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Development of an intelligent end-to-end solution for urban infrastructure-to-vehicle (I2V) and

vehicle-to-vehicle (V2V) data delivery schemes

Jean Pierre Cances

To cite this version:

Jean Pierre Cances. Development of an intelligent end-to-end solution for urban infrastructure-to- vehicle (I2V) and vehicle-to-vehicle (V2V) data delivery schemes. [Research Report] Xlim. 2014.

�hal-03134849�

(2)

XLIM/C2S2/ESTE Contribution ITACAS Décember 2011 :

Development of an intelligent end-to-end solution for urban

infrastructure-to-vehicle (I2V) and vehicle-to-vehicle (V2V) data delivery schemes

JP CANCES, Xlim UMR 7252

I. Introduction, summary:

In this proposal the goal is to present an end-to-end solution for urban infrastructure-to-vehicle (I2V) and vehicle-to-vehicle (V2V) data delivery based on some new coding scheme concepts.

The two main solutions we want to explore concern first the use of mobile users as active relay stations and secondly we propose to incorporate a class of unequal error protection (UEP) rateless codes based on Raptor code design. The use of mobile users as active relay stations may be attractive in a highly loaded network to reduce the number of access points (AP’s). Furthermore, the use of rateless codes together with relaying techniques presents a lot of potential advantages.

In networks with unpredictable dynamics such as traffic road networks, rateless codes are always able to work close to the theoretical channel capacities even in the presence of deep fading conditions and the innovative nature of each encoded packet makes both time-consuming retransmission and content-reconciliation mechanisms unnecessary. The use of unequal error protection (UEP) allows separation of delivered data in importance classes with different error protection and recovery time, enabling mobile users to retrieve rapidly the most important information with short delay. Hence, the new proposed transmission scheme can be well adapted to time-critical services. The addressed urban communication scenario may consist for example of large number of sensors that relay traffic flow information to network of access points (AP’s).

AP’s classically use the existing underlying communication infrastructure such as metropolitan area networks (MAN’s) to exchange traffic flow data, encode it using our proposed Raptor based rateless coding schemes, and finally disseminate it to roaming vehicles that join the network service in ad-hoc manner in order to retrieve information about the surrounding environment.

Typical application in vehicles concern real-time applications such as frequent periodic reporting of urban traffic conditions to improve the free traffic flow in big urban centers to save carbon dioxide.

II. Introduction, motivation and state of art:

Intelligent Transport Systems (ITS’s) represent a promising research area for real-time traffic

reporting and management to avoid for example traffic congestion in case of accidents. A lot of

projects at European level have already been conducted in this field [1-6]. ITS services availability

usually relies on the presence of an infrastructure which comprises typically fixed devices or

sensors interconnected by an underlying network, either wired or wireless. In the proposed study

the sensors are constituted by the vehicles themselves, no terrestrial fixed sensor network is

supposed present. Data exchange toward or from mobile terminals is inherently wireless since

information should directly reach the derivers through their smart phones or personal digital

assistant’s (PDA’s). To obtain a new standard transmission for this kind of application, the IEEE

802 committee has activated 11p Task Group to define a WI-FI extension for Wireless Access in

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Vehicular Environments (WAVE) [7]. Wireless connections can also be used to gather data from different sensors and to relay information to the core network [8].

Several communication paradigms are possible for this context. The case in which Access Points (AP’s) allow mobile nodes to join the network is referred to as infrastructure to vehicle (I2V) and comprises various advanced applications such as web surfing, multimedia streaming, remote vehicle diagnostics, real time navigation etc... On the other side, vehicle-to-vehicle (V2V) communications represent the option in which mobile nodes can directly communicate to each other without any need of infrastructure.

III. Examples of V2V communication protocols:

In this case, to help the communication between remote mobile terminals, the use of some mobile users acting as relay is sometimes necessary. A lot of works have been carried out in the field [9- 15]. However, the use and the design of rateless codes for relaying purpose is not clearly defined in such a context. One of our identified main tasks will consist in proposing new protocols for relay transmissions within the IEEE 802 11p frame. For example, we propose to use the basic following transmission protocol in the context of a vehicular multi-relay decode and forward (DF) system in which the mobile source transmits using rateless codes. In such context, the relay with the best source-relay (SR) channel will be the first to decode the source’s packet as it accumulates mutual information at the fastest rate. Thus, relay selection automatically occurs without channel state information (CSI) at the source. This fact could be exploited in the following way: the source broadcasts its rateless coded bits until the L >1 relays successfully decode the packet and send ACKs back to the source. Thereafter, these relays re-encode the packet using rateless codes and transmit it to the destination simultaneously over non-interfering channels. The other relays discard their received and processed signals of this packet. The destination then receives the packet from the L transmitting relays, and decodes it. Once the destination has decoded the packet, the source starts transmitting the next packet. Other protocol solutions, particularly those concerning the choice of relays, should be taken into account. We have already made some works on the field even if it was not related to the context of mobile to mobile communications [16].

Raptor codes are very famous rateless codes, they are made of the concatenation of an inner Luby transform (LT) code to provide the rate compatibility and a high-rate outer code to reduce the error floor of the LT code, and can approach the capacity limit of the additive white Gaussian noise (AWGN) channel with the optimized profile. The challenge we have to cope with is clearly to find the optimum parity generation profiles for LT encoding. The use of differential evolution algorithm together with the density evolution and its approximation by a mixture of Gaussian distributions are powerful tools to obtain it.

IV. Examples of I2V communication protocols:

Concerning the case of I2V communication schemes, the urban environment is typically composed of a large number of mobile users that are likely to quickly change their reference AP’s.

Due to frequent disconnection and reconnection procedures, it may not be viable to deliver the

total amount of required data to a mobile user within a single session. This is due to the fact that

mobile urban channels may encounter long deep fading periods that introduce additional delays

for data retransmissions in the case of Transmission Control Protocol (TCP) traffic or sensibly

lowers the data reliability in the case of User Datagram Protocol (UDP) traffic [17-18]. As the

proposed application scenario we target is concerned with fast and efficient information retrieval,

these drawbacks can be solved by introducing an appropriate data dissemination algorithm,

enhancing the information delivery throughout the network without an excessive overload in terms

of total packet transmissions. In general, content distribution through overlay networks is more

efficient when compared to traditional solutions using multiple unicasts. In order to achieve higher

throughput and failure resilience, parallel downloading from multiple overlay nodes represents a

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typical approach in recent proposals [19]. However, the same content may be unnecessarily supplied by multiple nodes, rising the problem of content reconciliation, which is usually a time and bandwidth consuming operation [20]. This can be avoided by employing rateless codes [21]

for data dissemination in vehicular networks as proposed in [22]. Potentially infinite number of encoded rateless packets can be created and delivered from any AP to connecting vehicles and each encoded packet is an independent, novel and innovative representation of the data, thus decreasing conflict and duplicate occurrences in parallel downloading.

The originality of our proposed scheme lies in the fact that we propose Unequal Error Protection (UEP) Rateless Codes to cope with the problem of high priority messages which have to be delivered with maximum reliability. Using LT codes, a transmitter can generate potentially infinite amount of encoded symbols from k information packets of a source block. LT encoding is a simple process where, for each encoded packet, a degree d is sampled from a degree distribution

( ) d

 , and d out of k information packets from the source message are uniformly selected and bit- wise XOR-ed to produce the encoded packet (see Fig. 1).

Fig. 1: LT codes

Fig. 2: EWF codes (1+).k encoded symbols

k information symbols

1 2 k

1

k

2

k

i

k

r

= k

innermost window

ith window

outermost window

(5)

The design of the degree distribution  ( ) d that will enable source message recovery from any slightly more than k received encoded symbols using the iterative Belief-Propagation (BP) decoding algorithm is fundamental to the LT code design. This problem has been addressed in [23] by using the so-called robust soliton degree distribution. Using this distribution it is possible to recover the source message from any k’ encoded symbols where k’ k asymptotically, with encoding/decoding complexity of the order  ( .log ) k k . However, to obtain linear encoding- decoding complexity with capacity-approaching performance, a reduced complexity inner LT code can be concatenated with an outer high-rate LDPC pre-code, resulting in a class of rateless codes called Raptor codes [24]. The optimization of such codes is quite complex and we propose a first approach in Appendix 1.

V. Network architecture:

The addressed urban communications scenario is modelled as a two level network as shown on the figure just before. In particular, the lower level is composed of a large number of sensor nodes (SN’s) positioned in such way that suitable and effective sampling of the road traffic is achieved within the area of interest. These sensor nodes are the cars themselves. Their goal is to collect traffic flow information such as average crossroad waiting times, presence of roadworks or accidents etc … and relay it to the higher layer AP network consisting of interconnected AP’s, where a subset of SN’s is connected in a star-wise or tree topology to an AP. The proposed network architecture is completely similar to those of a classical 3G; in this case AP’s would be replaced by Base Stations (BS’s) additionally endowed with a Wireless Personal Area Network (WPAN) interface in order to be connected with SN’s.

Fig. 3: Example of network architecture

An example of network architecture is depicted on Figure 3. Upon reception of SN data, AP’s exchange and encode data packets and broadcast the encoded data to Mobile Users (MU’s). MU’s can join the network without need of association with a specific AP by adopting a passive operation mode and continuously collecting information regarding the surrounding environment broadcasted by AP’s. MU’s are getting involved in the data dissemination algorithm as they

AP

AP

MAN

optical links

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operate both in transmit and receive mode. Furthermore, we assume that MU’s have on-board capabilities to process the downloaded data in order to interpret current traffic information.

Specifically, the collected real-time data provide opportunity for on-board computer to perform optimal route calculation, delay estimates and display visual map representation of critical locations.

Data processing will be implemented in an automatic periodic manner in order to guarantee as much as possible real-time monitoring of the traffic-load conditions. This mode of operation makes MU’s informed about dangerous situations (e.g. accidents) in a short time span, hence allowing for increased safety of people and vehicles.

Moreover, we think that it is important to introduce the concept of spatial importance of gathered data where the traffic data spatially closer to the MU is considered more important and is required with minimum reconstruction delay as compared to the traffic data originating in more distant parts of the sensed environment. Each AP is independently able to organize the data to be distributed to MU’s into several classes of different spatial importance by defining the set of appropriate expanding windows. EWF codes are then designed and applied in order to enable MU’s to download the most important data class more quickly and reliably, and the remaining importance classes with progressively decreasing reliability and increasing reconstruction delay.

The communication between MU’s and AP’s is assumed to be wireless. As recently shown, IEEE 802.11p standards demonstrate significant potential for vehicular applications. The communication between AP’s is accomplished by leveraging on a pre-existing infrastructure deployed in an urban area, i.e., connecting AP’s to wired Metropolitan Area Network (MAN) comprising high rate optical links. One can remark that the proposed network architecture fits in the infrastructure mode of the IEEE 802.11 standard in which AP’s are interconnected using an external distributed system, forming an Extended Service Set (ESS).

VI. Data gathering, Exchange, Encoding and Dissemination

We describe here the I2V main communication protocols, taking into account the use of EWF codes. The V2V communication protocols constitute a big challenge and are by far more complicated to define and describe. We have detailed one of the main difficult tasks we want to deal with in this field in Section III. It will constitute the main bottleneck of our project.

Concerning I2V communications, the system application, residing in AP’s, periodically performs the following four procedures: (i) data gathering from MU’s acting as sensor nodes, (ii) data exchange with other AP’s, (iii) encoding and (iv) disseminating encoded data to MU’s. We refer to these four stages as upload, exchange, encoding and download phase, respectively, and the period encompassing all of them as data refreshment period. According to the IEEE 802.11 standard, the link time in every AP coverage zone is divided in superframes [25], and the data refreshment period in each zone is aligned with superframe boundaries (see Fig. 4).

Upload, exchange and encoding delay

Other AP services Other AP services

(BC)

T

SF (BC)

T

SF

EE

UL

T

SF

T

SF

T

SF

T : data refreshment period

DL

download delay

(7)

Fig. 4: Data refreshment of the proposed application

During the upload phase, every AP polls all MU’s in its domain and collects the most recent measurements. As typically foreseen by most of the IEEE 802.11 standards, superframes are divided into the Contention-Free Period (CFP) and Contention-Based Period (CBP) where the former is used to avoid MAC collisions and deliver prioritized information. The polling phase can be accomplished within the CFP part of a typical frame. In particular, it starts after an AP beacon with a field dedicated to delivery traffic information map. As a consequence, the MU’s associated with AP become aware of CFP beginning and avoid entering a contention for a time interval equal to CFP duration. Then, AP individually polls each station with a poll message and waits for responding data and acknowledgement messages. We assume that AP’s are globally synchronized over the AP network, so the upload takes place in the first superframe period following the start of the data refreshment period. Each MU uploads its measurements within a single data packet of length L bits. Possible packet losses are managed by means of Automatic Repeat reQuest (ARQ) scheme, so that from an application point of view, data delivery could be considered reliable.

After the upload phase, each AP stores and uniquely indexes each received data packet, where the indexing scheme is known to all AP’s. The total number of stored data packets in APs network per data refreshment period is k. The k data packets represent a single data generation upon which the UEP rateless coding is performed. The differentiation among data generations can be achieved using an appropriate field in the packet header, allowing MU’s to maintain global time-references.

The data generation is distributed over all AP’s in the network and each AP contains only a subset of packets of the data generation. Therefore, prior to the encoding phase, each AP has to collect missing parts of the data generation from other AP’s, which is done during the exchange phase.

Ideally, during the exchange phase, each AP exchanges its own part of the global data generation with other AP’s. However, for large AP network, this may present a sizable communication burden on the infrastructure MAN. Therefore, for large AP networks, a separation into AP regions is possible where each AP would frequently exchange its data with the AP’s within the region it belongs to, and less frequently with the remote regions of the AP network.

After the exchange phase, the system application in each AP in the network performs EWF encoding over the data packets of a single generation. Prior to encoding, each AP defines the set of data importance classes by introducing the set of expanding windows over the data block to be transmitted. In addition, AP selects parameters of the EWF code to be applied: window selection distribution  ( ) x and the set of degree distributions 

( )i

( ) x for each of r windows. The division of the data block into importance classes or windows may be defined for each AP in advance. For example, an AP may select all the data exchanged with its neighboring AP’s as the most important data, and the data gathered from the remaining (non-neighbouring) AP’s as the least important data. Following the appropriate EWF code design, each AP independently produces a given number of EWF encoded packets. This number is chosen such that it is sufficient for successful data recovery of all data importance classes by the majority of MU’s with high detection probability.

In the final download phase, each AP disseminates EWF encoded packets by simply broadcasting

them to mobile users currently located in its coverage area. This approach is interesting since it

minimizes the complexity and the power consumption of MU receiver by always keeping it in a

receiving mode. The dissemination starts in the first superframe that follows the encoding phase,

and lasts until the next data collection phase (i.e. the next data refreshment period). For the

purpose of broadcasting it is natural to use the CFP part of the superframe, as it guarantees

delivery of traffic-info updates to all MU’s within the service area. While travelling within the

service area, each MU performs a channel sensing at periodic intervals and dynamically selects the

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best carrier while transparently roaming among adjacent AP’s. MU continuously downloads EWF encoded packets from each AP it is associated to, until it has enough data to recover the complete information using the BP algorithm. It is important to note that the decoding algorithm needs to be aware of the importance structure imposed by each AP over the data generation, as long as all the AP’s, which provide MU’s with encoded data, perform EWF coding over the same identical source message.

As the reception of packets and decoding progresses, a MU will sequentially recover data from consecutive importance classes, starting with the most important class. The average number of excessive encoded packets needed for recovering the k

i

data packets contained in the i-th window is measured by the reception overhead 

i'

. For successful recovery of the first i important classes, MU needs on average k

i'

  (1 

i'

). k

i

encoded packets, where 

i'

should be as small as possible positive number. Anyway, as differences among various k

i

can be significant, the number of received packets needed to recover the corresponding class will be also different. A small k

i

will cause small k

i'

and therefore, short recovery time. Apart from the values of k

i

, the differences in recovery times of importance classes are affected by the choice of window selection distribution

(x) and corresponding degree distribution 

( )i

( ) x .

Finally, since each encoded packet is an innovative representation of the original data, any subset of k

'

  (1 

'

). k received encoded packets allows for restoration of the whole original data.

Therefore, EWF codes, as a class of rateless codes, are suitable candidates to be used at the application level for content delivery in vehicular networks, as packet losses caused by the varying link characteristics are compensated simply by reception of the new packets without need for time-consuming TCP-like acknowledgement-retransmission mechanisms. Moreover, the division of data into importance classes by spatial criteria means that the importance classes of neighbouring AP’s significantly overlap. When entering a new AP coverage zone, partially reconstructed data from the previous zone should preserve retrieval times of the importance classes in the new zone. Finally, the flowchart of Fig. 5 illustrates the above described process of data gathering, encoding and dissemination.

MU SN send measured data to AP’s

AP’s exchange data

Each AP encodes data using its spatial importance division, applying predefined

number of data importance classes

Each AP broadcasts data to MU’s in its coverage zone

MU’s progressively recover data from consecutive importance classes, starting with the most

important class

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Fig. 5: Flowchart of the proposed application scenario Appendix 1: Optimization of Raptor codes

We propose in this work to jointly optimize the LT Fountain and the Precode; usually in the scientific literature, the two components of a Raptor code are sequentially decoded. To do that we propose an asymptotic analysis of the joint LT Fountain and Precode coder, by means of a Gaussian approximation on an AWGN channel.

We call input symbols the information symbols to be transmitted and output symbols the redundant symbols produced by the fountain. A LT code which can be considered as a LDGM code (Low-Density Generator-Matrix) is completely characterized by the degree distribution (DD) of its output symbols. To obtain an output symbol we retrieve a random variable d according to the Soliton distribution. The output symbol is the modulo 2 sum of d input symbols retrieved randomly from the K input information symbols. In this case, the d input symbols and the output symbol are implied in a parity check equation. Given

1

,

2

,...,

dc

   a distribution of discrete probability over 1,…,d

c

with 

d

representing the probability of obtaining a degree d output symbol. The degree distribution (DD) is represented by its generator polynomial form:

1

( ) .

dc

i i i

x x

    . We can associate this distribution with the following branch degree distribution:

1 1

( ) . '( ) / '(1)

dc

i i i

x x x

 

     . The input symbols are chosen according to an uniform law, this entails that their degree distribution follows a binomial law and it can be approximated by a Poisson law of parameter  : I x ( )  e

(x1)

. The associated branch distribution is then given by:

v

1 1

( ) '( ) / '(1)

d i i i

l x l x

I x I

   and is equal to e

 (x1)

. The two distributions have the same mean value .

A Raptor code is built by simply concatenating a LT code with an internal code named precode which is in fact a block error correcting code with a high rate. Despite their name, it is always possible to define a rate for a fountain code and this rate is given by: R   '(1) /  . For a given channel capacity C, this rate is related to a quantity  named overhead which represents the difference with the real capacity. We have the following relationship: C   (1  ) R . In the same way as for LDPC codes it is possible to represent Raptor codes by a bipartite graph as it is illustrated on Fig. 3 below.

Fig. 3: bipartite Tanner Graph for a Raptor code

Input symbols

Precoder Code LT Interleaver variable node

parity check node

(10)

Optimization step: We can consider the analysis of EXIT transfer functions over an AWGN channel with binary inputs.

Density evolution: we denote x

c( )vl

(resp x

v( )lc

) the mutual informations which are associated to the messages on a branch linking a parity check node to a variable node (resp a variable node to a parity check node) during the l

th

decoding step of the BP algorithm.

Fig. 4: Density evolution study

We denote x

ext( )l

as the mutual information for the messages from the fountain to the precoder at the l

th

decoding step. The transfer function of the precoder is written T: xT x ( ) , it represents the transform of the mutual information which transits from the precoder to the fountain. The mutual information associated to the messages given by the precoder to the LT code is then equal to

( )

(

extl

)

T x . Concerning the optimization step we can suppose that T(.) is known either numerically or analytically. Under some given assumptions [26-27] and in the context of a LDPC precoder which is described by polynomial forms (x) and  ( ) x , the transfer function T may be analytically expressed as:

v

1 1

2 2

( ) [ (1 [( 1) (1 )])]

d dc

i j

i j

T xJ i J

J j J

x

      (1)

With:

2 2

( ) 1 1 log (1 ).exp( ( ) / 4 ).

4. .

u R

J x e u x x du

x

   

  (2)

Remark: J(x) has all the necessary desired properties to guarantee the existence of the reciprocal function J

1

( ) x . Using the above mentioned notations we can write the following equations which correspond to the updating of input information at the entries of variable and parity check nodes.

a- updating of messages from variable to parity check nodes:

v

( ) 1 ( 1) 1 ( 1)

v ext

2

[( 1) ( ) ( ( ))]

d

l l l

c i u

i

x l J i J

x

J

T x

    (3)

b- updating of messages from parity check nodes to variable nodes:

( ) v l

x

c (l 1)

x

ext

( 1)

(

extl

) T x

( ) v

l

x

c

Parity check node Input symbol

Output symbol

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( ) 1 ( )

v v 0

1

1 . [( 1). (1 ) ]

dc

l l

c j c

j

xJ j J

x f

      (4)

With: f

0

J

1

[1  J (2 / 

2

)] (5)

c- updating of the information delivered by the precoder:

( ) 1 ( )

ext

[ . (

v

)]

dc

l l

i c

i

x   I J i J

x (5) Reporting (3) into (4) we obtain the definite recursion equation:

v

( ) ( 1) 2

v v

1 1 ( 1) 1 ( 1)

v ext 0

1 1

( , , (.))

1 [( 1) [1 (( 1) ( )) ( ( ))] ]

c

l l

c c

d d

l l

j i c

j i

x F x T

J j J l J i J x J T x f

         (6)

We can see that, for a given a distribution l(x), expression (6) yields to a linear form for distribution (x) and this is indeed a remarkable property which enable to use standard optimization tools.

In order to conduct the optimization steps, there are some necessary conditions to guarantee the convergence of the optimization [27].

Condition 1 (starting condition): The decoding can begin if and only if F (0, 

2

)  0 and we have the following relationships:

(0,

2

)

F      

1

 / (2 / J

2

) (7)

We can see that it’s mandatory to use a given number of degrees one in the distribution degrees,  is thus a parameter which directly influences the optimization problem. Furthermore, we know that the condition F '(0, 

2

) 1  holds for a distribution which enables to reach the capacity of a Gaussian channel. This condition can be translated into (8):

'(0,

2

) 1

F    

2

 1/ .  e

f0/ 4

(8)

This gives a condition on the number of degrees two in the distribution degrees.

Distribution optimization: The optimization of the distribution  ( ) x consists in finding a distribution which maximizes the coding rate of the fountain in order to minimize the gap with the theoretical capacity. This is equivalent to the maximization of '(1) .

i

i

   i  or, in other words, this is equivalent to the minimization of

i

/

i

i

 . Since equation (6) is linear in terms of 

i

we can write the distribution optimization algorithm under the following form:

( ) arg min

( )

/

opt x j

j

x

j

    (9)

(12)

With the following constraints :

[C1]

i

1

i

 

[C2] F x ( , 

2

)  x   x [0; x

0

  ] with  >0 [C3] F (0, 

2

)   with > 0

[C4] F '(0, 

2

) 1 

The parameters , d and d

c

are the main optimization parameters. Their influence has been studied in [27]. It is demonstrated that the most influent parameter is the mean  of the input distribution.

References

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[16] Référence public Amir Minaee à PIMRC 2011 ou à ISCLD 2011.

[17] V. Bychkovsky, B. Hull, A. Miu, H. Balakrishnan and S. Madden, “A Measurement Study of Vehicular Internet Access Using in Situ WIFI Networks”, In Proc of ACM Mobicom 2006, Los Angeles, USA, Sept. 2006.

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IEEE Infocom 2004, Hong Kong, March 2004.

[19] C. Wu and B. Li, “Outburst: Efficiency Overlay Content Distribution with Rateless Codes”, in Proc. IFIP Networking 2007, Atlanta, USA, May 2007.

[20] J. Byers, J. Considine, M. Mitzenmacher and S. Rost, “Informed Content Delivery Across Adaptive Overlay Networks”, in Proc. ACM SIGCOM 2002, Pittsburg, PA, USA, August 2002.

[21] J. Byers, M. Luby and M. Mitzenmacher and S. Rost, “A Digital Fountain Approach to

Asynchronous Reliable Multicast”, IEEE J. Sel. Areas Commun., vol. 20, n°8, pp. 1528-1540,

October 2002.

(13)

[22] P. Cataldi, A. Tomatis, G. Grilli and M. Gerla, “A Novel Data Dissemination Method for Vehicular Networks with Rateless Codes”, in Proc. IEEE WCNC 2009, Budapest, Hungary, April 2009.

[23] M. Luby, “LT Codes”, in Proc. IEEE FOCS 2002, Vancouver, BC, Canada, November 2002.

[24] A. Shokrollahi, “Raptor Codes, IEEE Trans. Inform. Theory, vol. 52, n°6, pp. 2551-2567, June 2006.

[25] IEEE, “IEEE 802.11-2007 Wireless LAN Medium Access Control and Physical Layers Specifications”, June 2007.

[26] A. Venkiah, D. Declercq, and C. Poulliat. Design of cages with a randomized progressive edge-growth algorithm. Communications Letters, IEEE, 12(4):301-303, Apr. 2008.

[27] A. Venkiah. Analysis and Design of Raptor Codes for Multicast Wireless Channels, PhD

thesis, Université de Cergy-Pontoise, November 2008.

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