Content uploaded by Pouya Ostovari
Author content
All content in this area was uploaded by Pouya Ostovari on Jan 18, 2015
Content may be subject to copyright.
Cache Content Placement Using Triangular
Network Coding
Pouya Ostovari∗, Abdallah Khreishah†, and Jie Wu∗
∗Department of Computer & Information Sciences, Temple University, Philadelphia, PA 19122
†Department of Electrical & Computer Engineering, New Jersey Institute of Technology, Newark, NJ 07102
Abstract—Video is one of the main causes of the dramatic
increase in data traffic over cellular networks. Caching is an
effective mechanism that decreases the download rate from base
stations and, as a result, the load on the base station, by storing
the most popular files or videos on the caches and providing
them to the users. The problem of efficient content placement
on the caches is known as an NP-complete problem. In this
paper, we study the role of network coding by increasing the
amount of available data to the users through the cache nodes.
We propose a network coding-based content placement method,
and we compare it to the best uncoded content placement and
the best triangular network coding strategies. Our method not
only increases the amount of available data to the users, but also
results in a fair distribution of data.
Index Terms—Linear network coding, triangular network
coding, caching, content placement, wireless networks.
I. INT ROD UC TI ON
Video is one of the main causes of the dramatic increase in
data traffic over cellular networks. This growth of data traffic
between the base station, e.g. 4G, and the users will lead to
a slowdown of the cellular systems. Live streaming uses a
relatively tiny fraction of the overall video traffic. In contrast,
most video traffic is generated by encoded and pre-stored
videos on large video on-demand servers, such as YouTube
and Netflix, and a large portion of the video on-demand traffic
corresponds to a few popular files [1]. For example, 20-30%
[2], [3] of the web traffic on the Internet is for YouTube and
Netflix.
Based on this observation, the concept of caching helpers
has been introduced [1], [4]–[8]. The authors in [1] propose
a system architecture to achieve a high throughput. The main
idea is that caching can decrease the required amount of
communication between the base station and the users if there
is enough content reuse going on and if many users are
requesting the same few files. Therefore, the files are always
available locally to the users who are requesting them.
The cache nodes (helpers) are assumed to have a large
storage capacity and high-bandwidth wireless communication
capabilities. They can cache popular files and serve users’
requests. The caches work in conjunction with the base station,
which provides the users with files that cannot be obtained
from the caches (Figure 2). It is obvious that the base station
will be able to serve more users if we can decrease the load
on the base station. For this purpose, it it critical to use a
mechanism to increase the number of available files through
the cache nodes to the users.
ܿ
ͳ
ܿ
ʹ
ܿ
Ͷ
ݑ
ͳ
ܿ
͵
ݑ
͵
Caches
Users
Server
ݑ
ʹ
Fig. 1. Setting: there are musers and ncaches in the network.
The main challenge in the wireless distributed caching
problem is determining which files should be stored on each
cache. In the case where each user only has access to one
cache, the most popular file should be stored on each cache.
However, when each user has access to multiple caches, the
placement of files on the caches becomes nontrivial. The
authors in [1] show that this problem is NP-complete.
Network coding [9]–[15] can be used to increase the ef-
ficiency of the content placement on cache nodes. Linear
network coding is introduced in [10], and it is shown in [16]
that linear network coding achieves the capacity for the single
multicast session problem. In this case, each node generates
and sends linear combinations of the received packets over
a finite field. A received packet is called innovative if its
coefficient vector increases the rank of the matrix formed
by the received coefficient vectors. When a node receives
an innovative packet, the node stores this packet and the
corresponding coefficients vector in its packet buffer and
coefficients buffer, respectively. Each relay node continues this
process. Assume that koriginal packets are linearly coded
together. After receiving klinearly independent coded packets,
the destination node will be able to decode the coded packets
and retrieve all of the original packets. The decoding process
is done by using Gaussian Elimination to solve a system of
linear equations. In [17], it is shown that randomly selecting
the coefficients of the coded packets achieves the capacity
asymptotically with respect to the finite field size.
Consider Figure 2 (a), in which there are three users u1,u2,
and u3. Each user is connected to two caches, and each cache
is adjacent to two users. Assume that we want to provide the
users with access to two files, p1and p2. Also, assume that
ܿ
ͳ
ݑ
ͳ
ݑ
ʹ
ܿ
͵
ߙͳͳߚͳʹ
ߙʹͳߚʹʹ
ߙ͵ͳߚ͵ʹ
ܿ
ʹ
ܿ
ͳ
ݑ
ͳ
ݑ
ʹ
ܿ
͵
ݑ
͵
ͳ
ܿ
ʹ
ݑ
ܿ
Cache
User
(a) (b)
ʹ
ͳ
ݑ
͵
Fig. 2. Motivation: the benefit of using linear network coding for content
placement.
the size of the caches and the files are the same. Without using
network coding, the efficient way to place the files is to place
one of them on two caches and place the other one on the last
cache, as shown in Figure 2 (a). In this case, users u1and u3
have access to both of the files, but user u2has access to just
file p1. In Figure 2 (b), three random linear combinations of
the files are stored on the caches. Here, αand βare random
coefficients. In this case, each user has access to two random
linearly coded files, so they are able to decode the coded files
and retrieve both p1and p2.
In [4], [18], the authors assume that the request of each
user is known, and they propose a joint bandwidth allocation
and content placement approach. In this paper, we consider a
different problem. We address the problem of layered video
placement on caches using network coding. In this problem,
the video layers have priority, and the i-th video layer will not
be useful unless all of the layers that have a higher priority
(smaller indices) are available to the user. We propose a con-
tent placement approach that achieves fairness in providing the
layers to the users, while increasing the number of available
video layers to the users.
The remainder of the paper is organized as follows. In
Section II, we introduce the setting and problem definition. We
propose our solution to the problem in Section III. Simulation
results will be presented in Section IV. Section V concludes
the paper.
II. SE TT IN G
We consider a single cell, equipped with a base station (such
as 4G), which serves musers, u1, .., umwith the help of n
independent caches, c1, .., cn. The cache nodes are placed in
fixed positions in the cell, and each cache node can cover a
subset of the users based on their locations. There are hvideo
layers, p1, .., phon a base station where h < n. The capacity
of the caches is equal to the size of the video layers, and
if a layer is not available on any adjacent caches to a user,
the user will contact the central server to download the layer.
However, the cost of downloading from the server is more
than downloading from the cache nodes.
The key point is that, if there is enough content reuse, such
that many users are requesting the same video layers, caching
can replace the communication between the users and the base
station. We assume that in order to use the layer pi, all of the
layers pj∀j, 0≤j≤ishould be available to the user. We
TABLE I
THE S ET OF S YM BOL S USE D IN T HIS PA PER .
Notation Definition
mThe number of users
nThe number of caches
hThe number of video layers
uiThe i-th user
cjThe j-th cache
pkThe k-th layer
diThe degree of the ith user
fiThe number of filled out adjacent caches to the ith user
riThe rank of the coded video layers on the filled out
adjacent caches to the ith user
siThe number of triangular codes of degree ithat are
available to a user
fThe fairness
f′The unfairness
vThe average number of available video layers to the users
qiThe number of available video layers to the ith user
represent the availability of the video layers to the users with
matrix Z=zij . If the layers p1to piare available to user uj,
then zij = 1; otherwise, zij = 0. The set of symbols used in
this paper is summarized in Table I. Our goal is to minimize
the number of contacts to the central server for layers retrieval.
In other words, we want to maximize the total number of video
layers that are available to the users. Therefore, our objective
becomes:
max
h
i=1
n
j=1
zij (1)
The solution is straightforward when the cache nodes are not
dense and each user is connected to a single cache. In this case,
each cache should store the first video layer (with the smallest
index), since other layers are not useful without accessing to
this layer. However, if the cache nodes deployment is dense
enough, each user will have more than one cache node that is
a part of a distributed caching system. In this case, the content
placement problem becomes more complicated because of the
correlation among the cache nodes. It is shown in [1] that the
uncoded distributed caching problem is NP-complete.
III. CON TE NT PL ACE ME NT AP PROACH US IN G NET WO RK
COD IN G
In the problem of content placement using network coding,
each video layer can be coded with any other layers. Therefore,
there are 2h−1possibilities for coding the video layers, where
his the number of layers on the server (the empty set should
not be considered). On the other hand, we have ncaches in
the network; in total, there are (2h−1)ndifferent possible
placements. To calculate the number of video layers that are
available to the users in each placement, we need to calculate
the layers that can be retrieved by each user. Note that we
cannot use the Gaussian Elimination directly on the coded
video layers that are available to a user nor compute the rank
of the available layers. This is because by using Gaussian
Elimination, or the overall rank of the coded video layers, we
can just find out if all of the original layers are decodable or
(a) (b)
ͳ
͵
ʹ
(c)
ͳ
ͳ
ʹ
ͳʹ͵
ͳ
͵
ͳʹ
ͳʹ͵
ͳ
͵
ʹ
, ,
, ,
ʹ
͵
Fig. 3. (a) Original video layers. (b) General form of random linear network
coding. (c) Triangular network coding.
not. Therefore, we need to calculate the rank of each subset
of the coded packets that are available to a user or use the
Gaussian Elimination to decode the coded video layers. As a
result, the total complexity becomes (2h−1)nmm
i=1(2di−
1).
One approach to decrease the complexity of the problem
is to use triangular network coding [19], which is a kind of
random linear network coding. In triangular network coding,
the encoded video layers are in the form of k
j=1 αjpj,
where 1≤k≤hand αjare random coefficients. In other
words, each coded layer is a random linear combination of the
first koriginal layers. Therefore, there are just npossibilities
for coding noriginal layers. Figures 3 (b) and (c) show
the possible coded layers of the original layers in Figure 3
(a) using the general form of network coding and triangular
coding, respectively. As shown in Figures 3 (b), there are
7 = 23−1choices for coding 3 original packets in the case
of the general form of random linear network coding, but just
3 possibilities for the case of triangular network coding. The
coefficients are not shown in the figures for simplicity. For
example, p1+p2means α1p1+α2p2, where α1and α2are
two random coefficients.
We prefer using triangular network coding over the general
form of network coding for three reasons. First, it limits the
coding space of the coding problem. Second, based on our
setting, the i-th video layer is not useful without accessing
to the layers with a smaller index. This assumption has the
same nature as the coding rule in triangular network coding.
Third, in addition to the lesser complexity of triangular coding,
compared with linear coding, we do not need to use Gaussian
Elimination to check the number of decodable video layers at
each user. This checking can be done by a simple algorithm
in order of O(h2)[20]. Assume that skrepresents the number
of coded packets in the form of k
j=1 αjpjthat are available
to a user. In this scheme, the user can decode the first ilayers
if i
j=i−ksj≥k+ 1,∀k∈[0, i −1]. The condition implies
that the rank of the coefficients matrix of the available encoded
video layers from coding any of the first ilayers is at least
i. Therefore, Gaussian Elimination will be able to decode the
first ilayers. For example, assume that three packets, α1p1,
α2p1+α3p2, and α4p1+α5p2+α6p3, are available to a user.
In this example, s3≥1,s2+s3≥2, and s1+s2+s3≥3,
so all three layers can be decoded by the user.
Lemma 1: the complexity of the content placement using
triangular network coding is hn+2m.
Algorithm 1 Checking the number of decodable packets in
triangular coding
for i=1 to m do
decodability=True
for k=0 to i-1 do
if i
j=i−ksj≤k+ 1 then
decodability=False
if decodability=True then
number of decodable layers=i
ܿ
ͳ
ݑ
ͳ
ܿ
͵
ͳ
ͳʹ
ͳʹ͵
ܿ
Ͷ
ܿ
ܿ
ʹ
ܿ
ͷ
ݑ
ͳ
ݑ
Ͷ
ݑ
͵
ݑ
ݑ
ݑ
ͷ
ͳ
ͳʹ
ͳʹ͵
(a)
ܿ
ͳ
ݑ
ͳ
ܿ
͵
ͳ
ͳʹ
ͳ͵
ܿ
Ͷ
ܿ
ܿ
ʹ
ܿ
ͷ
ݑ
ͳ
ݑ
Ͷ
ݑ
͵
ݑ
ݑ
ݑ
ͷ
ͳ
ͳʹ
͵
(b)
Fig. 4. A comparison of triangular network coding and random linear coding.
Coefficients are not shown for simplicity.
Proof: In this case, there are just hdifferent coding
possibilities since 1≤k≤h. Therefore, the total number
of different placements will be hn. As mentioned before, the
number of decodable original video layers at each user can be
calculated in order on O(h2). Therefore, the total complexity
of checking all possible triangular coding placements becomes
hn+2m.
Although the complexity of triangular network coding is
much less than random linear coding, it might not achieve
efficiency compared to linear coding. Consider Figures 4 (a)
and (b), where the optimal placement using triangular and
random linear coding are shown in Figures 4 (a) and (b),
respectively. In these figures, coefficients are not shown for
simplicity. For example, p1+p2means α1p1+α2p2, where
α1and α2are random coefficients. In the case of triangular
network coding, user u4will not be able to decode any packet.
However, when we use random linear coding, this user can
decode video layers p1and p3. Note that, based on our setting,
the layer p3is not useful for user u4since the user does not
have access to the layer p2.
A. Network Coding-based Content Placement Heuristic
Although the complexity of finding the optimal placement
using a triangular network coding is much less than random
linear network coding, it is still high. For this reason, we
propose a network coding-based content placement heuristic
(NCCP) in this section. Based on the proposed setting, we
know that the video layer piis not useful to a user unless the
layers pj∀j, 0< j < i −1are available to the user. Based on
this observation, we give more priority to the first layer, and
we try to provide it to all of the users. Then, if it is possible,
we provide the second layer to the users. In more detail, we try
to provide the second video layer to as many users as possible.
This process is repeated until we cannot provide the content
pito any user for a given 1< i ≤h. This method can also
provide a fair solution to the content placement problem. This
is because the algorithm tries to provide each layer that has a
greater priority (smaller index) to as many users as possible,
and then the algorithm will start to provide the next layer,
which is less popular to the users. We can observe that this
solution has a greedy nature, and thus we can use a greedy
algorithm to implement this solution.
In each step, our greedy algorithm selects one of the users
and fills up its adjacent cache with random linearly coded
video layers. Because of the greedy nature of our algorithm,
the generated coded layer will always be a triangular code.
The user selection rules are as follows:
•Rule 1: the user with the minimum degree is selected.
The degree of user ui, represented as di, is defined as
the number of its adjacent caches.
•Rule 2: in the case where two users have the same degree,
the user with a larger number of filled-up cache nodes is
selected.
•Rule 3: if two users have the same degree and the same
number of filled caches, the user whose adjacent caches
have less cumulative ranks is selected.
We give more priority to Rule 1 compared to Rule 2 and
Rule 3. Also, the priority of Rule 2 is more that that of the Rule
3. The reason for selecting user uiwith the minimum degree is
that there are less content placement choices for adjacent cache
nodes to that user. If we do not start with such a user ui, it is
possible for us to fill the adjacent cache nodes to user uiwith
an undecodable packet. For example, in Figure 5, user u1has
just one adjacent cache. Consequently, we can just provide
video layer p1to this user. By selecting user u1and filing
its adjacent cache c1, we can reduce the number of choices
for cache c2, which is adjacent to user u2. Then, user u3is
selected, and its adjacent cache will be filled with p1. In this
example, if we start from user u2and fill its adjacent cache
nodes with random linear combinations of p1and p2, users u1
and u3will not be able to decode the coded video layers on
cache nodes c1and c3, respectively. Note that network coding
does not have any benefit in this example, and we use this
simple example just to describe our user selection policy.
After selecting the appropriate user based on Rules 1, 2,
and 3, the user’s neighboring cache nodes should be filled up.
Let dibe the degree of user ui. We represent the number of
user ui’s filled-up adjacent cache nodes and their cumulative
rank as viand ri, respectively. Assume that, in the current
ܿ
ͳ
ܿ
ʹ
ݑ
ͳ
ݑ
ʹ
ܿ
͵
ݑ
͵
Fig. 5. User selection rules.
Algorithm 2 Content placement
while There is an empty cache do
Select an unprocessed node uibased on Rules 1, 2, and
3
g=di−vi+ri
for each empty adjacent cache ckto user uido
Fill up cache ckwith g
j=1 αjpj
Tag node uias a processed node
iteration, user uihas been selected based on the rules. The
degree of this user is di, so this user cannot receive more
than the first divideo layers. On the other hand, viof the
caches are already filled, and their communicative rank is ri.
As a result, the maximum number of decodable layers to user
uiis di−vi+ri. Therefore, the algorithm fills up all of the
empty adjacent cache nodes to user uiwith a random linear
combination of the di−vi+rifirst video layers. Then, the
algorithm selects another unprocessed user by utilizing the
user selection rules, and the algorithm uses the same policy
to fill the cache nodes that are adjacent to the new user. The
proposed greedy algorithm is described in Algorithm 2.
Assume that user uiis selected, and all of the diadjacent
caches are empty. The algorithm fills up all of them with
di
j=1 αjpj. In this case, the user will have access to di
linearly independent coded video layers. Thus, the user will
be able to decode all of the encoded layers. Now, assume that
the degree of user ujis 3, and two of the adjacent caches are
filed with α1p1and α2p1. In this case, the rank of the filled
caches is 1. Therefore, it is not possible to provide 3 layers to
the user, and if we fill up the remaining unfilled cache with
a linear combination of p1,p2, and p3, the user will not be
able to decode the coded packets. As a result, based on our
algorithm, we code the first g= 3 −2 + 1 layers together, and
assign α3p1+α4p2to the remaining cache.
Consider Figure 6, in which user u1has a minimum degree
of 2. As a result, in the first step, the content placement algo-
rithm selects user u1and places a random linear combination
of the first two layers on the cache nodes adjacent to the user
(caches c1and c2). After the first step, the user nodes u2,u3,
and u4have a degree equal to three. However, user u2has
two adjacent cache nodes that are filled. Consequesntly, in the
second round, the algorithm selects user u2and fills up the
remaining cache that is adjacent to the user, which is cache
c3. In this case, d2= 3,f2= 2, and r2= 2. Therefore,
ܿ
ͳ
ܿ
ʹ
ܿ
Ͷ
ݑ
ͳ
ݑ
ʹ
ݑ
Ͷ
ܿ
͵
ݑ
͵
ͳʹ
ͳʹ͵
ͳʹ
ͳʹ͵
Fig. 6. Content placement algorithm description. Coefficients are not shown
for simplicity.
we fill cache c3with a random linear combination of the
3−2 + 2 = 3 first packets. In the last round, the degree, the
number of filled-up caches that are adjacent to users u3and
u4, and their ranks are equal; thus, we select one of the users
randomly. Assume that we choose user u3. The algorithm fills
cache c4with a random coded layer of the first three layers.
Note that, in Figure 6, we do not show the coefficients of the
coded packets for simplicity.
IV. SIMULATION
In this section, we evaluate and compare the proposed
network coding-based cache placement method (NCCP) with
the best uncoded and triangular network coding placement
strategies. For this purpose, we implemented a simulator in
the MATLAB environment. In order to find the best uncoded
placement, we try all of the possible original video placements
on the caches, and we find the placement that provides the
largest amount of available video layers to the users. We
perform the same approach to find the best placement using
the triangular network coding.
A. Setting
We perform our simulations on random topologies with
different numbers of users and caches. For each setting, we
run the simulation for 1000 randomly generated topologies
(random adjacency of the users with the cache nodes). The
plots in this paper are based on the average outputs of the
simulation runs. The following metrics are compared in the
simulations:
1) Amount of available video layers to the users: the total
number of available layers to the users through the cache
nodes. Note that, based on the proposed setting, a layer
will not be useful to a user unless all of the layers with
a smaller index are provided to the user first.
2) Average utility: the utility of each user is defined as the
number of available layers to that user through its neigh-
boring caches (the cumulative rank of the neighboring
cache nodes) divided by the degree of the user.
3) Fairness: we define unfairness as the average difference
between the number of available layers to each user and
the average number of available layers to the users. We
represent the number of layers available to the i-th user,
unfairness, and fairness as qi,f′, and f, respectively.
Based on the definition, we have f′=∑m
i=1 |qi−e|
m,
8 12 16 20
20
30
40
50
60
70
Number of users
Number of available files
Optimal triangular coding
NCCP
No coding
(a)
8 12 16 20
20
30
40
50
60
70
Number of users
Number of available files
Optimal triangular coding
NCCP
No coding
(b)
Fig. 7. Total number of video layers that are available to the users. (a) n=5,
h=4. (b) n=7, h=4.
8 12 16 20
75
80
85
90
95
100
Number of users
Utility %
Optimal triangular coding
NCCP
No coding
(a)
8 12 16 20
75
80
85
90
95
100
Number of users
Utility
Optimal triangular coding
NCCP
No coding
(b)
Fig. 8. Utility of the content placement methods (the number of video layers
that are available to a user divided by its degree). (a) n=5, h=4. (b) n=7, h=4.
where e=∑m
i=1 qi
mis the average number of layers that
are available to the users. Fairness is defined as f=1
f′.
B. Results
In the first experiment, we evaluate the total number of
video layers that are available to the users. In Figure 7 (a), the
number of cache nodes and layers are 5 and 4, respectively.
This figure shows that the optimal triangular network coding
can provide the largest number of layers to the users, which is
about 14% more than that of the best no-coding placement
strategy. Also, the NCCP approach can provide the users
with about 9% more video layers than the best no-coding
placement strategy. This difference might not be huge, but it
should be noted that finding the best no-coding placement is
NP-complete, and the complexity of finding such an optimal
non-coding placement is O(knn
i=1 di). As we increase the
number of users, the effect of network coding increases, which
leads to a larger difference between the coding approaches and
the no-coding method.
In Figure 7 (b), we change the number of cache nodes to 7,
and we repeat the previous experiment. In this figure, the total
number of available packets in the optimal triangular network
coding method is about 17% more than that of the best no-
coding placement. Also, the gain of the NCCP approach is up
to 12% more than the no-coding method. The figure shows that
8 12 16 20
5
6
7
8
9
10
11
12
Number of users
Fairness
Optimal triangular coding
NCCP
No coding
(a)
8 12 16 20
4
6
8
10
12
14
16
18
Number of users
Fairness
Optimal triangular coding
NCCP
No coding
(b)
Fig. 9. Fairness is equal to one divided by unfairness. Unfairness is defined
as the average difference between the number of video layers that are available
to each user and the average number of available video layers to the users).
(a) n=5, h=4. (b) n=7, h=4.
the efficiency of the network coding increases as we increase
the number of users.
Figures 8 (a) and (b) show the comparison between the
average utility of the three approaches. We define the utility
of a user as the fraction of the number of video layers that
are available to that user and the degree of the user. The idea
behind dividing by the user’s degree is that, in the best case,
the number of layers available to a user can be equal to its
degree. It can be inferred from Figure 8 (a) that the utility
of both the optimal triangular network coding and the NCCP
methods are about 13% and 10% more than the best no-coding
method, respectively. We change the number of caches to 7 in
Figure 8 (b). By comparing Figures 8 (a) and (b), we can find
that the utility in all of the methods increases as we increase
the number of caches. However, increasing the number of
caches has more of an effect on the NCCP method compared
to that of the other approaches.
In the last experiment, we evaluate and compare the fairness
of the methods. We define the unfairness (one divided by
fairness) as the average difference between the number of
layers that are available to each user and the average number
layers that are available to the users. Figure 9 (a) shows that
the fairness of the optimal triangular network coding and the
NCCP approaches are up to 90% and 75% more than that
of the best no-coding content placement strategy, respectively.
We increase the number of cache nodes in Figure 8 (b) from
5 to 7 and evaluate the fairness of the approaches. In this
setting, the fairness of the best no-coding approach is more
than 56% and 50% less than that of the the best triangular
network coding and the NCCP approaches, respectively.
V. CONCLUSION
In this paper, we study the effects of network coding on
increasing the amount of available data to the users through the
cache nodes in cellular networks. Providing a larger portion of
the data through the caches decreases the pressure on the base
station (such as 4G) and enables the base station to serve more
users. We propose a network coding-based content placement
method, and we compare it with the best uncoded content
placement strategy and the best triangular network coding
strategy. Our method not only increases the amount of video
layers that are available to the users, but it also results in a
fair distribution of the data.
ACK NOWLEDGMENT
This research was supported in part by NSF grants ECCS
1231461, ECCS 1128209, CNS 1138963, CNS 1065444, and
CCF 1028167.
REF ER EN CE S
[1] N. Golrezaei, K. Shanmugam, A. Dimakis, A. Molisch, and G. Caire,
“Femtocaching: Wireless video content delivery through distributed
caching helpers,” Arxiv preprint arXiv:1109.4179, 2011.
[2] A. Finamore, M. Mellia, M. Munaf`
o, R. Torres, and S. Rao, “Youtube
everywhere: impact of device and infrastructure synergies on user
experience,” in ACM SIGCOMM Conference on Internet Measurement,
2011, pp. 345–360.
[3] C. Labovitz, S. Iekel-Johnson, D. McPherson, J. Oberheide, and F. Ja-
hanian, “Internet inter-domain traffic,” in ACM SIGCOMM, 2010, pp.
75–86.
[4] H. Hao, M. Chen, A. Parekh, and K. Ramchandran, “A distributed
multichannel demand-adaptive P2P VoD system with optimized caching
and neighbor-selection,” in SPIE, 2011.
[5] J. Wang, C. Yeo, V. Prabhakaran, and K. Ramchandran, “On the role
of helpers in peer-to-peer file download systems: Design, analysis and
simulation,” in IPTPS, 2007.
[6] J. Wang and K. Ramchandran, “Enhancing peer-to-peer live multicast
quality using helpers,” in IEEE ICIP, 2008, pp. 2300–2303.
[7] H. Zhang, J. Wang, M. Chen, and K. Ramchandran, “Scaling peer-to-
peer video-on-demand systems using helpers,” in IEEE ICIP, 2009, pp.
3053–3056.
[8] Y. He and L. Guan, “Improving the streaming capacity in p2p vod
systems with helpers,” in IEEE ICME, 2009, pp. 790–793.
[9] S. Katti, H. Rahul, W. Hu, D. Katabi, M. M´
edard, and J. Crowcroft,
“Xors in the air: practical wireless network coding,” in ACM SIGCOMM,
2006.
[10] R. Ahlswede, N. Cai, S. Li, and R. Yeung, “Network information flow,”
IEEE Transactions on Information Theory, vol. 46, no. 4, pp. 1204–
1216, 2000.
[11] R. Koetter and M. Medard, “An algebraic approach to network coding,”
IEEE/ACM Transactions on Networking, vol. 11, no. 5, pp. 782– 795,
Oct 2003.
[12] P. Ostovari, J. Wu, and A. Khreishah, “Deadline-aware broadcasting in
wireless networks with local network coding,” in IEEE ICNC, Jan 2012.
[13] P. Ostovari, A. Khreishahand, and J. Wu, “Deadline-aware broadcasting
in wireless networks with network coding,” in IEEE GLOBECOM, Dec
2012.
[14] A. Khreishah, I. Khalil, P. Ostovari, and J. Wu, “Flow-based xor network
coding for lossy wireless networks,” IEEE Transactions on Wireless
Communications, vol. 11, no. 6, pp. 2321–2329, 2012.
[15] A. Khreishah, C. Wang, and N. Shroff, “Rate control with pairwise
intersession network coding,” IEEE/ACM Transactions on Networking,
vol. 18, no. 3, pp. 816–829, 2010.
[16] S. Li, R. Yeung, and N. Cai, “Linear network coding,” IEEE Transac-
tions on Information Theory, vol. 49, no. 2, pp. 371–381, 2003.
[17] T. Ho, M. M´
edard, R. Koetter, D. Karger, M. Effros, J. Shi, and
B. Leong, “A random linear network coding approach to multicast,”
IEEE Transactions on Information Theory, vol. 52, no. 10, pp. 4413–
4430, 2006.
[18] S. Pawar, S. Rouayheb, H. Zhang, K. Lee, and K. Ramchandran, “Codes
for a distributed caching based video-on-demand system,” in Asilomar
Conference on Signals, Systems, and Computers, 2011.
[19] D. Wang, J. Liu, Q. Zhang, and F. Chen, “Cooperative coding and
caching for streaming data in multihop wireless networks,” EURASIP
Journal on Wireless Communications and Networking, vol. 2010, no. 10,
pp. 2:1–2:13, 2010.
[20] D. Koutsonikolas, Y. Hu, C. Wang, M. Comer, and A. Mohamed,
“Efficient online WiFi delivery of layered-coding media using inter-
layer network coding,” in 31st International Conference on Distributed
Computing Systems (ICDCS), 2011, pp. 237–247.
