9 figures, Submitted to INFOCOM'0
Network Coding in a Multicast Switch
We consider the problem of serving multicast flows in a crossbar switch. We
show that linear network coding across packets of a flow can sustain traffic
patterns that cannot be served if network coding were not allowed. Thus,
network coding leads to a larger rate region in a multicast crossbar switch. We
demonstrate a traffic pattern which requires a switch speedup if coding is not
allowed, whereas, with coding the speedup requirement is eliminated completely.
In addition to throughput benefits, coding simplifies the characterization of
the rate region. We give a graph-theoretic characterization of the rate region
with fanout splitting and intra-flow coding, in terms of the stable set
polytope of the 'enhanced conflict graph' of the traffic pattern. Such a
formulation is not known in the case of fanout splitting without coding. We
show that computing the offline schedule (i.e. using prior knowledge of the
flow arrival rates) can be reduced to certain graph coloring problems. Finally,
we propose online algorithms (i.e. using only the current queue occupancy
information) for multicast scheduling based on our graph-theoretic formulation.
In particular, we show that a maximum weighted stable set algorithm stabilizes
the queues for all rates within the rate region.Comment: 9 pages, submitted to IEEE INFOCOM 200
Network Coding Meets TCP: Theory and Implementation
The theory of network coding promises significant benefits in network performance, especially in lossy networks and in multicast and multipath scenarios. To realize these benefits in practice, we need to understand how coding across packets interacts with the acknowledgment (ACK)-based flow control mechanism that forms a central part of today's Internet protocols such as transmission control protocol (TCP). Current approaches such as rateless codes and batch-based coding are not compatible with TCP's retransmission and sliding-window mechanisms. In this paper, we propose a new mechanism called TCP/NC that incorporates network coding into TCP with only minor changes to the protocol stack, thereby allowing incremental deployment. In our scheme, the source transmits random linear combinations of packets currently in the congestion window. At the heart of our scheme is a new interpretation of ACKs-the sink acknowledges every degree of freedom (i.e., a linear combination that reveals one unit of new information) even if it does not reveal an original packet immediately. Thus, our new TCP ACK rule takes into account the network coding operations in the lower layer and enables a TCP-compatible sliding-window approach to network coding. Coding essentially masks losses from the congestion control algorithm and allows TCP/NC to react smoothly to losses, resulting in a novel and effective approach for congestion control over lossy networks such as wireless networks. An important feature of our solution is that it allows intermediate nodes to perform re-encoding of packets, which is known to provide significant throughput gains in lossy networks and multicast scenarios. Simulations show that our scheme, with or without re-encoding inside the network, achieves much higher throughput compared to TCP over lossy wireless links. We present a real-world implementation of this protocol that addresses the practical aspects of incorporating network coding and decoding with TCP's wind ow management mechanism. We work with TCP-Reno, which is a widespread and practical variant of TCP. Our implementation significantly advances the goal of designing a deployable, general, TCP-compatible protocol that provides the benefits of network coding.National Science Foundation (U.S.) (Grant CNS-0627021)National Science Foundation (U.S.) (Grant CNS-0721491)National Science Foundation (U.S.) (Grant CCF-0915922)United States. Defense Advanced Research Projects Agency (Subcontract 18870740-37362-C)United States. Defense Advanced Research Projects Agency (Subcontract 060786)United States. Defense Advanced Research Projects Agency (Subcontract 069145)United States. Defense Advanced Research Projects Agency (Contract N66001-06-C-2020)Space and Naval Warfare Systems Center San Diego (U.S.) (Contract N66001- 08-C-2013
On the Delay of Network Coding over Line Networks
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
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