Int. J. Communications, Network and System Sciences, 2011, 4, 205-218
doi:10.4236/ijcns.2011.44025 Published Online April 2011 (
Copyright © 2011 SciRes. IJCNS
Forwarding vs. Network Coding: Efficient Broadcasting in
Multihop W ir eless Networks
Suranjit Paul1, Thomas Kunz1, Li Li2
1System and Computer Engineering, Carleton University, Ottawa, Canada
2Communications Research Centre Canada, Ottawa, Canada
Received March 5, 2011; revised March 27, 2011; accepted March 30, 2011
Broadcasting is used as a building block in many MANET (Mobile Ad hoc Network) routing protocols. In
addition, broadcasting is a key primitive in ad hoc networks to support group-based applications. Efficiently
supporting broadcasting in multihop wireless networks is therefore important. In this paper, we compare ef-
ficient broadcasting protocols based on packet forwarding with those based on network coding. Using a
number of network scenarios, we derive lower bounds for the required number of packet retransmissions at
the MAC layer to support broadcast with and without applying network coding techniques. We compare
these lower bounds with each other, as well as with protocols proposed for each approach. More specifically,
we use SMF and PDP as sample forwarding-based broadcast protocols, and a simple XOR-based coding
protocol over SMF and PDP as representative network coding solution. The results show that neither packet
forwarding protocols nor network coding protocols achieve the theoretical lower bounds, in particular as the
size of the network area (at constant density) increases. The comparison of the lower bounds also shows that
network coding does have a potential performance advantage over packet forwarding solutions for broad-
casting in multi-hop wireless networks, in particular for larger fixed density networks, justifying its inherent
increased complexity.
Keywords: MANETs, Broadcasting, Multi-hop Networks, SMF, PDP, Network Coding
1. Introduction
In recent years, multi-hop wireless networks have at-
tracted significant attention due to their potential appli-
cations in tactical networks. A multi-hop wireless net-
work consists of numerous devices that are equipped with
processing, memory and wireless communication capa-
bilities, and are linked via short-range ad hoc radio con-
nections. There is no pre-installed infrastructure in this
type of network, communication is supported by inter-
mediate nodes relaying packets between communicating
Broadcast communication is an important mechanism
to communicate information in such ad hoc wireless
networks. In addition, many routing and other network
protocols for wireless ad-hoc networks need a broadcast
mechanism to update their states and maintain informa-
tion between nodes. Many packet forwarding and net-
work coding techniques have been proposed so far for
improved performance of broadcast communications in
packet networks. Recent research has also applied net-
work coding to mobile ad hoc networks (MANET) for
improved network throughput and robustness. In a mul-
ti-hop wireless network, each node has limited energy
resources. Reducing the number of transmissions re-
quired to broadcast messages to the whole network saves
energy and improves spectrum efficiency, which is very
critical in bandwidth limited multi-hop radio communi-
cations. Different packet forwarding and network coding
protocols have been proposed to reduce the number of
This paper studies the performance of packet for-
warding and network coding broadcast approaches in a
multi-hop wireless networks, aka the MANET environ-
ment. In particular, we are interested in minimizing the
number of packet transmissions at the MAC layer, as this
directly translates into reduced energy consumption and
more efficient spectrum utilization. We therefore study
This work was supported by the Communications Research Centre
Canada under Intergovernmental Agreement Number 9003930.
206 S. PAUL ET AL.
lower bounds of the packet transmission and compare the
performance of actual broadcast protocols against the
derived lower bounds. We approximate the lower bound
for any packet forwarding solution, using the Minimum
Connected Dominating Set (MCDS). We also derive
lower bounds for any network coding solution based on a
linear program. We then compare these lower bounds
with two protocols in each category and with each other.
The paper is organized as follows. In Section 2, the re-
sults of a literature survey for packet forwarding and
network coding approaches are summarized. This section
also identifies the packet forwarding and network coding
protocols we selected for comparison purposes. In Sec-
tion 3, the implemented MCDS heuristic is described,
which approximates the lower bound on packet trans-
missions for any packet forwarding solution. A linear
program that derives the lower bound for network coding
is described in Section 4. Section 5 discusses the per-
formance of the packet forwarding protocols, with re-
spect to their lower bound; Section 6 likewise discusses
the performance of the network coding protocols, rela-
tive to their lower bound. Section 7 compares the lower
bounds themselves, and Section 8 concludes the paper
and points to avenues for future research.
2. Related Work
The review of related work is broken down in two main
sections. We first review work on efficient broadcasting
using packet forwarding only, followed by a review of
the use of network coding in the context of broadcast
2.1. Broadcasting via Packet Forwarding
2.1.1. The Minimum Connected Dominating Set
Efficiently broadcasting packets to all nodes in the net-
work can be modeled either as a graph problem or via
appropriate routing protocols. In graph theory, the
neighbors of a vertex are all the vertices which are con-
nected to that vertex by a single edge. A dominating set
(DS) for a graph is a set of vertices whose neighbors,
along with themselves, constitute all the vertices in the
graph. A connected dominating set (CDS) of a graph G =
(V,E) is a subset of nodes, S such that S is a dominating
set of G and the sub-graph of G induced by S is also
connected. The Minimum Connected Dominating Set
(MCDS) problem is to find a connected dominating set
of minimum cardinality. An MCDS provides an efficient
way to broadcast packets to all nodes in a network: as-
suming that the wireless links are inherently a broadcast
medium, only nodes in the MCDS need to (re-)broadcast
packets to ensure that all nodes receive a packet. In addi-
tion, as the MCDS itself is connected, once one node
within the MCDS knows about the packet, it will propa-
gate through the MCDS via broadcasting. Unfortunately,
computing a minimum connected dominating set over a
given graph is an NP-complete problem [1].
There exist several centralized approximations and
exact algorithms in the literature to solve the minimum
connected dominating set problem. All exact algorithms
are at best only small improvements of the trivial O (2n)
solution. The trivial solution requires checking every
possible subset of nodes to determine whether this subset
constitutes a minimum connected dominating set. Refer-
ence [2] proposes an exact algorithm for the MCDS
problem of an arbitrary graph with an improved runtime
complexity of O (1 .9407n). The algorithm makes use of
some new domination rules and reduction rules and its
analysis is based on the Measure and Conquer technique.
But this algorithm is not practical for networks as small
as even only 100 nodes as it will take a long time to find
the minimum connected dominating set.
Guha and Khuller first proposed a two-stage greedy
ln 3
-approximation in [3] for MCDS in general
graphs, where
is the maximum node degree in the
graph. In the first step of this algorithm, a CDS is built
from one node, then the search space for the next domi-
nator(s) is restricted to the current set of dominatees and
the CDS expands until there are no uncovered nodes left.
All the possible dominators determined in the first phase
are then connected through some intermediate nodes in
the second phase.
A new efficient heuristic algorithm for the MCDS
problem was proposed in [4]. The algorithm starts with a
feasible solution containing all vertices of the graph.
Then it reduces the size of the CDS by excluding some
vertices using a greedy criterion. This algorithm is espe-
cially valuable in situations where setup time is costly
because it maintains a feasible solution at any time dur-
ing the computation. This algorithm provides a better
approximation of
than that of Guha and
Khuller’s. Here, is the maximum degree of the graph
112 1
n  is the harmonic function.
In [5], the authors proposed a new approximation al-
gorithm based on Steiner trees, which produces an ap-
proximation solution within a factor of 6.8. This ap-
proximation algorithm can also be implemented in a dis-
tributed manner. This algorithm consists of two steps. In
the first step, a maximal independent set is being con-
structed. In the second step, a 3-approximation for the
ST-MSN (Steiner Tree with Minimum Number of
Steiner Nodes) to interconnect the maximal independent
set is determined. Note that the size of the optimal solu-
tion for the ST-MSN cannot exceed the size of the min-
imum connected dominating set since the latter can also
Copyright © 2011 SciRes. IJCNS
interconnect the maximal independent set. A Steiner tree
is defined as a subset of the vertices of a graph G which
is a minimum-weight connected sub-graph of G that in-
cludes all the vertices. It is always a tree. Therefore, the
ST-MSN has at most 3*opt Steiner nodes in the second
step, where opt denotes the optimal solution (MCDS
size). The resulting connected dominating set has a size
bounded by 6.8*opt.
On the other hand, in [6], another greedy algorithm
called S-MIS (Steiner tree with Maximal Independent
Set) was proposed. The algorithm, with the help of
Steiner trees, constructs a CDS within a factor of 5.8 +
ln 4 from the optimal solution. This is also a two-step
algorithm. In the first step, a MIS is constructed and in
the second step a greedy approximation for the ST-MSN
to interconnect the nodes in the MIS was employed. The
resulting CDS has a size bounded by (5.8 + ln 4) opt +
Since NP-hard problems cannot be solved in polyno-
mial time, approximation algorithms are more efficient
to use. On the other hand, exact algorithms provide the
optimal solution; however their running time is very high
even for small problem sizes. After reviewing a range of
algorithms, we found that the algorithm proposed in [7]
has better execution time than others. Also the proposed
algorithm produces an MCDS of smaller size than others.
In addition, this algorithm is less complex than others.
Hence this one has been chosen to be implemented. In
Section 3, we discuss the proposed algorithm in detail.
2.1.2. Distributed Efficient Flooding Algorithms
In addition to these graph-based approaches, a number of
authors have proposed distributed broadcast algorithms
to efficiently flood data packets in a network. All these
proposals aim to improve on the trivial flooding protocol,
where a node rebroadcasts a packet the first time it re-
ceives it. In general, research on efficient broadcast sup-
port in mobile ad hoc networks has proceeded along two
main approaches: deterministic and probabilistic. Deter-
ministic approaches predetermine and select the neigh-
boring nodes that forward the broadcast packet. On the
other hand, probabilistic or gossiping-based approaches
require each node to rebroadcast the packet to its neigh-
bors with a given forwarding probability. The key chal-
lenge with these approaches is to tune the forwarding
probability: keeping it as low as possible for maximum
efficiency while maintaining it high enough so that all
the nodes are able to receive the broadcast packets. In
this work, we selected two deterministic protocols SMF
and PDP. Both SMF and PDP apply the two-hop neigh-
borhood information in selecting relay nodes, which is
collected via periodic HELLO messages.
SMF is described in detail in [8,9]. The concept of
“multipoint relaying” is used to reduce the number of
duplicate re-transmissions while forwarding a broadcast
packet. This technique restricts the number of re-trans-
mitters to a small set of neighbor nodes, instead of all
neighbors, as would be the case in flooding. This set is
kept as small as possible by efficiently selecting the
neighbors which cover (in terms of one-hop radio range)
the same network region as the complete set of neighbors.
This small subset of neighbors is called multipoint relays
of a given network node. The technique of multipoint
relays (or MPRs) provides an adequate solution to reduce
the flooding of broadcast messages in the network, while
attaining the same goal of transferring the message to
every node in the network with high probability. The
information required to calculate the multipoint relays is
the set of one-hop neighbors and the two-hop neighbors,
i.e. the neighbors of the one-hop neighbors. To obtain the
information about one-hop neighbors, most protocols use
some form of HELLO messages that are sent locally by
each node to declare its presence. In a mobile environ-
ment, these messages are sent periodically to get the
most updated information. To obtain the information of
two-hop neighbors, one solution may be that each node
attaches the list of its own neighbors, while sending its
HELLO messages. With this information, each node can
independently calculate its one-hop and two-hop neigh-
bor sets. Once a node has its one-hop and two-hop neigh-
bor sets, it can select a minimum number of one- hop
neighbors which covers all its two-hop neighbors. MPRs
are dynamically selected by each node and selections are
advertised and dynamically updated with hello messages.
The variant of SMF we selected is based on the
source-specific MPR forwarding. A node will forward
packets if and only if it receives a unique multicast pack-
et from any of its neighbors and the neighbor from which
the packet was received has selected the node as an MPR.
The basic algorithm for the S-MPR selection process is
described in [8]. N(n) and N(N(n)) indicate one-hop
neighbors and two-hop neighbors of node n, respectively.
1) Start with an empty multipoint relay set MPR(n).
2) First select those one-hop neighbor nodes in N(n)
as multipoint relays which are the only neighbor of
some node in N(N(n)), and add these one-hop
neighbor nodes to the multipoint relay set MPR (n).
3) While there still exists some node in N(N(n)) which
is not covered by the multipoint relay set MPR(n):
a) For each node in N(n) which is not in MPR(n),
compute the number of nodes that it covers
among the uncovered nodes in the set N(N(n)).
b) Add that node of N(n) to MPR(n) for which this
number is maximum.
Partial Dominant Pruning (PDP) is another algorithm
which also utilizes the neighborhood information for re-
Copyright © 2011 SciRes. IJCNS
208 S. PAUL ET AL.
ducing redundant packet transmissions. In PDP, when a
node v receives a packet from another node u, it selects a
minimum number of forwarding nodes from the set
that can cover all the nodes in the set
 
Nv Nu
U NNvNu Nv NNuNv
. A node
can obtain its one-hop and two-hop neighborhood infor-
mation by periodically sending hello messages. Upon
receiving the hello messages, each node updates its
neighborhood information. Each forwarding node then
again follows the same procedure to select its own for-
warding nodes. The forwarding stops when all forward-
ers have received a packet at least once. The PDP algo-
rithm is described below. Details of this algorithm are
described in [10].
Step 1: Node v uses
NNv, , and
to obtain
PNNu Nv
 
UNNvNuNv P, and
 
BNv Nu.
Step 2: Node v then calls the selection process to de-
termine the set of forwarding nodes, F.
Selection Process:
Step 1: Let
,Fuv (empty list), z
set), and K = U Si, where for vi ε B.
Step 2: Find the set Si, whose size is maximum in K.
(use the one with the smallest identification i in case of a
Step 3:
ZUS, K = K – Si, and Sj = Sj
– Si for all Sj K.
Step 4: If Z = U, exit; otherwise, goto Step 2.
2.2. Broadcasting via Network Coding
Research in information theory discovered that routing
alone is not sufficient to achieve maximum throughput in
the general model of data networks. Network coding
techniques have been proposed for improved perform-
ance for broadcast and multicast traffic. Network coding
is a technique which looks beyond the traditional store-
and-forward approach followed by routers in communi-
cation networks. Network coding is a generalization of
routing in which nodes can generate output data by en-
coding previously received input data. Thus, network
coding allows information to be “mixed” at a node.
Ahlswede et al. in [11] first formally introduced the pa-
radigm of network coding, where they also demonstrated
its use in case of single-source multiple-sink network
multicast in a wired network. Additional examples of
networks are also presented in [11] where it is shown
that network coding can improve the overall throughput
of the network which can not otherwise be realized by
the conventional store-and-forward approach. Network
coding has drawn significant interest, especially for
broadcast and multicast traffic. However, it is not obvi-
ous whether network coding further reduces the number
of packet transmissions for random networks in the case
of broadcasting. This section briefly reviews several
network coding techniques that were proposed for wire-
less networks.
The approach proposed in [12] applies network coding
to a deterministic broadcast protocol, resulting in a sig-
nificant reduction in the number of transmissions in the
network. To reduce the number of transmissions, two
algorithms that rely only on local two-hop topology in-
formation and make use of opportunistic listening were
proposed. The first algorithm is a simple XOR-based
coding algorithm, similar to the approached described in
[13], and the second one is a Reed-Solomon based cod-
ing algorithm. The simulation results show that the de-
terministic coding approach (Nodes pre-select a few
neighbors for rebroadcasting) outperforms the probabil-
istic coding approach (Each node rebroadcasts a packet
with a given probability).
CodeCast, a network coding based ad hoc multicast
protocol which is well-suited especially for multimedia
applications with low loss and low latency is proposed in
[14]. The main component of CodeCast is random net-
work coding, which is used to implement both localized
loss recovery and path diversity transparently. The au-
thors demonstrated through simulation that CodeCast
achieves a near perfect packet delivery ratio while main-
taining lower overhead than conventional multicast.
On the other hand, the authors of [15] present a theo-
rem that unifies and generalizes Edmonds’ theorem on
routing (i.e. if all nodes other than the source are destina-
tions, the cut bound, which is any cut separating the
source from a destination, can be achieved by routing)
and Ahlswede et al.’s theorem on network coding (i.e.
the cut bound can be achieved by performing network
coding) by classifying the links in a network into two
categories: links entering relay nodes (Steiner edges),
and links entering destinations (Terminal edges). The
authors show that the multicast capacity can be achieved
by performing nontrivial network coding (Mixing) only
at links entering relay nodes. Links entering destinations
will only require routing, which leads to a saving in the
processing/implementation complexity.
In [16] the authors develop a network coding scheme
for broadcast traffic in ad hoc networks and compare its
performance against simpler solutions, based on flooding
and deferred broadcast. They show that network coding
is advantageous only in certain cases, such as dense net-
works, by comparing random linear network coding with
two broadcast schemes under a range of scenarios. Their
Copyright © 2011 SciRes. IJCNS
analysis shows that network coding significantly outper-
forms other broadcasting schemes in terms of end-to-end
packet loss probability and protocol overhead only for
large neighborhood sizes (i.e., more than 12 neighbors)
and generation sizes smaller than or equal to three. A
generation is defined as a collection of packets that can
be allowed to be linearly combined. Dividing packets
into generations decreases the decoding complexity and
allows to decode data faster (And thus to empty the re-
spective memory).
In [17], random linear network coding for time divi-
sion duplexing channels for broadcasting is studied. The
authors also studied the mean time to complete the
transmission of a block of packets to all receivers. Nu-
merical results show that the coding scheme proposed in
[17] outperforms a Round Robin broadcast scheme in a
time division duplexing channel.
Reliability gain as a performance metric for random
linear network coding in relay networks is studied in [18].
The work studies the expected number of channel uses
per data bit successfully received. By analysis they show
that random linear network coding provides limited per-
formance gains in comparison to other protocols.
Reference [19] explores the efficiency of broadcasting
via network coding in general and whether it is beneficial
to use network coding over routing. It argues that for
wireless networks in the 2D space, the asymptotic coding
gain for a single-source broadcast is between 1.642 and
1.684 when both the area and the density of the network
converge toward infinity. The paper also provides
bounds of 1.432 and 2.035 for networks of the Euclidean
space of dimension 3.
Reference [20] investigates benefits in terms of energy
efficiency that the use of network coding can offer for
the problem of broadcasting over ad-hoc wireless net-
works. The authors also show that network coding can
result in a coding gain of 2 in ring networks and a coding
gain of 1.3333 for grid networks and provides protocols
that achieve this gain for such specific network topolo-
gies, using scenarios where all nodes are sources. Their
work also indicates that there is a potential for significant
benefits when deploying network coding over a practical
wireless ad hoc network environment, especially when
we are restricted to use low complexity decentralized
For comparison purposes, we selected the XOR-based
coding approach proposed in [12]. This is a fairly simple
protocol, which can extend PDP and SMF and has been
shown to reduce the number of MAC packet transmis-
sions while achieving good broadcast performance. Each
node maintains one-hop and two-hop neighborhood in-
formation, based on the HELLO message exchange of
the underlying SMF or PDP protocols. For each data
packet a node u receives from a neighbor v, it will as-
sume that those of its neighbors that are also v’s neigh-
bors will also have received that packet. So a node will
promiscuously, and without any additional messaging
overhead, maintain information about which packets
were already received by what neighbor (called the
neighbor reception table), to guide its encoding decision.
A node u with a set of native packets P in its output
queue seeks to find a subset of native packets Q to XOR.
Let the set of neighbors of u, each of which can decode a
missing packet be N1(u) (determined by Q and the
neighbor reception tables). As shown in [12], determin-
ing the optimal combination of packets (maximal cardi-
nality of N1(u), optimized across all packets in u’s output
queue) is NP-hard. So instead, the following greedy heu-
ristic is proposed: Start with the packet p at the head of
the output queue and sequentially look for other packets
in the queue that, when combined with p, will allow all
neighbors of node u to decode the packet. If successful,
these packets are added to the coded packet. Once such a
coded packet is received by a node, it can extract the
missing packet by XOR-ing the received packet with the
remaining N – 1 packets it already received and buffered.
This requires that the coded packet carries with it an in-
dication that it is a coded packet, and the unique identifi-
ers of its contributing native packets. In case that the
neighbor reception table of a node u was inaccurate, a
node will be unable to successfully decode a packet. Al-
so a node may not gain any new information from this
packet, as it already received all constituent native pack-
ets. In the following, we refer to the XOR coding over
2.3. Summary
Network coding enables more efficient, scalable and
reliable wireless networks. Based on the reviewed stud-
ies, we conclude that the potential advantages of network
coding over routing include a reduction in resource usage
(e.g., bandwidth and power), and robustness to network
dynamics. Besides, network coding can increase the pos-
sible network throughput and, in the multicast case, it
can achieve the maximum data rate theoretically possible.
In addition to maximizing throughput, network coding
can also maximize the energy efficiency by reducing the
number of transmissions required to deliver a message to
the whole network. But there is also some evidence that
network coding is not always beneficial. In this work, we
explore a range of network scenarios to study this ques-
tion in more detail. We compare the performance of effi-
cient packet forwarding approaches and network coding
protocols to support broadcasting in multi-hop wireless
networks. The comparison is based on both lower bounds
Copyright © 2011 SciRes. IJCNS
210 S. PAUL ET AL.
derived from analytical models and also the simulation
results. More specifically, we compare the following:
A lower bound for packet forwarding based broad-
cast protocols generated using the centralized MCDS
heuristic proposed in [7].
The number of PDP forwarders and SMF MPRs,
where both PDP and SMF are representative packet
forwarding broadcast protocols.
A lower bound for network coding approaches
generated using an integer linear program.
The number of data packets forwarded by network
coding protocols employing XOR coding as repre-
sentative network-coding based broadcast protocols.
3. Packet Forwarding Lower Bound
The MCDS algorithm that we implemented is proposed
in [7] and it uses a heuristic to find the minimum con-
nected dominating set. This algorithm is divided into
three phases. In the first phase, a dominating set D is
constructed, in the second phase a set of connectors are
found which can connect nodes in D, with the help of a
Steiner tree, and in the final phase, pruning is done,
where the number of nodes in the MCDS is reduced to
make it a near-optimal minimum connected dominating
set. A black node is a node which is to be present in the
Connected Dominating Set or is a Dominator. A gray
node is a dominatee and a blue node is a connector which
is to be present in the Connected Dominating Set. The
algorithm proceeds in three stages.
Stage 1: In Stage 1, a dominating set is constructed
which consists of the minimum number of nodes. This
stage consists of the following steps:
1) An arbitrary unique number say ID is assigned to
each Node in the graph G(V,E),
2) Each node is assigned white color,
3) The node u with maximum degree is taken from
G(V,E) and colored as black, i.e. it indicates that it is
a Dominator,
4) All the neighbor nodes of the node u are colored as
5) Repeat steps 3 and 4 till all the nodes in the graph
G(V,E) are colored either as black or gray.
Stage 2: In Stage 2, a set of connectors B is found
such that all the nodes in the dominating set are con-
nected. Let a black node be a node in D and a blue node
represent a node in B. A node in B is connected by at
most K nodes in the graph G(V, E). The set of blue nodes
with given D could be found using a Steiner tree. It is a
tree interconnecting all the nodes in D by adding new
nodes between them. The nodes that are in the Steiner
tree but not in set D are called Steiner nodes. In the
minimum connected dominating set, the number of
Steiner nodes should be minimal. After this stage a CDS
is constructed, which consists of black and blue nodes.
This involves the following steps:
1) Select a gray node which is connected to the max-
imum (K) number of black nodes, set its color as
2) Check whether the Dominating Set D is connected
or not,
3) If D is connected stop,
4) Else go to step 1 with K-1 number of Black nodes.
Stage 3: Stage 3 is a pruning stage. In this stage, re-
dundant nodes are deleted from the CDS constructed in
Stage 2, to obtain the MCDS. Let the CDS constructed in
the previous stage be set F. Initially, all nodes in the set
are unmarked.
1) Select a minimum degree, unmarked, node u from F.
2) Check if N[u] is a subset of N[1] and N[2] and …
N[n] where i belongs to F- {u}.
3) If step 2 returns true then remove node u and goto
step 1.
4) Otherwise do not remove node u (but mark it) and
goto step 1.
After implementing the original algorithm (referred to
as Unconstrained MCDS algorithm in the following), we
developed a revised version where we enforce that a spe-
cific node (node 0) is always in the final MCDS. This
reflects more accurately the deployment of protocols in a
network, where a specific node (or group of nodes) is
chosen as source. Since node 0 is the source node in our
simulations, this revised version (referred to as Con-
strained MCDS algorithm in the remainder of this paper)
allows us to directly compare the results.
4. Network Coding Lower Bound
We are determining the lower bound on the number of
required packet retransmissions for network coding using
the linear program originally proposed in [21]. Here, the
lower bound on the number of required packet retrans-
missions for network coding is determined by formulat-
ing this as an integer linear program and solving it for a
range of randomly generated multi-hop wireless networks.
The linear program is based on the intuition that, as-
suming the NC protocol is optimal, working on genera-
tions of size N, than all packet transmissions will be in-
novative for all neighbors. So, if each node receives at
least N packets, with all of them being innovative, they
can then decode and therefore receive all native packets
in a generation. In addition, flow constraints have to be
met: flows exist from the sender to each receiver; these
flows are subject to the typical flow constraints: the
amount of flow on an edge cannot exceed the capacity of
the edge and a flow must satisfy the restriction that the
Copyright © 2011 SciRes. IJCNS
amount of flow into a node equals the amount of flow
out of it, except when it is a source, which has more
outgoing flow, or sink, which has more incoming flow.
Flow variables Fi,j(d) are introduced which capture the
data flow from source 0 over link i, j destined to node d.
In a broadcast scenario, all nodes are receivers, but to
simplify the formulation, it is assumed that node 0, the
implied source, trivially receives all packets and there-
fore d 0. Finally, to correctly capture the broadcast
nature of the wireless media, a dummy node is intro-
duced where node i will transmit its packets to its dum-
my node ī first, and the dummy node will then forward
the packets to all neighbors of i.
Let Xi be the number of packet transmissions of node i
(for a given generation of size N), let N(i) be the set of
one-hop neighbors of node i, The integer linear program
to determine the minimum number of packet transmis-
sions at the MAC layer is:
min i
Subject to:
 
for 0
,: for
0 otherwise
,: 0
:0, is integer
ii ji
ij ii
id FdX
id FdFdNi=d
iX X
 
Here, the first constraint limits the flows out of a real
node i (which are all destined to the nodes’ dummy node
ī) to the number of physical packet transmissions of that
node. The second set of constraints imposes the flow
balance condition: if the node is the source node, it gen-
erates N more packets than potentially received from the
dummy nodes of its neighbors. If the node is a destina-
tion, it consumes N more packets than forwarded to its
dummy node. For all other nodes, it passes on all re-
ceived packets. The third set of constraints expresses
flow balance constraints on the newly introduced dummy
nodes: as these are neither sources nor destinations, their
flow balance is always zero. Finally, the last set of con-
straints enforces that the number of physical packet
transmissions by each node are always a positive integer
or zero.
5. Performance of Packet Forwarding
5.1. Scenario Descriptions
To compare lower bounds and actual routing protocols,
we generated a number of multihop wireless network
scenarios, distributing a number of nodes in a rectangular
area of a given size using a uniform distribution. These
scenario files were then used as the basis for NS-2 (NS-2
version 2.29) simulations of SMF, PDP, and the XOR-
based coding variants thereof. We also process these
scenario files to approximate the MCDS size, using both
constraint and unconstrained versions of the MCDS
heuristic described in Section 3. Finally, we also used
these scenario files to derive integer linear programs that
were then solved with glpk, a free LP solver. Before de-
scribing the results, we first discuss the simulation setup
and relevant parameters.
We study both fixed area and fixed density networks.
For the fixed area network, we consider an area of 500 ×
500 square-meters and then increase the number of nodes
from 10 to 100 in steps of 10. For all network sizes, the
network diameter was slightly over 3. On the other hand,
for fixed density networks, we generated scenarios for an
increasing number of nodes (again, from 10 to 100 in
steps of 10), but this time we kept the density constant by
scaling the network area with the number of nodes. Ta-
ble 1 shows the number of nodes, corresponding areas,
and average network diameter. In both cases, the gener-
ated network scenarios are static. In essence, we consider
mobile networks as a sequence of static snapshots, so
this simplifies the analysis significantly.
The NS-2 simulations were run for 100 seconds. Dur-
ing the first 50 seconds, nodes exchange HELLO mes-
sages at an interval of 5 seconds, allowing enough time
for nodes to learn about their neighborhood, selecting
MPRs, and signaling this to the selected nodes. Node 0
starts sending data packets in the 51st second and we are
sending a total of 10 data packets (256 bytes each) at a
rate of two packets per second. These settings are delib-
erately low to not stress the network (except where noted
Table 1. Number of nodes, corr esponding networ k size, and
network diame ter for fixed density network.
Number of NodesNetwork Area Average Network Diameter
10 346 × 346 2.1
20 490 × 490 3
30 600 × 600 4.2
40 693 × 693 4.6
50 774 × 774 5.3
60 848 × 848 5.9
70 916 × 916 6
80 979 × 979 6.4
90 1039 × 1039 7.1
100 1096 × 1096 7.3
Copyright © 2011 SciRes. IJCNS
212 S. PAUL ET AL.
later). Additionally, to reduce timer synchronization
problems, all packet transmissions are jittered by an ad-
ditional random delay, distributed uniformly in a range
from 0 to 20 ms. Consequently, and as anticipated, all
simulations achieve 100% (or close to it) packet delivery
ratio. From the NS2 tracefile, we then extract the number
of packet transmissions at the MAC layer, not counting
the periodic HELLO messages. For SMF, that number
represents the transmission by the source node, and all
MPRs that re-transmit a packet. Similarly, for PDP, that
number represents again, the transmission by the source
node and the forwarding by the selected forwarders, until
the packet is delivered to all nodes.
In general, we consider only one source, node “0” for
simulating packet forwarding algorithms (PDP and SMF).
On the other hand, in our simulation for network coding
protocols (PDP/XOR and SMF/XOR), we consider four
sources, as having only one data source will not generate
enough coding opportunities. We confirmed that in-
creasing the number of sources further (To six or eight,
for example) does not provide additional coding oppor-
tunities. Therefore, nodes “0”, “1”, “2”, and “3” are cho-
sen as sources in this case and results are presented in
terms of the required number of forwards per source.
The MAC and PHY settings are based on the default
values in NS2 when simulating IEEE 802.11 networks:
The transmission range is a perfect circle with a radius of
250 m, carrier sensing range is 550 m, and the raw data
rate is 2 Mbps. Again, as the network load is deliberately
kept low, these parameters are not expected to impact the
findings reported here, except for the case where we
stress the network.
5.2. Packet Forwarding Performance for Fixed
Area Networks
In a first step, we evaluated the performance of the pack-
et forwarding protocols in a fixed area network, as we
increased the number of nodes. For each network size, 50
different scenarios have been generated and evaluated.
Moreover, we generated scenarios for a (Comparatively
speaking) sparse and also a (Comparatively speaking)
dense network and evaluated the protocol performance.
Table 2 shows the average number of forwarding nodes
required to cover all nodes in the network for both the
unconstrained and constrained MCDS version along
with PDP and SMF. The table shows that the uncon-
strained MCDS algorithm provides the lower bound for
all cases. The constrained version, where we ensure that
node “0” is always in the resulting MCDS, also provides
a smaller number of re-broadcasting nodes compared to
the two distributed algorithms. To evaluate the statistical
significance of the differences in the results, we con-
ducted a number of t-tests at a 95% confidence level and
found the following results:
For small networks (10 to 30 nodes), there is evi-
dence of statistically significant difference between
the means of the two MCDS versions, with the
unconstrained version producing a smaller MCDS
size than the constrained version. When the num-
ber of nodes increase in the network (up to 100
nodes), the difference becomes statistically insig-
Comparing SMF and PDP, for all network sizes,
the differences between the total numbers of active
forwarding nodes for both algorithms are statisti-
cally insignificant.
Comparing PDP/SMF to MCDS, unconstrained
MCDS always determines a statistically significant
smaller MCDS size than the number of active for-
warders in PDP/SMF.
Additionally, when we performed t-tests for con -
strained MCDS and PDP/SMF, for any network
with 10 or 20 nodes, the constrained MCDS will
determine an MCDS size that is similar to the
number of active forwarding nodes in PDP. How-
ever, as the network size grows, constrained MCDS
will result in a statistically significant smaller
MCDS size, compared to the number of active
forwarders in PDP/SMF.
We also analyzed scenarios for dense and sparse net-
works. For this purpose, we considered two additional
network areas. The first one is a (relatively speaking)
denser network, i.e. a network with an area of 350 by
350 square-meters. For the second scenario, we consider
Table 2. Average number of forwarding nodes for packet
forwarding in fixed ar e a ne tworks.
No. of
Average # of
nodes in
Average #
of nodes in
Average #
of Active
for PDP
Average #
of Active
MPRs for
10 2.52 3.14 3.30 3.30
20 2.88 3.52 3.82 3.82
30 3.26 3.68 4.54 4.44
40 3.70 3.88 4.60 4.54
50 3.90 3.96 4.78 4.72
60 4.04 4.12 4.82 4.86
70 4.16 4.40 5.20 5.20
80 3.90 4.38 4.94 4.88
90 4.32 4.40 5.12 5.10
100 4.38 4.64 5.48 5.62
Copyright © 2011 SciRes. IJCNS
a sparser network, i.e. a network with an area of 750 by
750 square-meters. We generated 100 scenarios (10 sce-
narios for network size) for both networks and conducted
statistical analysis as the number of nodes increases from
10 to 100 in steps of 10 again.
In the denser network, for all network sizes, we always
find statistically significant differences between the
means of unconstrained MCDS compared to constrained
MCDS, PDP and SMF. Additionally, we find no evi-
dence of statistically significant difference between the
means of PDP and SMF. When there are 10 to 30 nodes
in the network, t-test results for constrained MCDS vs.
PDP as well as constrained MCDS vs. SMF show no
evidence of statistically significant difference between
the means. But when we added more nodes in the net-
work (in our cases, more than 30 nodes), there exists a
statistically significant difference between their means.
For the sparser network, we could not randomly gen-
erate a connected scenario with 10 nodes only. But for all
other network sizes (20 to 100 nodes), t-test results indi-
cate that there is no evidence of statistically significant
differences between the means of unconstrained MCDS
and constrained MCDS; and also between PDP and SMF.
On the other hand, t-test analysis between unconstrained
MCDS and PDP, unconstrained MCDS and SMF, con-
strained MCDS and PDP, and constrained MCDS and
SMF show that the differences between their means are
always statistically significant when the number of nodes
in the network is more than 20.
For all protocols, as the network area increases, the
number of re-broadcasting nodes increases. But for the
distributed algorithms (PDP and SMF), the total number
of re-broadcasting nodes increases more rapidly in com-
parison to the centralized MCDS heuristic as the number
of nodes in the network increases.
As a final experiment for our fixed size network, we
conducted simulations for 200 to 500 nodes and observe
how that affects the total number of forwarding nodes.
We do not find any significant difference when we add
200 or 300 nodes in the network. But when there are 400
or more nodes, the performance deteriorates severely and
PDP and SMF both have more forwarding nodes, as
shown in Table 3.
Table 3. Average number of forwarding nodes for high-
density networks (200 - 500 nodes).
Nodes in
Network unconstrained
MCDS constrained
200 4.9 5.4 6.2 6.5
300 5.0 4.9 6.2 6.7
400 5.4 5.5 11.56 16.43
500 5.2 5.3 17.4 18.67
The performance deteriorates since we now stress/
overload the network. Each node has many neighbors,
and all nodes contend for access to the wireless medium
to send their (large) HELLO messages and data packets.
This results in many observable collisions, despite the
added random jitter. Increasing the jitter value does not
help the situation. The collisions cause nodes to have
only a partial view of their neighborhood, impacting the
efficiency of the MPR/forwarder selection. Using SMF
as an example protocol, the following diagrams show
how inaccurate 2-hop neighborhood information may
result in a significantly higher number of active MPRs,
which then will forward the data packet originated from
node 0. As a result, the protocol performance deteriorates
In the case of SMF, Figure 1 shows that when source
0 has complete and accurate neighborhood information,
there is only one active MPR, which is node 1. Once this
node (selected by node 0 as its MPR) receives and re-
broadcasts the packet, all nodes in the network received
the packet, either via the original transmission from node
0 or the retransmission by node 1, resulting in a total of
two packet transmissions at the MAC layer. But if node 0
does not have any information of node 1 (lost a succes-
sion of HELLO messages because of collisions), nodes
will select a different set of MPRs (Figure 2). Once node
0 broadcasts the original data packet, its MPRs (nodes 2
and 3) rebroadcast the packet. Nodes 4 and 5, having
been selected as MPRs by nodes 2 and 3, respectively,
will then rebroadcast the packet. Depending on whether
node 1 did overhear the initial transmission of the packet
from node 0, it may rebroadcast the data packet once it
Figure 1. MPR selection for a network with 6 nodes (no
missing neighborhood information).
Figure 2. MPR selection for a network with 6 nodes (node 0
has no knowledge of node 1).
Copyright © 2011 SciRes. IJCNS
214 S. PAUL ET AL.
hears the first broadcast from nodes 4 and 5 (which se-
lected node 1 as an MPR), resulting in at least 5 and pos-
sibly 6 packet transmissions at the MAC layer.
In summary, for a fixed-size network, when we do not
restrict the MCDS algorithm (i.e., for the unconstrained
version), it always performs better than PDP and SMF in
all cases. Even for the denser and sparser networks, the
unconstrained MCDS algorithm is superior to both dis-
tributed algorithms except for the sparse network with 20
nodes; there was no significant difference in the means.
On the other hand, when we restrict the MCDS algo-
rithm (i.e., the constrained version), PDP and SMF per-
form similar to the constrained version for small sized
networks (10 to 20/30 nodes). There is no significant
difference between PDP and SMF. The same is true for
denser and sparser networks. But when we increased the
number of nodes in the network (30/40 to 100 nodes), the
performance of PDP and SMF eventually deteriorates,
due to the increased number of collisions and the result-
ing loss of accurate topology information.
5.3. Packet Forwarding Performance for Fixed
Density Networks
In a second set of experiments, we compare packet for-
warding protocols when we keep the network density
fixed as we increase the number of nodes. We generated
100 random scenarios, 10 for each network size. The av-
erage number of forwarding nodes required to cover all
nodes in the network are shown in the following table
(Table 4) for both the unconstrained and constrained
MCDS version along with PDP and SMF. According to
Table 4, the unconstrained MCDS algorithm provides a
lower bound for all cases. The constrained version of our
Table 4. Average number of forwarding nodes for packet
forwarding in fixed de nsity ne tworks.
No. of
Nodes in
Average # of
nodes in
Average #
of nodes in
Average #
of Active
for PDP
# of
for SMF
10 1.2 1.9 1.8 1.8
20 2.7 3.7 3.69 3.69
30 5.1 5.4 6.3 6.34
40 6.1 6.9 8.77 8.77
50 7.7 8.1 11.76 11.87
60 9.5 9.8 15.14 15.08
70 10.5 11.1 17.37 17.37
80 12 12.5 20.55 20.55
90 13.8 14.4 27.01 26.64
100 15.5 15.8 26.43 26.58
MCDS algorithm also provides a smaller number of
re-broadcasting nodes compared to the two distributed
algorithms. Similar to the previous section, we conduct
t-test to evaluate the statistical significance of the differ-
ences in results, at a 95% confidence level, with the fol-
lowing results:
For a small number of nodes (10 to 30), uncon-
strained MCDS results in a statistically significant
smaller MCDS size than the constrained version.
But when there are more nodes in the network (40
to100), both versions compute almost the same av-
erage MCDS size.
The difference in performance for SMF and PDP is
not statistically significant for all network sizes, i.e.,
both protocols result in approximately the same
number of packet (re-)transmissions at the MAC
The unconstrained MCDS always results in a
smaller MCDS size than number of active nodes in
PDP or SMF, for all network sizes.
For small networks (10 to 30 nodes), the difference
between constrained MCDS and PDP or SMF is
not statistically significant, but for larger network
sizes, constrained MCDS always results in a
smaller MCDS size than number of active nodes in
In summary, for fixed density networks, when we do
not restrict the MCDS algorithm (i.e., for unconstrained
version), it is always better than PDP and SMF in all
cases. On the other hand, when we restrict the MCDS
algorithm (i.e., constrained version); PDP and SMF per-
form similar to the constrained version for small sized
networks (10 to 20/30 nodes). There is no significant
difference between them. But as the number of nodes
increases, constrained MCDS performs better than PDP
or SMF. These results correspond to the insights we
collected for the fixed area networks. The one difference
we can observe is that the performance gap between
MCDS and SMF/PDP widens faster in the case of fixed
density networks: as we increase the number of nodes,
the network diameter grows. As a consequence, the
two-hop neighborhood of a node in both PDP and SMF
reflects an increasingly smaller portion of the network,
and the resulting local decisions by a node become more
suboptimal, compared to a solution that has a more glob-
al view of the network topology.
6. Performance of Network Coding
Similar to the results in the previous section, we com-
pared the performance of the network coding broadcast
protocols (XOR over SMF or PDP) with the network
Copyright © 2011 SciRes. IJCNS
coding lower bound, using both fixed size and fixed den-
sity networks. Table 5 shows the results for fixed area
networks, averaging over 10 repetitions for each network.
As discussed above, the results were derived by generat-
ing traffic from 4 different source nodes to provide am-
ple coding opportunities, and are presented here on a
per-source basis.
We observe that the derived lower bound is indeed
lower than PDP/XOR or SMF/XOR. Though the differ-
ence among means is not much for smaller networks, it
increases as the number of nodes increases. To test
whether these differences are statistically significant or
not, we conducted t-tests, with the following results:
For 10 to 20 node networks, the differences are not
statistically significant. Beyond this, the network
coding lower bound is statistically significantly
lower than the observed performance of SMF/XOR
and PDP/XOR.
Again, the difference in performance between
SMF/XOR and PDP/XOR is not statistically sig-
Table 6 shows the corresponding results for fixed
density network. Again, 10 different scenarios have
been generated for each network size, and the pro-
tocols were executed with 4 sources generating da-
ta packets, reporting the results on a per-source ba-
According to Table 6, PDP/XOR or SMF/XOR are
not close to the lower bound when we have fixed density
and the network scales up. The differences are statisti-
cally insignificant for smaller networks (10 to 20 nodes),
but the derived lower bound is significantly better than
Table 5. Average number of re-broadcasting nodes for
network co ding in fixe d area networks.
No. of
Nodes in
Average # of
nodes in
Network Coding
Lower Bound
Average # of
nodes in
Average # of
nodes in
10 3.35 3 2.9925
20 3.15 3.585 3.5825
30 3.0833 4.3125 4.2825
40 3.3167 4.435 4.4375
50 3.333 4.42 4.395
60 3.375 4.92 4.8775
70 3.5033 4.8075 4.85
80 3.2499 4.705 4.6825
90 3.333 4.715 4.7325
100 3.5 5.515 5.525
Table 6. Average number of re-broadcasting nodes for
network coding in fixe d de nsity networks.
No. of
Nodes in
Average # of
nodes in Network
Coding Lower
Average # of
nodes in
Average # of
nodes in
10 1.8 1.725 1.725
20 2.933 3.23 3.245
30 4.741 5.81 5.845
40 5.3 7.7975 7.935
50 6.5167 10.2575 10.64
60 7.3917 13.155 13.14
70 8.1376 15.6225 15.47
80 9.2658 17.5525 17.7175
90 9.8213 21.505 21.5175
100 10.716 22.955 23.06
both coding protocols as the number of nodes increases
in the network.
In summary, PDP/XOR and SMF/XOR are only capa-
ble of approaching the lower bound for small networks.
As the network size increases, a performance gap opens
up and widens. This gap is particularly noticeable for
fixed density networks, where the reduced local view of
each node, deciding on packet forwarders/MPRs based
on 2-hop neighbourhood information only, becomes less
optimal, similar to our conclusions in the case of the
packet forwarding protocols.
7. Comparing Packet Forwarding and
Network Coding
Section 3 describes the centralized MCDS heuristic that
we used as to determine the near-optimal number of
required re-transmitting nodes. Section 4 describes the
analytically derived lower bound for network coding.
This section compares the two lower bounds, to gain
insights into the relative performance of network coding
versus packet forwarding protocols.
Figure 3 plots lower bounds for fixed size networks,
both for packet forwarding protocols and for network
coding protocols. The figure indicates that the network
coding lower bound is lower than the bounds derived for
both MCDS versions. However, the difference in net-
works with 10 to 20 nodes is hardly noticeable. This is
confirmed by the statistical tests, where network coding
results in a statistically significant lower bound for the
number of re-broadcasting nodes only for network sizes
of 40 or above.
Copyright © 2011 SciRes. IJCNS
216 S. PAUL ET AL.
Figure 3. MCDS size and network coding lower bounds in
fixed area networks.
Figure 4 plots MCDS size for both MCDS heuristics
and network coding lower bound for fixed density net-
works. It clearly shows that network coding can achieve
significant gain (reduced number of packet retransmis-
sion) compared to packet forwarding solution, in par-
ticular as the network size increases. Again, the t-tests
bear out the statistically significant improved perform-
ance for network sizes from 40 nodes and more.
8. Summary and Conclusions
In this paper, we conducted a comparative analysis be-
tween packet forwarding and network coding approaches
for broadcasting in multihop wireless networks. In our
study, for fixed size and fixed density network, a lower
bound derived via an unconstrained MCDS was always
lower than the lower bound derived by the constrained
version. This difference was statistically not significant
for larger network sizes, but it does matter for smaller
networks. This shows the importance of accurately mod-
eling the lower bound, as a fair comparison with any
network protocol can only be made using the lower
bound derived by the constrained version. In real net-
works, when selecting a source, we cannot assume/enforce
that the node will naturally be part of the MCDS. In the
case of packet forwarding techniques, the lower bound
derived via the MCDS heuristic is statistically significant
lower than the performance of both PDP and SMF, spe-
cifically when there are more than 20 to 30 nodes in the
network. This is also true for network coding techniques
where the number of re-broadcasting nodes in PDP/XOR
and SMF/XOR is much higher than the network coding
lower bound.
PDP and SMF (and the XOR coding over these proto-
cols) perform very similar. A more in-depth analysis of
the simulation results revealed that, for some network
Figure 4. MCDS size and network coding lowe r bounds for
fixed density networks.
scenarios, PDP may result in a lower number of active
forwarders, yet in other scenarios SMF has a slight edge,
using fewer MPRs to re-broadcast a packet. PDP and
SMF only achieve close to optimal performance for
small networks. As the network size increases, for both
fixed area and fixed size networks, a performance gap
opens up between the lower bounds and the actual pro-
tocol performance. This gap is more pronounced in the
case of fixed-density networks, where we also scale the
network area and, as a result, the network diameter (see
Table 1). In this case, the local decisions by the proto-
cols, selecting forwarders/MPRs based on 2-hop neigh-
borhood information only, result in suboptimal decisions.
While this is obviously the price to be paid for local vs.
global information in the case of routing protocols, it is
not clear whether network coding could not improve on
the performance further, closing the gap. Finally, any
actual protocol is only as good as the network topology
information it can gather. As we have shown for the case
of the packet forwarding solutions, in the presence of a
large number of collisions, nodes will make poor deci-
sions about packet forwarders/MPRs. The same problem
holds for the network coding solution that run over PDP
or SMF. In addition, a large number of collisions for the
chosen network coding solution may result in inaccurate
neighbor reception tables, which will lead to decode
failure and negatively impact the broadcast performance.
Comparing the packet forwarding lower bound and the
network coding lower bound, we find that network cod-
ing does potentially have a performance advantage, com-
pared to packet forwarding, requiring a smaller number
of re-broadcasting nodes. This difference is not all that
noticeable/statistically significant for small networks,
however, where packet forwarding can achieve competi-
tive performance while avoiding the extra complexity of
coding and encoding operations. As network size grows,
Copyright © 2011 SciRes. IJCNS
however, the added complexity of network coding pays
off. In particular for fixed density networks, the per-
formance of network coding is potentially much better as
we scale the number of nodes, network area, and network
diameter, though this is also the scenario where existing
packet forwarding and network coding protocols perform
most poorly (relative to the lower bounds).
In future work, we will address some of the open is-
sues. For example, while we selected XOR coding over
PDP and SMF due to its performance and direct compa-
rability with the underlying packet forwarding protocols,
the majority of network coding protocols implement
(random) linear network coding. We are currently de-
veloping our own random linear network coding protocol
that supports coding across data generated from multiple
sources and will compare its performance against other
protocols and the lower bounds derived here. We will
also explore further network characteristics to more
clearly identify what networks benefit most from net-
work coding, and, conversely, in what scenarios the ad-
ditional overhead due to network coding is not worth the
limited additional gain. For example, based on our ob-
servations to date, it seems that both network density and
network diameter are important factors to consider.
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