Selection of network coding nodes for minimal playback delay in streaming overlays

0.67 MB·English

by  Nicolae Cleju

1
Selection of network coding nodes for minimal
playback delay in streaming overlays
Nicolae Cleju∗, Nikolaos Thomos† and Pascal Frossard†
†Signal Processing Laboratory (LTS4), Ecole Polytechnique Fe´de´rale de Lausanne (EPFL), Lausanne, Switzerland
∗The “Gheorghe Asachi” Technical University of Iasi, Iasi Romania.
[email protected], {nikolaos.thomos,pascal.frossard}@epfl.ch
1 Abstract—Networkcodingpermitstodeploydistributedpacket max-flow min-cut bound of the network graph. Overall, the
1 deliveryalgorithmsthatlocallyadapttothenetworkavailability network coding systems have shown improved resiliency to
0 in media streaming applications. However, it may also increase
dynamics,delays,scalabilityandbuffercapacitiesinnetworks
2 delay and computational complexity if it is not implemented
with diversity [3].
efficiently.Weaddressheretheeffectiveplacementofnodesthat
n
implement randomized network coding in overlay networks, so Theapplicationofnetworkcodingalgorithmsinmultimedia
a
J that the goodput is kept high while the delay for decoding stays streamingsystemsishowevernotstraightforward.Specifically,
small in streaming applications. We first estimate the decoding multimedia streaming imposes strict timing constraints that
0
delay at each client, which depends on the innovative rate in
2 impact the design of network coding algorithms. A practical
the network. This estimation permits to identify the nodes that
network coding system has been presented in [4] and ad-
have to perform coding for a reduced decoding delay. We then
M] propose two iterative algorithms for selecting the nodes that dresses the specific characteristics of streaming applications.
shouldperformnetworkcoding.Thefirstalgorithmreliesonthe It implements randomized network coding (RNC) techniques
M knowledge of the full network statistics. The second algorithm [5] in the network nodes and devises a protocol to deal with
usesonlylocalnetworkstatisticsateachnode.Simulationresults
bufferingissuesandtimingconstraints.Moreover,itintroduces
s. show that large performance gains can be achieved with the the concept of generations that restricts coding operations
c selection of only a few network coding nodes. Moreover, the
[ secondalgorithmperformsverycloselytothecentralestimation to packets that share similar decoding deadlines. However,

strategy, which demonstrates that the network coding nodes can networkcodingsystemsstillfaceimportantissuesinpractical
1
beselectedefficientlyinadistributedmanner.Ourschemeshows systems due to the decoding delays imposed by successive
v
large gains in terms of achieved throughput, delay and video
9 network coding operations. This delay as well as the com-
quality in realistic overlay networks when compared to methods
7 putational overhead in the system grow with the number of
that employ traditional streaming strategies as well as random
9 network nodes selection algorithms. networkcodingnodes.Itbecomesthereforeimportanttoselect
3 efficiently the subset of nodes that perform network coding
. Index Terms—Network coding, delay minimization, through-
1 in order to control delay and complexity and still exploit
put maximization, overlay networks.
0 efficiently the diversity in the network.
1
In this paper, we discuss solutions for the selective place-
1 I. INTRODUCTION
ment of a few network coding nodes in order to reduce the
:
v Therecentdevelopmentofoverlaynetworksoffersinterest- delay for video delivery. The nodes in the network are cate-
i ing perspectives for multimedia streaming applications, since
X gorized into network coding (NC) and store and forward (SF)
network diversity can be used advantageously for improved
nodes. The network coding nodes use the practical network
r
a quality of service. The traditional streaming systems based coding algorithm described in [4], which has been selected
on ARQ or channel coding techniques however generally
for its effectiveness and simplicity. Similarly, we adopt the
fail to efficiently exploit this diversity. They either suffer
conceptofcodinggenerationandbuffermodels[4]forproper
from relatively high computational cost, require coordination
handling of the timing constraints in the stream delivery. We
between network nodes or lead to suboptimal performance
first build on our previous work [6] and estimate the rate of
in large scale networks where local channel conditions are
non-redundant packets in each network node. This rate is an
hard to estimate. A different paradigm has been initiated
indication of the goodput of the system as it measures the
recently with network coding [1], [2], where some processing
number of useful and non-redundant packets that are received
is requested from the network nodes in order to improve
atanode.Itpermitstoestimatethedecodingdelayintheclient
the packet delivery performance. Specifically, network coding
nodes; this corresponds to the time necessary for collecting
nodes combine buffered packets before forwarding them to
enough useful packets to build a full rank decoding system.
next hop nodes. This coding strategy is particularly appealing
We use the delay estimation to select the subset of nodes
in distributed streaming systems, as it removes the need for
that should implement network coding such that a maximal
reconciliationbetweennodes.Itlocallyadaptstotheavailable
goodput or a minimal delay is attained. We propose two
bandwidth and packet loss rate and even permits to approach
algorithms that iteratively choose the SF nodes to be turned
into NC nodes for improving the system performance. Both
This work has been partly supported by the Swiss National Science
Foundation,undergrantPZ00P2-121906. algorithms differ in their view of the network status. The first
2
Client
algorithmassumesthatacentralnodehascompleteknowledge
about the status of the overlay network in terms of available
bandwidth and packet loss rate. The second algorithm only
uses local estimations of the network status at each node and Server SF
provides a solution for distributed systems. The simulation SS
results show that the proper selection of only a few network
NC
codingnodesalreadyleadstothroughputgainsthatcomeclose Server
to max-flow min-cut bound and greatly decrease the delay Source SS
necessary for media stream delivery. Moreover, the algorithm SF
that only considers local network statistics performs very
Lossy packet network
competitively with the algorithm that uses full knowledge of
Client
the network topology. Both algorithms even select the same
nodes for network coding in most of the cases. Furthermore,
theybothoutperformbasicstreamingalgorithmsbuiltonstore Fig. 1: Illustration of a system for streaming on overlay
and forward approaches as well as solutions where network networks. Multiple streaming servers (SS) send information
coding nodes are selected randomly. These observations are to clients on a lossy packet network via intermediate nodes
confirmed inrealistic overlaynetworks whereour methodcan that can be either network coding (NC) or ’store and forward’
improve users’ video experience even in the case where only (SF) peers.
fewnodesimplementrandomizednetworkcoding.Thisisdue
to a good balance between decoding delay and efficient use
of the network diversity. Finally, minimal network knowledge based packet delivery strategy that involves lower communi-
is often sufficient for determining the efficient positioning of cation and coordination overhead than a pull-based solution.
the network coding nodes. We consider that the servers can also implement randomized
Thepaperisorganizedasfollows.InSectionII,wepresent coding on the source packets for improved robustness. The
the framework under consideration and briefly overview the coded packets are then pushed to the clients through the
network coding principles. In Section III, we describe the successive intermediate nodes. Finally, the clients perform
model of the SF node buffer that is eventually used for delay network decoding after receiving enough packets to build a
computation. Then we present in Section IV a methodology full rank decodable system of packets.
for estimating the useful flow rate in the network nodes TheSFnodessimplysendateachtransmissionopportunity
as well as the decoding delay. The centralized and semi- the first packet in their buffer, which has not been sent
distributed algorithms for selecting the network coding nodes previously.Thebufferismanagedinafirst-in-first-outmanner,
are presented in Section V. Simulation results are proposed in where the oldest packets are replaced by new ones when the
Section VI where the benefits of the proposed algorithms are buffer is full. When the outgoing bandwidth is larger than
evaluated for video streaming applications in various realistic the incoming capacity, a SF node sends random replicates of
networkcases.Finally,therelatedworkisdiscussedinSection packets from its buffer. On the other hand, the intermediate
VII and conclusions are drawn in Section VIII. nodes that perform network coding combine randomly the
buffered packets in order to generate network coded packets
II. NETWORKCODINGFRAMEWORK that are further transmitted to neighbor nodes. As suggested
in [4], the NC nodes first check whether the received packets
We consider a streaming system that consists of servers, are innovative, where innovative packets characterize pack-
clients and intermediate nodes, as illustrated in Fig. 1. The
ets carrying novel information. Non-innovative packets are
overlay network offers source and path diversity, which can
discarded immediately as they do not increase the symbol
be efficiently exploited with network coding techniques that
diversity into the network. Then the NC nodes randomly
randomly combine packets in the nodes. This increases the
combine the remaining packets with coding operations based
packet diversity in the network and leads to efficient exploita-
on randomized network coding (RNC) [7]. It is a simple and
tion of the channel resources without the need for complex
efficient network coding solution in distributed systems. RNC
scheduling or nodes coordination mechanisms [1]. The net-
codesworksimilarlytoratelesscodes[8],[9]andcangenerate
work is modeled by a directed acyclic graph G = (V,E)
an arbitrary number of coded packets from a given set of
whereV isthesetofnetworknodesandE isthesetofedges
source packets. It provides a means for simple bandwidth
(links)inthenetwork.Eachnetworklinkbetweennodesuand
adaptation.
v is characterized by a bandwidth b (expressed in terms of
u,v Formally,thenetworkcodingoperationsperformedinapeer
packets per second) as well as a packet loss rate π . We
u,v node can be written as follows. A NC node u generates M
assume that all servers transmit the same multimedia content packets by RNC. The mth network coded packet c is of the
m
to clients via intermediate nodes that could either be network
form
coding (NC) or “store and forward” (SF) nodes. We consider (cid:88)
c = f ·p (u)
m m,i i
thattheintermediatenodesarenotnecessarilyinterestedinthe
transmitted content, but rather act as helper nodes and assist pi(u)∈N(u)
the packet delivery system. The system implements a push- where N(u) corresponds to the set of packets of the same
3
p1 f’1 c1(p1, p2, p3)
p2
overlay node
p3 f’2 c2(p1, p2, p3)
Fig. 2: A NC node combines incoming packets p and gener-
i
ates network coding packets c . A header f(cid:48) is appended to
m m
each coded packet and carries the coding coefficients.
generation that are available at node u, p (u) denotes either
i
a network coded packet or a native (uncoded) packet, and
f is a random coefficient over the Galois field of size q,
m,i
GF(q).ThebasisoftheGaloisfieldistypicallysettoq =256,
as it has been shown in [4] that this guarantees high symbol
diversityandlowprobabilityofbuildingduplicatepackets.As
the packets combined in a node are actually combinations of
theoriginaldatapackets,theencodedpacketscanbeexpressed
as a function of the native packets
N Fig. 3: Packet replications procedure followed in a SF node
(cid:88) (cid:48)
cm = fm,i·ni (1) after the reception of the hth innovative packet.
i=1
where N is the total number of native packets, e.g., for video
transmission N can be the number of video packets. The packetsinthenetworkbycodingoperations.Thisisnecessary
parametersn andf(cid:48) representrespectivelythenativepack- asthereisanon-zeroprobabilityforthereceptionofduplicate
i m,i
ets and their corresponding coding coefficients after random packets in the network nodes when the network is mostly
networkcodingoperations.Itisworthnotingthatsomeofthe composed of SF nodes. These duplicates can be generated by
coefficients f(cid:48) can be zero, which means that c does not a node that does not receive enough diverse packets, or from
m,i m
contain information about the native packet n . As the coding different nodes that independently transmit identical packets.
i
coefficientsarechosenrandomly,aheaderofconstantlengthis Theseduplicatepacketslowersignificantlythestreamdelivery
appended to each packet with coefficient information, so that performance especially in networks containing bottlenecks.
the received can decode the stream and recover the original However,thecarefulplacementofafewnetworkcodingnodes
data packets. A network coded packet is thus augmented in the overlay can help to reduce the number of duplicates in
with a header containing the vector of coding coefficients. the network. If the number of network coding nodes however
Fortunately,theheaderdoesnotgrowwiththenumberofhop becomestoolarge,theprobabilityfortherandomizednetwork
transmissionsduetoEq.(1).Theencodingprocedureinapeer codingoperationstogenerateduplicatepacketsbecomesagain
node is depicted in Fig. 2. non-negligible.Thisisespeciallythecaseifcodingoperations
The decoding operations at the client basically consist in arerestrictedtosmallgenerationsduetodelayconstraints.As
solvingthesystemofequationsthatcorrespondtothenetwork redundancy,delayandcomputationaloverheadmightincrease
coding operations. Upon collecting a network coded packet, with the number of coding nodes, it becomes quite apparent
the client stores it in a buffer and adds a line into a matrix F that efficient systems should not implement network coding
that contains the coding coefficients. When a full rank system in every overlay node. Instead, one has to find an effective
is collected, the original packets are reconstructed by solving placement of network coding nodes in order to fully exploit
the following equations the network diversity in overlay streaming applications.
 c   f(cid:48) ··· f(cid:48)   n 
1 1,1 1,N 1
c=F·n=⇒ ... = ... ... ... · ...  III. SFBUFFERMODEL
We provide in this section a buffer model for the SF nodes,
cN fN(cid:48) ,1 ··· fN(cid:48) ,N nN which forward and possibly replicate packets if the outgoing
where c and n are respectively vectors with the coded and bandwidth is sufficient. The buffer model is used to estimate
source packets. The solution of the equations system is typi- therateofreplicatedpackets,whichisanimportantparameter
cally computed by gaussian elimination [4]. in the computation of the decoding delay in the receivers.
The proposed streaming system leads to the following As illustrated in Fig. 3, we consider that each SF node has
observations. First, the network coding nodes act somehow two buffers of capacity h (in packets): the Main Buffer (MB),
similarly to sources in the sense that they refresh the set of where the incoming packets are stored, and the Copies Buffer
4
(CB) where copies of the packets that have been recently replicated, since they do not traverse fully the buffer. If
transmittedarestored.BothbuffersfollowaFIFOmodelasthe k(cid:48) = k−K denotes the position of the packets in CB when
oldestpacketsareoverwrittenbythenewoneswhenthenode’s the buffer is flushed, the number of copies of the late packets
buffer capacity is exceeded. In addition, since our system can then be written as
workswithdeadline-constraineddata,thepacketsareremoved
from the buffers when their decoding deadline expires. h−k(cid:48)+1
The buffering process works as follows: when a packet Rk(u)=1+(R(u)−1)· h , fork ∈[K+1,|N(u)|],
arrives in a SF node, it is stored in MB. When the SF node (4)
has a transmission opportunity, a packet from MB is sent and where |N(u)| is the number of packets of the same coding
thus removed from MB. A copy of this packet is kept in CB. generation that reach the node u.
Whenever MB is empty and the node has other transmission In summary, two main factors affect the packet replication
opportunities,itrandomlyselectsapacketfromCBandtrans- rate,theFIFObehavioroftheCBbufferandtheexpirationof
mits it. In other words, the node transmits packet replicates thedecodingdeadlinethatcausesthedeletionofpacketsinthe
when the outgoing bandwidth is sufficient. The packets in buffer. Thus, the first h−1 packets are replicated more than
CB are overwritten after some time by newer packets. In average and the last packets are replicated less than average,
our model, if a SF node does not have sufficient outgoing while the intermediate packets have constant replication rate.
bandwidthforreplication,itdoesnotuseCB.Alternatively,if Finally, it should be noted that, depending on the bandwidth
the outgoing bandwidth is large, CB is used extensively and value and the delay constraints, there are situations where the
MB is often empty. buffer does not reach the stationary regime of Eq. (3) and
We are now interested in computing the number of packet the computation of the number of replicates shall be adapted
replicates generated by the SF node u under the proposed accordingly.
buffer model. A priori, the average number of replicates per Weusetheabovebufferingmodeltocomputeanequivalent
packet R(u) at node u is given by the ratio of outgoing and packetreplicationrateRˆ(u)forallpacketsinaSFnode,which
incoming bandwidths b (u) and b (u) respectively. We can is more precise than the average value R(u) = bo(u). The
write R(u)= bo(u). Hoowever, the pirobability for a packet to equivalent replication rate is estimated so that the nbiu(mu)ber of
bereplicateddebpi(eun)dsontheorderofitsarrivaltotheSFnode. packets at the client c is preserved with respect to the case
Typically, a packet that arrives early spends more time in the where the packet replication rate is computed independently
buffer and thus has a higher probability to be replicated than for each packet. We assume that each packet travels indepen-
a packet that arrives late and close to the decoding deadline. dently to the client c, and we pose the following equivalent
Wethusconsiderthreecasesdependingontheorderofarrival condition:
of the packets. We denote the arrival by the position k of
a packet in a coding generation. The first case includes the |N(u)|
earliest packets, which reach the node while CB is not full. (cid:88) (cid:110)1−((cid:15) (u))Rk(u)(cid:111)=|N(u)|·(cid:110)1−((cid:15) (u))Rˆ(u)(cid:111),
c c
Every packet is replicated with a uniform probability in CB,
k=1
but the packets that stay longer in the buffer have a higher (5)
chance to be replicated. The number of copies for the kth where (cid:15)c(u) is the probability of loosing a packet between
packet is thus given by: the node u and the client c. The number of copies Rk(u)
is computed from Eqs. (2), (3) and (4). Rewriting the above
equation, we can express the equivalent replication rate as
(cid:32) h (cid:33)
(cid:88) 1 1
Rk(u)=1+(R(u)−1) x +(k−1)h , fork ∈[1,h] log(cid:18)1− (cid:80)k|N=(1u)|{1−((cid:15)c(u))Rk(u)}(cid:19)
x=k |N(u)|
(2) Rˆ(u)= . (6)
log((cid:15) (u))
The second case corresponds to packetsthat reach the node c
whileCBisfull.WhenCBisfull,eachnewpacketoverwrites We use this replication rate estimate in the computation of
theoldestpacketinCB.EachpackethasalifetimeinCBthat the decoding delay in the next section.
corresponds to the time necessary to collect h new packets
in the SF node. The replication probability is equal to 1/h
IV. DELAYANALYSIS
and the number of copies is then equivalent to the average
A. Estimation methodology
replication rate in the node. In this stationary mode, we have
Our objective is to minimize the decoding delay by the
proper placement of NC nodes in the overlay. The decoding
R (u)=R(u), for k ∈[h+1,K], (3)
k
delay is the time required to gather a sufficient number of
where K is the number of packets that fully traverse CB innovative packets for decoding. In the analysis below we
until the head of the buffer’s queue. Finally, the third case restrict our attention to cases where a full rank system is
corresponds to the packets that do not spend a full lifecycle built at decoder and estimate the delay necessary for this
in CB due to the expiration of the decoding deadline. When situation to happen. We further construct our analysis for one
the decoding deadline expires, CB is flushed, and the packets codinggeneration,whiletheextensiontomultiplegenerations
in the buffer at that moment have less opportunities to be is straightforward. The decoding delay depends on the rate of
5
(a) (b) (c) (d) (e)
Fig. 4: Flow decomposition of the network graph by the proposed algorithm. The top (red) node and the bottom (green) node
are respectively the source and the client of the considered topology. The SF and NC nodes are represented respectively by
the big and small black nodes. Flow from the (a) source, (b) first NC node, (c) second NC node, (d) third NC node, and (e)
fourth NC node.
innovative packets at the client. The innovative rate increases and we define
b
monotonically with the number of useful packets at the client ρ = u,v
u,v (cid:88)
[4], whichcorrespondsto thenumber ofdifferent packetsthat b
u,v
reach the client. Hence, a higher rate of useful packets leads v∈D(u)
to a smaller decoding delay.
as the probability that a packet transmitted by node u is
Inordertocomputethedecodingdelay,weconsiderthatSF forwarded to a descendant node v ∈ D(u). In addition, we
nodes replicate packets in case of large outgoing bandwidth. write the probability that a packet is deleted in a node due to
We further consider that new packets are generated only at buffer overflow as
sources and NC nodes. We treat these nodes independently in (cid:40)1− bo(u), b (u)<b (u)
the computation of the delay at the client as illustrated in Fig. β(u)= bi(u) o i
0, b (u)≥b (u)
4. We assume that the probability of generating two identical o i
packets in the sources or NC nodes is negligible due to the Recall that b (u) and b (u) are respectively the cumulative
o i
largesizeoftheGaloisfield.Inmoredetails,wefirstestimate incoming and outgoing bandwidth of node u. Then, a packet
the delay noticed by the client when packets are sent from a sent by node u might not reach the client c due to one of
given source through all the paths connecting this source to the following three causes. The packet can be lost during its
the client, except for the paths that traverse NC nodes (see transmissiontothechildnodev oritcanbelostatthenodev
Fig. 4a). Next, we consider the NC node that is the closest duetobufferoverflow.Finally,itcanbelostalongwithallits
to the source and all the paths that connect it to the client, possible copies during the transmission from the child node v
except for those passing through other NC nodes (see Fig. to the client c. Overall, the probability (cid:15) (u) is given as
c
4b). Similarly, all other NC nodes are considered only when
all their parent NC nodes have been visited. This procedure is (cid:88)
(cid:15) (u)= ρ ·{π +(1−π )·β(u)}
repeatedfortheunprocessedNCnodesandthecorresponding c u,v u,v u,v
graphsareshownrespectivelyinFigs.4c,4dand4e.Thetotal v∈D(u)
(7)
delay is computed under the assumption that all sources and + (cid:88) ρ (1−π )·(1−β(u))·(cid:15) (v)Rˆ(v).
u,v u,v c
NCnodessendindependentstreams.Equivalently,weassume
v∈D(u)
that the total useful flow is equal to the sum of the useful
The probability (cid:15) (u) can be computed recursively back-
flows generated by the source and all the NC nodes. c
wards starting from the clients up to the server or NC nodes.
As we consider lossy network paths, we have to consider Specifically, we first set to zero the loss probabilities for all
that some of the packets generated by network nodes do not the clients. Then, all nodes in the directed acyclic subgraph
reach their destination. We thus estimate the probability (cid:15) (u) are visited backwards. Each node is visited only when all its
c
that a packet sent by the node u does not reach the client c. children nodes have been processed already. Once (cid:15) (u) is
c
Thisprobabilityiscomputedonthesubgraphthatcontainsall known,wecancomputetherateofusefulpacketsreceivedby
the paths connecting the node u with the client c but excludes the client c from a source or a NC node by multiplying the
the paths that traverse other NC nodes since these typically respectiveoutgoingratebytheprobabilityofcorrectreception
alterthesetofreceivedpackets.Thecorrespondingsubgraphs 1−(cid:15) (u).
c
are colored in red in Fig. 4. We denote by D(u) the set of Next, we define N (u), the number of packets received by
c
children of node u (excluding the NC nodes) in the subgraph any node u that are potentially useful for the client c. These
6
packets correspond to the data that reaches the node u and procedure is applicable in our framework as we consider the
contains information that is potentially useful for the client iterativeselectionofnetworkcodingnodes.Nodesarechecked
c. It depends on the paths connecting the source nodes and in a greedy way and the algorithm improves at each stage
the NC nodes to the node u, i.e., the subgraphs colored in the current solution by the selection of the additional network
green in Fig. 4. It also depends on the set of SF nodes on codingnodethatbringsthelargestdelayreduction.Theoverall
these paths. The rate of useful packets transmitted by the algorithm typically converges only after a few iterations.
sources corresponds to their outgoing bandwidth, as they are We describe now the delay estimation algorithm in more
able to generate any number of different packets via network details. The steps 7-11 of Algorithm 1 correspond to the
coding. However, the useful rate in NC nodes may be smaller estimation of the useful rate N (u) in NC nodes, which is
c
than their outgoing bandwidth, as they may have only part of necessaryforcomputingtheinitialreplicationrateofthenode
the source information in their buffer. Finally the number of u.Asthisrateisdifficulttoestimateinadirectway,wechoose
useful packets in SF nodes cannot be larger than the number a differential method by comparing the delay t (u) observed
c
of incoming packets. It is however difficult to estimate in a by the client when the node u is active and respectively
direct way, so that the estimation of the delay based on the silent. From the delay difference ∆t (u) we compute the rate
c
usefulratesentbynetworknodesbecomeshard.Wetherefore difference ∆N (u) that is the useful rate at node u. Finally,
c
propose below to compute the delay in a recursive manner. the rate N (u) of the packets at node u that are useful for the
c
client c is computed by solving
B. Decoding delay (cid:40)N (u)·(cid:16)1−(cid:15) (u)Rˆ(u)(cid:17), b (u)>b (u)
c c o i
In this section, we estimate the delay t at a client node ∆N (u)=
c. The decoding delay depends on the ratecof useful packets c Nc(u)· bboi((uu)) ·(1−(cid:15)c(u)), bo(u)<bi(u)
received from the multiple sources or network coding nodes. (8)
We estimate the time necessary to form a system of full rank where the first and second conditions correspond to the cases
G at the decoder, where G is the generation size in packets. when the node u in SF mode has a small incoming, respec-
In practice, the client might need to collect a slightly larger tively outgoing bandwidth. Note that, when the network does
number of packets, G˜ =G/(1−x) [4] for forming a system not contain any NC nodes, the rate of useful packets that are
with G innovative packets. This is due to the possibility that transmitted is simply equal to the output bandwidth of the
useful packets from a source might still be redundant and not sources. In this case, the useful rate received by the client is
completelyindependentofpacketsgeneratedbyothersources. simply Nc(s)=bo(s)·(1−(cid:15)c(s)).
Theexactvalueoftheoverheadfactorxdependsonthecoding Then we compute the delay due to packets sent by the
system(e.g.,itcanbeupper-boundedby1/qforRNC,whereq different sources and NC nodes in the network. We consider
istheGFsize).However,ouranalysisisrelative,andcompare two cases. First, we consider the NC nodes that have limited
different configurations to select the option that leads to the incomingbandwidth(i.e.,Nc(u)<bo(u)inline12orAlg.1)
minimal decoding delay. It becomes therefore equivalent to andthesourceswithoutgoingbandwidthlargerthanthesource
work with G or G˜ since the solutions that lead to the fastest rate.Theprobabilityofgeneratingusefulpacketsinsuchnodes
delivery of G and respectively G˜ packets are identical. We evolvesasthebufferfillsin.Westartbyestimatingthenumber
choose to work with G in the rest of this section. of different packets received by the client c when the node
We compute the average decoding delay by first estimating u is the only source of information. In average, the node u
thetimenecessarytocollectenoughpacketsfromeachsource sends ν(u) = bo(u) packets in the inter-arrival time of two
Nc(u)
orNCnodeindependently.Undertheassumptionthateachone consecutivepacketsinitsbuffer,whicharecombinationsofthe
of these multiple collection processes represents a uniform samesetofinputpackets.Outoftheseν(u)packets,kpackets
flow of packets, we can finally approximate the expected can be considered as useful for the client c if the decoding
decoding delay as the time necessary for the collection of a system has a rank deficiency of k < ν(u). Furthermore, due
sufficientnumberofpacketsfrommultipleindependentflows. topacketlossesandbandwidthvariationsinthenetwork,each
The complete algorithm for computing the decoding delays of the packets generated by the node u arrives at the client c
is given in Algorithm 1. Note that the algorithm uses an with probability (cid:15)c(u). The probability Ak(u) that k out of
iterative procedure to compute the decoding delays, since the the ν(u) packets arrive at the client c is
equivalent packet replication rate in SF node (see Section III)
(cid:18) (cid:19)
cannot be exactly computed at first. The algorithm initializes A (u)= ν(u) (1−(cid:15) (u))k(cid:15) (u)ν(u)−k (9)
the replication rate to an average value given by the input and k k c c
output bandwidths of each node, and refines this value along
withthesuccessivedecodingdelayestimations.TheNCnodes Note that in general, ν(u) has not an integer value. We there-
areexaminedintheorderoftheirproximitytothesources,i.e., fore perform an interpolation between the values of Ak(u)
thenodesthatareclosertothesourcesareprocessedfirst.The evaluated on the integer values nearest to ν(u).
numberofusefulpacketsN (u)iscomputedrecursivelyatall We then consider the probability P (u,r,n) for the client
c c
NC nodes, starting from those that are close to the sources. c to collect r useful packets from data sent by a node u that
Then the algorithm considers NC nodes that receive packets possesses n useful packets. This probability can be computed
from NC nodes that have been already visited. This specific recursively as
7
Algorithm 1 Delay computation algorithm
P (u,r,n)=ν(cid:88)(u)P (u,r−k,n−1)·A (u),∀r ∈[1..n−1] 1: Initialize replication rates for every node: Rˆ(u)= bboi((nn)).
c c k 2: repeat
k=0 3: for each client node c do
(10)
Eq. (10) holds for r <n. When r =n, it becomes 4: Compute (cid:15)c(u) for sending nodes u from Eq. (7).
5: Compute Nc(s)=bo(s)·(1−(cid:15)c(s)) for all sources
ν(cid:88)(u) ν(cid:88)(u) s.
P (u,n,n)= P (u,n−k,n−1)· A (u) (11)
c c l 6: for each NC node u do
k=1 l=k 7: Compute tc(u) using Eqs. (10)-(14) setting node
We further denote by Pc(u,r,n) the probability that the u in SF mode.
client c collects k useful packets precisely due to the arrival 8: Compute tc(u)(cid:48) using Eqs. (10)-(14). setting node
of the nth useful packet in the sending node u. It can be u in silent mode.
written as 9: Compute ∆tc(u)=tc(u)−tc(u)(cid:48).
10: Compute ∆Nc(u)=1/∆tc(u).
 
ν(u) ν(u) 11: Compute Nc(u) using Eq. (8).
(cid:88) (cid:88)
Pc(u,r,n)= Pc(u,r−k,n−1)· Al(u), (12) 12: if Nc(u)<bo(u) then
k=1 l=k 13: Computetc(u)usingEqs.(10)-(14)settingnode
u in NC mode.
whereP (u,r−k,n−1)includesallpossibleeventsthatlead
c
14: else
the node u to collect packets with rank r−k when it receives
the n−1 useful packet for client c. 15: Compute the expected decoding delay tc(u)
using Eq. (15).
Thearrivaltimeofthenth usefulpacketatthesendingnode
16: end if
u can be computed from the useful packet rate N (u).We
c
17: end for
assume that N (u) represents a constant rate and that the
c
arrival times of packets in node u are uniformly distributed. 18: Compute the average decoding delay tc considering
all sources and NC nodes simultaneously, with Eq.
Now, one can compute the expected number of useful packets
(16).
E (u) that are necessary at the sending node u for the client
c
19: end for
c to receive G useful packets. It is expressed simply as
20: for each SF node u do
(cid:88)∞ 21: Estimatethetotalnumberofpacketsreceivedbyeach
Ec(u)= p·Pc(u,G,p) (13) node, per generation: |N(u)|=bi(u)·maxtc.
c
p=G 22: Update the replication rate Rˆ(u) with Eq. (6).
The decoding delay for the client c when the NC node u is
23: end for
the only source of information can be estimated by dividing
24: until Until convergence of tc.
the expected number of necessary packets by the inter-arrival
time between two useful packets. It is written as
t (u)=E (u)/N (u) (14) V. SELECTIVEPLACEMENTOFNCNODES
c c c
Then, we consider the sources and the NC nodes that are Equipped with methods to estimate the decoding delay on
over-provisioned in bandwidth (i.e., the set of nodes u where theoverlaynetwork,wecandesignalgorithmstodecidewhich
Nc(u) > bo(u), line 14 in Alg. 1). We assume that they nodes in the network should perform network coding. We
transmit packets that are all potentially useful for the client c. addresstheproblemofplacingAnetworkcodingnodesinthe
Thenumberofusefulpacketsfromnodeuthatreachtheclient overlay network, such that the average delay observed by the
c in this case is given by the rate Nc(u)=bo(u)·(1−(cid:15)c(u)). clients is minimized. This is typically achieved by selecting
When this rate is uniform, the decoding delay when the node network coding nodes such that the packet replication rate
u is the only source of information is given by: is decreased and the innovative flow rate in the network is
increased.
G
tc(u)= b (u)·(1−(cid:15) (u)) (15) However, the optimal selection of the NC nodes is known
o c to be an NP-hard problem [10]. Hence, we design a greedy
Finally, the average decoding delay at client c is computed
approach that iteratively searches for the optimal placement
by considering all the sources and NC nodes as independent
of a new network coding node while all the previously added
sources of information with uniform useful rates 1/t (u). We
c NC nodes are fixed. The candidate nodes for implementing
can write the decoding delay as
network coding are all the remaining SF nodes in the overlay
1 network. Our node selection algorithm examines all the SF
tc = (cid:88) 1 , (16) nodes backwards from the clients to the servers. It selects the
SF node whose transformation into an NC node brings the
t (u)
c
u∈S highestbenefitfortheclients.Thisprocedureisrepeateduntil
where S is the set of sources and NC nodes. all the A NC nodes have been selected.
8
Weproposenowtwovariantsoftheiterativeselectionalgo- Algorithm 3 NC node selection with local information
rithm that both use Algorithm 1 for computing the innovative 1: for i = 1 to A do
flowrate,butdifferintheirviewofthenetworkresources.The 2: for every SF node u do
first algorithm assumes that a central node possesses a global 3: Temporarily transform node u into an NC node.
knowledge of the network; it iteratively selects the network 4: Estimate the average delay tˆc(u) at the clients using
coding nodes in a centralized manner. When global network Algorithm 1 with local information.
knowledge is not a reasonable assumption, the centralized 5: Transform node u back into an SF node.
algorithm still serves as a performance benchmark for other 6: Transmit tˆc(u) to a central agent.
greedy NC node placement algorithms. The second algorithm 7: end for
uses only a local view of the network resources at each node 8: Select the node u∗ that maximizes the innovative rate,
forcomputingthegainsininnovativerateanddecodingdelay. u∗ =argmax (cid:80) tˆ(u)
u c c
This algorithm is probably more realistic in practice and can 9: Turn permanently u∗ into a NC node.
be implemented in a distributed way. 10: end for
In more details, the centralized algorithm uses the knowl-
edgeaboutthefullnetworkandavailableresourcesinorderto
determine the number of innovative packets received by each ofNCnodesistypicallydeterminedbytheadmissibledelayor
client. It leads to the iterative selection of A NC nodes by tolerable complexity in the network. For example, constraints
computing at each stage the benefit of turning any of the SF ondecodingdelayimposealimitonthemaximumnumberof
nodes into an NC node. The candidate node that brings the NCnodesinthesystem.However,theproblemofdetermining
highest innovative flow rate with its transformation is selected the optimal number of NC nodes is out of the scope of this
as a new NC node. The algorithm is described in Algorithm paper. We rather assume that the number of coding nodes or
2. helpersinthestreamingsystemisgivenapriori.Theproposed
algorithmsthensolvetheproblemofplacingefficientlytheNC
Algorithm 2 Centralized NC node selection nodes in the overlay network.
1: for i = 1 to A do Finally, it has to be noted that the second algorithm is not
2: for each node u in the set of SF nodes. do fully distributed, as it still uses a central agent to select the
3: Turn temporarily u into a NC node NC nodes. However, since it uses only local information, the
4: Estimate the average decoding delay at the clients tc proposed solution is certainly amenable to a fully distributed
(using Algorithm 1). algorithm. One could imagine that each node decides inde-
5: Turn u back into a SF node. pendently if it should implement network coding or not, by
6: end for comparingthelocalestimationofthegainininnovativerateto
7: Select the node u∗ that minimizes the decoding delay, a pre-defined threshold. Alternatively, a distributed consensus
i.e., u∗ =argmin (cid:80) t solution could be deployed for a coordinated selection of the
u c c
8: Turn permanently u∗ into a NC node. NC nodes with minimal information exchange between the
9: end for overlay nodes.
VI. SIMULATIONRESULTS
The second algorithm relaxes the assumption that a central
node is aware of the full network status. Instead, the nodes A. Setup
only use local network information for the estimation of the Inthissection,weanalyzetheperformanceoftheproposed
innovative flow rate. We define a neighborhood around each NC node selection algorithms for the transmission of video
node. Then, an algorithm similar to the centralized solution streams in overlay networks. We generate overlay networks
above is applied in each neighborhood in order to determine based on realistic network bandwidth values and adjacency
the benefits of turning SF nodes into NC nodes. In particular, measurementsfromthePlanetLab[11],asprovidedinasnap-
each node uses the estimation of the reception probability shot of their network taken on 24 Nov. 2009 by their Scalable
(cid:15)c(u) that is given by all nodes u in the neighborhood and Sensing Service (S3) [12]. The networks under consideration
computes an estimation of the decoding delay based on local haveonesourcenode,threeclientnodesandavariablenumber
information, i.e., the capacities and the loss rates of the sub- of intermediate nodes. We create network topologies in the
network around the node u. Note that (cid:15)c(u) is also calculated followingway.First,thesourcenodesarepositioned,thenthe
consideringonlythestatisticsofnode’suneighborhood.These nodes are randomly added one-by-one to the topology. For
estimations are transmitted periodically to a central agent, every new node, four nodes are randomly chosen as parent
which finally makes the decision on the placement of new nodes. However, if the new node is not directly connected
NC nodes. The procedure is summarized in Algorithm 3. to any of the selected parents according to the Planet Lab
Both algorithms permit to select a few network coding measurement data, the node is removed and a new node is
nodes in the system, such that the coding delay and overall selected. After all nodes have been added to the network, the
computational complexity in the network is limited. At the nodes thatcannot bereached bythe sourceand the nodesthat
same time, the system maintains a high innovative rate for are not connected with any client are removed. The resulting
sustained streaming performance. The choice of the number networkgraphsaredirectedacyclicbyconstruction.Theedge
9
capacityofeachlinkissetto1/200ofthePlanetLabcapacity the performance of Algorithm 3 for different sizes of the
values, in order to get realistic values for the link bandwidth. neighborhoodinthelocalgainestimations.Weobserveasharp
Finally, the packet loss rate of each link is set to 5%. reduction of the delivery times with the addition of the first
The network coding operations are performed in a Galois few NC nodes for all the algorithms, but especially for the
field of size GF(28) since this field size has been shown to proposed algorithms. The gains become less important after
result in a good compromise between performance (packets a few NC nodes have been placed in the network. We can
are innovative with high probability) and information over- thus see that the NC nodes are well positioned in order to
head [4]. The generation size is set to 32 packets, which is improve the delivery performance. The results also highlight
reasonable for real time video streaming applications. The the inefficiency of the RANDSEL algorithm, which becomes
packet size is 512 bytes. The decoding is performed by competitive with the other methods only for large number of
gaussian elimination. Since we are interested in analyzing NC nodes. Finally, we can see that the Algorithm 2 performs
the performance in terms of decoding delay, we compute the similartotheALGO2R.Thisconfirmsthattheproposeddelay
average delay as the time needed by each client to receive 32 estimation strategy in ALGO2 is accurate as it comes close to
linearlyindependentpackets(i.e.,acompletegeneration).This the actual delay values measured by the network simulator.
istheminimalnumberofpacketsfortheclientstodecodethe
source information. We use a set of 10 random networks that C. Innovative rate
consist of 32 to 56 nodes with two different radii of 6 and 8
Wefurtherlookattheaveragenormalizedeffectivethrough-
hops(i.e.,themaximumdistancebetweenanypairofnodesin
putinthenetwork(i.e.,thenumberofusefulpacketsreceived
the network is 6 or 8 hops). We consider the placement of up
by the clients), as a function of the number of NC nodes
to10NCnodesineachnetwork.Ineachcase,theperformance
in the network. Normalization is performed with respect to
resultsareaveragedover100simulationsperformedusingthe
the effective throughput achieved by the scheme where all
NS-3 [13] network simulator.
nodes perform network coding. Figs. 6 (a) and (b) show
We evaluate the performance of the centralized and semi-
the effective throughputs for two different network radii. The
distributed algorithms (resp. the Algorithm 2 and Algorithm
results confirm the earlier observations on the decoding delay
3) denoted as “ALGO2” and “ALGO3” respectively). We
performance. A few well selected nodes are able to bring
compare them with a greedy search algorithm (ALGO2R)
a large throughput gain. Further performance improvements
similartoAlgorithm2butthatusestheactualdelaysobtained
become less important as the number of NC nodes increase.
by NS-3 simulations instead of the delay estimates from
Weseealsothatthealgorithmsproposedinthispaperprovide
Algorithm 1 for the node selection. We also compare to a
the best performance among the schemes under comparison.
baseline scheme called in the following as “RANDSEL” that
The node selection algorithm with local information improves
randomlyplacestheNCnodesinthenetwork.Forthesakeof
with the size of the neighborhood but generally stays close to
completeness, we finally study the performance of a scheme
thecentralizedalgorithmwhentheneighborhoodissufficiently
whereallnodesareNCnodes(thisschemeiscalled“Allnodes
large. In the case where the neighborhood is limited to one
NC”), a Linear NC scheme [4] and a scheme with only SF
node, the proposed algorithm still outperforms RANDSEL
nodes. The performance of the later is equal to the theoretical
since the decisions are not totally blind. The reason for the
maximum that can be sustained when only routing is enabled
inferiorperformanceofthesemi-distributedschemecompared
and can be found by typical maximum flow algorithms).
tothecentralizedonesimplycomesfromthefactthatthelocal
Note that the minimum delay and maximum effective
network statistics are not sufficient for accurately estimating
throughput obtained with Linear NC are computed by consid-
thedelaywhentheneighborhoodissmall.Inaddition,wecan
ering that a high capacity hyper-source node connected with
observethatafewNCnodesaresufficientforobtaininghigher
all sources. In this case, the overall throughput is computed
throughputsthantheoneinroutingalgorithmswherethenodes
as the sum of the throughputs from the hyper-source to each
simply forward packets randomly to their descendants. It con-
clientnode.Fortheroutingcase,weconsideraswellahyper-
firmsthefactthatourmethodsareappropriatefordeployment
sink node linked with all client nodes, and we compute the
in low-cost networks, where a few helpers or network coding
maximum throughput between the hyper-source and hyper-
nodesaresufficientforimprovedthroughputandefficientdata
sink with standard graph maximum flow algorithms. We
delivery. Finally, we can observe that our algorithms tend to
should point out that the links connecting the hyper nodes
performbetterinlargernetworks(i.e.,largerradiusvalues),as
with the networks sources and clients are error free and have
theyareabletoexploitmoreefficientlytheavailableresources
infinite capacities, so they do not introduce extra delays.
and the diversity in the overlay network.
B. Decoding delay D. Video quality
Wefirststudythedecodingdelayforeachofthealgorithms. Finally, we study the performance of the video delivery
Figs. 5 (a) and (b) illustrate the normalized average decoding schemes from the viewpoint of video quality. We estimate the
delays for the network clients as a function of the number average PSNR quality measured at the clients with respect to
of NC nodes added in the network, for two different network thenumberofNCnodesinthenetworkforallmethodsunder
sizes. The decoding delays are normalized to the performance comparison in the transmission of the Foreman CIF sequence
obtained when all nodes perform network coding. We show encoded by the the JM12.2 [14] of the H.264/AVC standard
10
1.8 2.5
RANDSEL RANDSEL
ALGO3 (range=1) ALGO3 (range=1)
1.7 ALGO3 (range=2) ALGO3 (range=2)
ALGO3 (range=3) ALGO3 (range=3)
malized average delivery delay1111....3456 AAALLll GGnoOOd22eRs NC malized average delivery delay 1.25 AAALLll GGnoOOd22eRs NC
Nor1.2 Nor
1.1
1 1
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
Number of NC nodes Number of NC nodes in the network
(a) (b)
Fig. 5: Normalized average decoding delays versus the number of NC nodes, in networks with maximum distance between
any pair of nodes equal to: (a) six and (b) eight.
1 1
0.95
0.9
0.9
w
Normalized average total flo00..0078..5578 RRAALLoAGGuNtOODin33Sg E((rrLaannggee==21)) Normalized total flow000...678 RRAALLoAGGuNtOODin33Sg E((rrLaannggee==21))
ALGO3 (range=3) 0.5 ALGO3 (range=3)
0.65 ALGO2 ALGO2
ALGO2R ALGO2R
All nodes NC All nodes NC
0.4
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
Number of NC nodes Number of NC nodes
(a) (b)
Fig. 6: Normalized achievable throughput versus the number of NC nodes, in networks with maximum distance between any
pair of nodes equal to: (a) six and (b) eight.
[15]. The quality is estimated by setting the encoding rate to VII. RELATEDWORK
the value of the network throughput in the different schemes.
The corresponding results are illustrated in Figs. 7 (a) and (b) The problem of finding a minimal set of network coding
fornetworkswitharadiusofsixandeighthops,respectively.It pointsinanetworkhasbeenmostlystudiedfromatheoretical
isinterestingthattheimprovedthroughputvaluestranslateinto perspective so far. First, the special case of two source
higher PSNR quality which confirms the above observations messages is examined in [16] where it is proved that the
about the benefits of proper NC node selection. We can have number of coding nodes is independent of the total number
gainsthatexceed1.5dBwithonlytwoNCnodes,whereaswe of network nodes. In [17], the minimum number of network
reachgainsof3dBforsevenNCnodes.ThePSNRgainssatu- coding nodes is computed through graph coloring techniques.
rateasthenumberofNCnodesincreases,butqualitygainscan It is then shown in [18] that the number of coding nodes is
still be noticed. As expected, larger gains are observed for the upper bounded by the number of receivers. A unification of
centralizedalgorithm,however,thesemi-distributedalgorithm networkcodingandtreepackingtheoremsisfurtherpresented
offers significant gains as well. For a neighborhood of three in [19], where network coding is restricted to pre-selected
hops, the performance of the semi-distributed even becomes edges. These include only input edges of relay nodes and not
identical to that of the centralized scheme. Finally, we see theinputedgesofclientswheresimpleroutingisapplied.This
that RANDSEL gives small PSNR gains for a few NC nodes, choice is made in order to achieve the min-cut max-flow limit
which confirms the poor performance of a random selection of the network and save both processing and implementation
of the network coding nodes and supports the development of complexity. The relation between links capacities and the
effective selection algorithms. number of coding nodes is investigated in [20], where it is
shown that in directed acyclic networks arbitrary amounts of
gaincanbenoticedwhensubsetsofnodesofarbitrarysizeare