Wireless Communications and Mobile Computing
(IV) data transmissions. However, since the available spec-
trum resources allocated to vehicular networks are in general
limited, having a large number of infrastructures may also
generate severe cochannel interference issues and hence aect
the quality of service (QoS) in practice.
e analysis of IV transmission strategies has been
investigated by several recent research works. It has been
shown that properly designed transmission schemes can lead
to signicant performance improvement in terms of en-
hanced capacity [] and energy eciency [, ] and reduced
delay [, ]. However, in most current works, all roadside
infrastructures and vehicles are considered to be located
along a single road. Hence each vehicle’s desired signals
and interference signals are modeled to come from a one-
dimensional space. Clearly this is hardly the case in practice,
sincenormallytherearemultipleroadswithinacertainarea
and the interference signals may come from all directions.
e deployment of multiple roads is taken into account
in []. But all infrastructures are still assumed to locate
only along each road, which leads to the one-dimensional
homogeneous Poisson point processes (H-PPPs) model.
It is expected that multiple types of infrastructures (e.g.,
eNodeBs) can serve to provide IV communication appli-
cations. Hence this model may still be unable to reect the
most general conditions in future ITS, where some cochannel
interference generators may randomly distribute in the D
space [].
To further improve the performance of IV commu-
nications, [–] propose using extra relay terminals (e.g.,
vehicles running on the roads) to assist in the message
delivery procedure. Requiring relays to repeat the infrastruc-
ture messages would provide vehicle receivers with spatial
diversitygainthatcancombatthenegativeimpactofthe
complex fading and interference characteristics in vehicular
communication environments. Although clear performance
enhancement can be observed, the repetition coding opera-
tion adopted at relays may in fact still be spectrally inecient
[]. is is because that each relay uses multiple orthogonal
channels to separately repeat the source’s messages, which
potentially requires an unnecessarily large channel usage. It is
wellknownthatforthisissuetheconceptofnetworkcoding
[] serves as an elegant solution. Instead of individually
retransmitting the source messages, each relay combines
them to form a new codeword such that a single channel
usage suces to deliver it to the intended destination. To real-
ize ecient transmission of multiple independent messages, a
class of maximum distance separable nite-eld network codes
(MDS-FFNCs), whose coding principle lies in the summation
in higher order nite elds, is hence proposed by [].
In this paper, we propose applying MDS-FFNC to relay-
assisted IV communications in ITS. e system model
considers the wireless distribution of multiple independent
messages from roadside infrastructures to the vehicles in
their coverage areas. Some vehicles can be selected to act
as relays and apply MDS-FFNC to assist in the IV trans-
missions in order to improve system performance. Based on
stochastic geometry, the distribution of vehicles and roadside
infrastructures are modeled following two independent PPPs.
We derive the successful transmission probability in such
a complex system. rough comparisons with the classic
direct IV transmissions, the potential benets of exploiting
relay and network coding techniques in IV communication
systems are exhibited.
e remainder of this paper is organized as follows.
We rst present the system model and our proposed trans-
mission scheme in Section . e successful transmission
probability analysis is introduced in Section . Section
demonstrates comparisons between our proposed scheme
and two benchmark schemes via numerical results. Finally,
Section concludes the paper.
2. System Model
In this section, we rst introduce the system model and then
present the proposed network coding based relay-assisted
IV transmission process.
2.1. System Model. We consider an urban road system in the
innite plane R
2
with a lattice pattern as shown in Figure (a).
e system consists of many horizontal roads separated
by distance
road,𝑋
meters (denoted by
𝑖
,∈Z and
Z {...,−1,0,1,...})andmanyverticalroadsseparatedby
distance
road,𝑌
meters (denoted by
𝑗
,∈Z). It is common
toseethiskindofroadsysteminmanycities,suchasNew
YorkandBarcelona[].elocationsofthevehiclesrunning
on these roads are considered to be distributed following one-
dimensional H-PPPs []. e wireless transceiver module
equipped at each vehicle is activated with a certain probability
to broadcast the vehicle’s status information to surrounding
vehicles. At any time instant, the simultaneously activated
vehicles running on the horizontal road
𝑖
, denoted by a
set Π
𝑋
𝑖
, can thus be modeled by a PPP with density
𝑋
𝑖
.
Similarly, the simultaneously activated vehicles running on
the vertical road
𝑗
, denoted by set Π
𝑌
𝑗
,aremodeledbya
PPP with density
𝑌
𝑗
. e ITS infrastructures are assumed to
be randomly deployed in the plane R
2
. Each infrastructure
is also activated with a probability to broadcast trac status
information to the vehicles running on a road (these vehicles
would normally be interested in the same information)
within its coverage area. At each time instant, the locations
of the simultaneously activated infrastructures, denoted by
asetΠ
𝑆
, can be modeled to follow an independent two-
dimensional PPP with intensity
𝑆
[].
Let us consider the IV information transmission from
one of the ITS infrastructures to one of the vehicles within its
coverage area. Denote the infrastructure by and the target
vehicle by . Without loss of generality, we assume that is
running on the road
0
. intends to send a set of ≥1
independent messages I ={
𝑆
1
,...,
𝑆
𝑀
},whichmaycontain
rich information such as trac lights’ signals, road congestion
status, and speed limits, to .Duetotheothersimultaneously
activated infrastructures and vehicles, the reception of
would be corrupted by cochannel interference so that a
satisfactory quality of message delivery may not be attainable.
To handle this issue, we adopt the concept of cooperative
communications and select a vehicle also running on
0
to
serveasarelaytohelpthrough a vehicle-to-vehicle (VV)