Liang Zhou

Benoît Geller

Xiaojun Wang

Anne Wei

Baoyu Zheng

Han-Chieh Chao

H.-C Chao

Multi-User Video Streaming over Multiple Heterogeneous Wireless Networks: A Distributed, Cross-Layer Design Paradigm

Keywords: cross-layer design, QoS provisioning, video transmission, heterogeneous networks

In this paper, we address the problem of QoS (Quality of Service) provisioning for multi-user video streaming over multiple heterogeneous wireless networks based on the distributed, cross-layer design framework. By jointly considering the rate allocation and the Joint Source-Channel Coding (JSCC), our proposal aims at maximizing the QoS provisioning under the given resource constraint. At first, we develop and evaluate a framework for optimal video rate allocation over multiple networks based on the observed Available Bit Rate (ABR) and the Round Trip Time (RTT) over each access network, as well as the video rate-distortion characteristics. The rate allocation is formulated as a convex optimization problem that minimizes the sum of all video streams expected distortion. Then, we propose an analytical JSCC scheme for error-resilient scalable encoded video, and integrate the JSCC with the specific rate allocation algorithm to improve the constructed video quality by optimally applying the appropriate channel coding rate given the constraints imposed by the transmission rate and the prevailing channel conditions. Objective and subjective simulation results are provided which demonstrate the effectiveness of our proposed joint scheme.

I. INTRODUCTION

As multimedia is expected to be the major traffic source on the next-generation wireless networks, QoS (Quality of Service) provisioning for wireless video transmission has become a critically important issue. In addition, recent years have also witnessed the increasing efforts towards standardization of architectures for convergence of heterogeneous access networks, and moreover, the integration of heterogeneous networks has fully become part of the 4G network design [1]. IEEE 802. 21 [2] is delineating a framework to enable handovers and interoperability between heterogeneous wireless and wireline networks. Therefore, supporting multimedia applications over heterogeneous networks has been one of the main fields of research in the networking and video coding communities. For example, the IMS (IP Multimedia Subsystems) platform [START_REF] Cuevas | The IMS platform: A solution for next generation network operators to be more than bit pipes[END_REF] has defined an overlay architecture for providing multimedia services on top of heterogeneous wireless networks. Note that, the problem of video streaming over heterogeneous networks is further complicated by the heterogeneity of both the video contents and the network conditions.

Up to now, providing a satisfactory communication quality in a heterogeneous wireless system is still a challenging problem because the end-to-end QoS guarantee is difficult to be provided [START_REF] Akyildiz | A ubiquitous mobile communication architecture for next-generation heterogeneous wireless systems[END_REF].

The issue of supporting error-resilient video transport over error-prone wireless networks has received considerable attention recently. [START_REF] Wang | Multiple description coding for video communications[END_REF], [START_REF] Akyol | A Flexible Multiple Description Coding Framework for Adaptive Peer-to-Peer Video Streaming[END_REF], [START_REF] Wang | Multiple-Description Coding for Overlay Network Streaming[END_REF], and [START_REF] Radulovic | Multiple Description Coding with Redundant Expansions and Application to Image Communication[END_REF] presented some source coding-based approaches that divide the original bit-stream into multiple streams, called Multiple Description Coding (MDC), to tradeoff the error-resilience and the coding complexity; [START_REF] Kim | Distributed Video Streaming Using Multiple Description Coding and Unequal Error Protection[END_REF] and [START_REF] Tian | Robust and efficient path diversity in application-layer multicast for video streaming[END_REF] amplified the benefits of using MDC by combining it with path diversity; in this context, each stream is explicitly transmitted over an independent path to the receiver in order to achieve higher tolerance to packet loss and delay due to network congestion. In [START_REF] Fu | A Joint Source and Channel Coding Algorithm for Error Resilient SPIHT-Coded Video Bitstreams[END_REF], [START_REF] Qu | An Adaptive Motion-Based Unequal Error Protection Approach for Real-Time Video Transport Over Wireless IP Networks[END_REF], and [START_REF] Chan | Video Loss Recovery With FEC and Stream Replication[END_REF], the effect of different FEC (Forward Error Correction) coding schemes on reconstructed video quality had been investigated. In order to trade-off between the sustained quality of video stream and the network capacity, [START_REF] Setton | Rate-distortion analysis and streaming of SP and SI frames[END_REF], [START_REF] Chakareski | Rate-Distortion Optimized Distributed Packet Scheduling of Multiple Video Streams over Shared Communication Resources[END_REF], and [START_REF] Vleeschouwer | Dependent packet transmission policies in rate-distortion optimized media scheduling[END_REF] investigated the impact of the operating rate on the overall video quality; [START_REF] Zhu | Joint Routing and Rate Alloction for Multiple Video Streams in Ad Hoc Wireless Networks[END_REF] discussed both centralized and distributed solutions for joint routing and rate allocation of multiple video streams in wireless ad hoc networks. Moreover, the rate adaptation of multimedia streams was studied in the context of heterogeneous networks in [START_REF] Szwabe | Dynamic multimedia stream adaptation and rate control for heterogeneous networks[END_REF], where the authors proposed an architecture to allow online measurement of network characteristics and video rate adaptation via transcoding. Typically, for real-time video communications over wireless networks, there are two main factors which can greatly affect the perceived video quality: the operating rate and the transmission error. On one hand, for video streaming, high bandwidth requirements are coupled with tight delay constraints as packets need to be delivered in a timely fashion to guarantee continuous media playout. More specifically, if the operating rate is higher than the optimal transmission rate along a path, many packets will be discarded due to late arrival caused by congestion. On the contrary, if the operating rate is lower, performance loss will occur due to the source coding inefficiency. Hence, a rate control scheme is both desirable and necessary to achieve a satisfactory level of received video quality over wireless networks. On the other hand, transmission errors are generally caused by multi-path channel fading, interference from other electronic devices, and node mobility [START_REF] Chan | Video Loss Recovery With FEC and Stream Replication[END_REF]. In addition, most of the video compression coding standards, including MPEG-4 and H.264, are designed to achieve high compression efficiency at the expense of error-resilience. This poses a severe problem, namely error propagation, where errors due to packet loss in a reference frame propagate to all of the dependent frames leading to visual artifacts that can be long lasting and annoying [START_REF] Martini | Content adaptive network aware joint optimization of wireless video transmission[END_REF], [START_REF] Shiang | Multi-user video streaming over multi-hop wireless networks: a distributed, cross-layer approach based on priority queuing[END_REF]. To provide a reasonable QoS, it is important that the source coders be both error-resilient and network-adaptive. In order to achieve improved video quality supported by heterogeneous wireless networks, and to provide an overall more robust video delivery system, these two factors are jointly considered in this paper.

In this work, we explore the potential synergies of exchanging information between different layers to support video streaming over heterogeneous wireless networks. The main contributions and novelties of this paper are: (1) developing a framework for optimal video rate allocation over heterogeneous networks, based on the observed ABR (Available Bit Rate) and the RTT (Round Trip Time) over each network as well as the video rate-distortion characteristics; (2) proposing an analytical JSCC (Joint Source-Channel Coding) scheme for error-resilient scalable encoded video, in which the video sequence is encoded into multiple independent streams based on 3-D SPIHT (Set Partitioning In Hierarchical Trees) algorithm and each stream is assigned a FEC (Forward Error Correction) code to avoid error propagation; (3) integrating the JSCC with the specific rate allocation algorithm, which optimally applies the appropriate channel coding rate given the constraints imposed by the transmission rate obtained from the proposed rate The rest of the paper is organized as follows. In Section II, we propose a cross-layer distributed rate allocation scheme for multiple video streaming sessions sharing multiple heterogeneous networks. In Section III, an analytically optimized JSCC is proposed given the optimal transmission rate and the prevailing channel conditions. We present some selected simulation results for the proposed joint scheme transmission over heterogeneous wireless networks in Section IV, and finally make some concluding remarks in Section V.

II. CROSS-LAYER RATE ALLOCATION SCHEME

In this section, we address the problem of rate allocation among multiple streams over multiple heterogeneous networks. At first, we propose a distortion model which captures both the impact of the encoder quantization and the packet loss on the overall video quality caused by the operation rate. Then, a distributed rate allocation scheme is presented to minimize the distortion, in which some cross-layer information exchange ensures that the allocated rates are updated according to changes in network conditions.

A. Distortion Model

In general, the reconstructed video quality is affected by both the source compression and the quality degradation due to packet losses caused by either transmission errors or late arrivals.

Here, we assume that the two forms of induced distortion are independent and additive. Thus, we can calculate the overall distortion D all as:

D all = D comp + D loss (1)
where the distortion introduced by quantization is denoted by D comp , and the additional distortion caused by packet loss is denoted by D loss . According to [12], the distortion caused by source compression can be approximated by:

D comp = θ R -R 0 + D 0 (2)
where R is the rate of the video stream, θ, R 0 and D 0 are the parameters of the distortion model which depend on the encoded video sequence as well as on the encoding structure. Using nonlinear regression technique, these parameters can be estimated from empirical rate-distortion curves obtained by encoding a sequence at different rates [START_REF] Zhu | Rate Allocation for Multi-User Video Streaming over Heterogenous Access Networks[END_REF]. Likewise, the distortion caused by packet loss can be modeled by a linear model related to the packet loss rate P loss :

D loss = αP loss (3)
where α depends on parameters related to the compressed video sequence, such as the proportion of intra-coded macro-blocks and the effectiveness of error concealment at the decoder [12]. The packet loss rate P loss reflects the combined rate of random losses and late arrivals of video packets. In a bandwidth-limited network, this combined loss rate can be further modeled based on the M/M/1 queuing model. In this case, the delay distribution of packets over a single link is exponential [START_REF] Zhu | Rate Allocation for Multi-User Video Streaming over Heterogenous Access Networks[END_REF]. Note that, since the end-to-end delay of packet delivery in wireless network is dominated by the queuing delay at the bottleneck link, the empirical delay distribution for realistic traffic patterns can still be modeled by an exponential formulation:

P r{Delay > T } = e -λT ( 4
)
where P r{•} denotes probability, T reflects the delay constraint and λ is the arriving rate which is determined by the average delay:

λ = 1 E{Delay} (5)
E{•} represents the expectation value. Generally, λ needs to be determined empirically from end-to-end delay statistics over the network. In order to present a general solution for online operation, here we construct a model to approximate the average packet delay.

Consider multiple wireless networks N = {1, 2, ..., N } simultaneously available to multiple users S = {1, 2, ..., S}. Each network n ∈ N is characterized by its Available Bit Rate ABR n and Round Trip Time RT T n , which are measured and updated periodically. It should be noted that as channel conditions in wireless environments change on very short time scales (e.g., up to a few tens of ms), we assume that ABR n and RT T n represent average values computed on a larger time scale (e.g., one to a few seconds), and represent the average channel conditions for user s ∈ S on the given period.

Therefore, the rate allocation can be expressed in matrix form: R = {R n s } S×N , where each element R n s corresponds to the allocated rate of user s ∈ S over network n ∈ N. Consequently, the total allocated rate over network n is R n = s∈S R n s , and the total allocated rate for user s is

R s = n∈N R n s .
We denote RB n , the Residual Bandwidth (RB) over network n, as:

RB n = ABR n - s∈S R n s (6)
From the perspective of user s in network n, the observed available bandwidth ABR n s is :

ABR n s = ABR n - s =s,s ∈S R n s (7)
As the allocated rate on each network approaches the maximum achievable rate, average packet delay typically increases due to network congestion. We use a simple fractional function to approximate the non-linear increase of packet delay with traffic rate over network n ∈ N, as:

E{Delay} = β n RB n = β n ABR n - s∈S R n s (8)
which is reminiscent of the classical M/M/1 queuing model [START_REF] Draper | A universal approach to queuing with distortion control[END_REF]. Assuming equal delay on both directions, the value of β n can be estimated from the most recent observations of RT T n and RB n :

β n = RB n • RT T n 2 (9)
More specifically, if current residual bandwidth is equal to the past observation value for network

n ∈ N (RB n = RB n ), the average current delay is RT T n /2. Therefore, for each network n ∈ N P r{Delay > T } = e -λT = e - 2(ABR n - P s∈S R n s ) RB n RT T n T ( 10
)
Taking into account P n B , the average random packet loss rate in network n ∈ N due to transmission errors, the total packet loss rate in network n ∈ N is then:

P n loss = P n B + (1 -P n B )P r{Delay > T } = P n B + (1 -P n B )e - 2(ABR n - P s∈S R n s ) RB n RT T n T (11)
Therefore, the distortion from packet loss in network n ∈ N can thus be expressed as:

D n loss = αP n loss = α P n B + (1 -P n B )e - 2(ABR n - P s∈S R n s ) RB n RT T n T (12)

B. Rate Allocation Algorithm

Based on the previous discussion, we seek to minimize the sum of the total distortion D all as follows:

min s∈S,n∈N D all (R n s ) = s∈S θ s n∈N R n s -R 0 s + D 0 s + n∈N α P n B + (1 -P n B )e - 2(ABR n - P s∈S R n s ) RB n RT T n T ( 13
)
subject to R n s = ABR n s P n∈N ABR n s R s , ∀n ∈ N R n s ≤ ABR n s , ∀n ∈ N
where θ s , R 0 s and D 0 s are the corresponding parameters for user s ∈ S. Intuitively, reconstructed video quality is limited by coarse quantization at lower rates, whereas at high rates, the video stream will cause more network congestion. This, in turn, leads to higher loss rates and reduces the video quality. For video steaming in bandwidth-limited environments, we therefore expect to achieve maximum decoded quality for some intermediate rate.

In order to get the optimal result with fast convergence adapting to the online operation, we now propose a heuristic approach for solving the rate allocation optimization problem based on the utility framework introduced in [START_REF] Jurca | Joint Network and Rate Allocation for Video Streaming over Multiple Wireless Networks[END_REF], which iteratively takes a locally optimal decision on each user at each network. We define R n s → R n s as the transition of the next allocation rate for the user

s ∈ S in network n ∈ N, R n s = R n s + R n s
, where R n s is the rate improvement varied at each iteration 1 . The utility of this transition can be computed as:

U n s = D all (R n s ) -D all (R n s ) R n s -R n s ( 14
)
1 In theory, the original R n s can be chosen at random as long as it is less than ABR n s ; here the original value of R n s is set to ABR n s /2. The total utility matrix is U = {U n s } S×N . During each iteration, the proposed algorithm finds the R = {R n s } S×N that brings the highest utility U * = {U n s } S×N to the overall system by its transition:

U n s = D all (R n s )-D all (R n s ) R n s -
U * = arg max R U (15)
The proposed rate allocation algorithm is executed by each node (i.e. each user) and starts to allocate resources to user s in network n. Once the resources of the network n are depleted, the algorithm will find a different user that can free the required resources for user s in the other network, by allocating part of its rate. This operation is performed as long as the overall utility of the system is still improved, and as long as free network resources still exist in the overall system. The algorithm stops when there are no more free resources in the network system, or when no other possible user transition can bring any improvement in the overall system utility.

The proposed Novel Distributed Rate Allocation (NDRA) algorithm (see Table I) represents a sketch of the proposed algorithm. In this algorithm, the IntraNet procedure always attempts to increase the system's utility by allocating the resource in the network n ∈ N to the best user. If the free resources are not sufficient, the InterNet procedure tries to find a new user that can free up enough resources by allocating parts of its allocated rate through other network n = n ∈ N.

As long as the network resources allow it, the whole procedure is repeated until no extra utility improvement can be brought to the overall system.

In order to adapt video source rates at the transport layer according to network states reported from the network layer, some cross-layer information exchange is needed. Fig. 2 illustrates various components in such a system. At the network layer, the distributed allocation scheme would require track the observations of ABR n and RT T n over all available access networks. It also records the intended rate allocation R n s advertised by each user, and calculates the value of D all and U n s accordingly. At the transport layer, the video rate controller at the source advertises its intended rate allocation R n s . The network state monitor traversed by the stream then calculates the relevant parameters based on its local cache of ABR n , RT T n and RB n within the same access network. The destination node extracts such information from the video packet header and reports back to the sender in acknowledgment packets, so that the video rate controller can re-optimize its intended rate R n s based on the proposed NDRA algorithm, with updated network state information.

III. PROPOSED JOINT SOURCE-CHANNEL CODING

In this section, we describe the application of JSCC approach subject to the allocated transmission rate obtained from the proposed rate allocation scheme. In what follows, we first introduce the architecture of JSCC, and describe the employed packet-loss pattern approximation to represent the channel packet-loss process. Then, we propose a JSCC algorithm to optimize the perceived video quality by optimally setting the channel coding rate.

A. The Architecture of JSCC

The proposed JSCC architecture contains two parts as shown in Fig. 3. Unit-1 generates independent embedded streams using the 3-D SPIHT codec, while Unit-2 uses the coding constraints and channel conditions to pack the bit-streams into pack-streams of quality layers. This two-unit structure collects incremental contributions from the various streams into SNR (Signal-to-Noise Ratio) scalable quality layers in a way similar to that of embedded block coding with optimized truncation. The streams and rate-distortion functions generated by Unit-1 can be processed independently to channel conditions. The source and channel allocation algorithm in Unit-2 must be efficient to cope with the time varying channel conditions. In Unit-1, a video is divided into several independently encoded sections for additional functionality. The video coder divides the 3-D wavelet coefficients into multiple blocks according to their spatial and temporal relationships, and then encodes each block into sub-stream independently using the 3-D SPIHT algorithm.

Fig. 4 shows an example of separating the 3-D wavelet transform coefficients into four independent blocks, each of which retains the spatiotemporal structure of 3-D SPIHT. Fig. 5 shows how the concept of video layer is used in the encoding-decoding procedure. In this figure, dark areas represent the low resolution of the video sequence, and the other parts are used for high resolution. After encoding some points of the video sequence, most of the remaining bit budget is used for encoding the higher frequency bands which contain video details not usually visible at reduced spatial-temporal resolution. Fig. 5 illustrates this idea for a two-layer case of spatially scaled 352 × 288 video sequence. A low-resolution video can be decoded from the first layer only, and the frame size is 176 × 144. If we use three layers, the lowest layer's size would be 88 × 72.

B. Packet-Loss Pattern Approximation

For the RS (Reed-Solomon) correction code operating on b-bit symbols, the maximum block length is 2 b -1 symbols. A systematic (n, k) RS code appends n -k redundant symbols to k source symbols to make a block length n. The source symbols can be recovered correctly when the number of loss symbols is less than the minimum distance d min = n -k + 1 of the code.

The performance of a RS decoder P c (n, k) can be characterized by the code correct probability

P c (n, k) = n-k m=0 P (n, m) ( 16
)
where P (n, m) is the probability of m erasures within a block of n symbols. In a binary symmetric memoryless channel, we have

P (n, m) =   n m   P m B (1 -P B ) n-m ( 17
)
where P B is the average packet loss rate. For channels with memory, it is more complicated to calculate P (n, m). Here, we use a two-state Markov model (i.e.Gilbert model) to simulate the bursty packet loss behavior. The two states of this model are denoted as G (Good) and B (Bad).

In state G, packets are received correctly and timely, whereas, in state B, packets are assumed to be lost. This model can be described by the transition probabilities P GB from state G to B and P BG from state B to G. Then the average error probability P B is given by P B = P GB P GB + P BG [START_REF] Altman | Performance analysis of AIMD mechanisms over a multi-state Markovian path[END_REF] and the average burst length

L B = 1 P BG ( 19
)
which is the average number of consecutive symbol errors. The Markov model is a renewal model, and such models are determined by the distribution of error-free intervals, known as gap.

Let the gap of length σ be the event that after a lost packet, σ -1 packets are received correctly and then a packet is lost again. The gap density function g(σ) gives the probability of a gap length σ. The gap distribution function G(σ) is the probability of a gap length greater than σ -1.

These functions can be derived as [START_REF] Chan | Video Loss Recovery With FEC and Stream Replication[END_REF] g Let R(n, m) be the probability of m -1 erroneous symbols within the next n -1 symbols following an erroneous symbol. It can be evaluated using the following

(σ) =    1 -P BG , σ = 1 P BG (1 -P GB ) σ-2 P GB , σ > 1 (20) G(σ) =    1 -P BG , σ = 1 P BG (1 -P GB ) σ-2 , σ > 1 (21)
R(n, m) =      G(n), m = 1 n-m+1 σ=1 g(σ)R(n -σ, m -1), 2 ≤ m ≤ n (22)
Then the probability of m errors within a block of n symbols becomes:

P (n, m) =        n-m+1 σ=1 P B G(σ)R(n -σ + 1, m), 1 ≤ m ≤ n 1 - n σ=1 P (n, m), m = 0 (23)
C. Proposed JSCC Fig. 6 shows how multiple encoded sequences of different quality layers are protected based on systematic RS codes. For notational convenience, we define layer 1 as the highest layer and layer I n s as the lowest layer to be sent for user s ∈ S in network n ∈ N. Let N n s be the number of packets that are used to send the combined source data and redundancy for user s ∈ S over network n ∈ N in a GOP (Group Of Picture) and let L be the packet size in bytes. In this scheme, for user s in network n, the source bits belonging to layer i (1

≤ i ≤ I n s ) are k n s,i
packets and the remaining c n s,i = N n s -k n s,i packets are filled with channel coding redundancy. In other words, the source data for layer i is protected by RS(N n s , k n s,i ) code .

Our proposed coding scheme is performed on GOP basis. We define the total number of packets at period t to be sent from source s ∈ S for a GOP period N s (t) as

N s (t) = R s (t) × N GOP F × L ( 24
)
where R s (t) is the total rate in bytes/s at period t for the combination of data and redundancy for user s over all networks; N GOP is the number of frames in one GOP; F is the frame rate in frames/s. In this work, we assume that each user transmits his stream over N networks (N ≥ 1).

Then the proposed algorithm divides N s (t) into N 1 s (t), N 2 s (t),..., N N s (t) so as to maximize the expected quality at the receiver.

N n s (t) (n ∈ [1, N ]
) represents the number of packets transmitted by user s over network n for at GOP period t. Taking into account the rate of user s over network n, N n s (t) should satisfy the following condition:

N n s (t) = R n s (t) × N GOP F × L ( 25
)
where R n s (t) is the rate of user s over network n at the GOP period t, which can be obtained from the proposed rate allocation scheme described in the previous section.

In order to get the optimal expected quality, for each user s, given R n s (t), it is necessary to find N n s and K n s = (k n s,1 , k n s,2 , ..., k n s,I n s ) for n ∈ [1, N ] to minimize the overall distortion function [START_REF] Kim | Distributed Video Streaming Using Multiple Description Coding and Unequal Error Protection[END_REF]. However, the computational complexity of this classic two-fold optimization problem is usually huge and it is hard to operate online. To get around the difficulty, we make use of the video layer concept to approximate and simplify the total distortion function as follows:

P SN R(t) = N n=1 I n s l=1 N n s j=N n s -k n s,l +1 P (N n s (t), j) I n s i=l P SN R i (t) (26)
subject to

N n=1 N n s (t) = N s (t), N n s (t) = R n s (t)×N GOP F ×L
where P SN R i denotes the ith video layer Peak Signal-to-Noise Ratio (PSNR), which represents the image distortion at the receiver relative to the original video sequence. Its definition is: where MSE is the mean-square error between the original and the decoded luminance frame.

P SN R(dB) = 10 log 10 ( 255 2 M SE ) (27)
P (N n s (t), j) is the probability that j packets are lost out of N n s (t) packets sent by user s over network n.

Each source and network independently runs the proposed rate allocation algorithm to get its optimal number of packets to transmit for a GOP period, using the information contained in the control packets that the receiver sends to all users. In theory, the proposed JSCC algorithm should try all possible combinations of (N n s , K n s ) that satisfy the constraints in (26) and choose one that maximizes the expected quality. In order to get a fast solution, we set a predefined RS set which contains a number of RS codes acting as the potential channel codes. Of course, the computational complexity is proportional to the number of RS codes. According to our numerous experiments, the algorithm can achieve a good trade off between the performance and the computational complexity when N n s varies from 10 to 25 and K n s is more than half of the N n s . Therefore, for the finite number of networks, layers and the combination of (N n s , K n s ), we can find a satisfying solution through exhaustive search.

IV. SIMULATION RESULTS AND DISCUSSIONS

In this section, we conduct simulation experiments to study the performance of the proposed joint rate allocation and JSCC scheme in a distributed video streaming framework. First of all, we describe the simulation environment. Secondly, we present the main simulation results where we show the objective results of the performance of the proposed scheme under different scenarios.

Finally, we conclude the section by summarizing the selected simulation results.

A. Simulation Environment

Here, we use the HD (High-Definition) City test sequence in our simulations to stream from two sources to two receivers with a maximum allowable total delay T = 350 milliseconds. The sequence has spatial resolution of 1280 × 720 pixels, and the frame rate is F = 60fps. The layer number is I n s = 3 and frame number in one GOP is N GOP = 30 for all experiments. For simplicity, we use the Constant Bit Rate (CBR) model to represent video traffic. In this work, we simulate our joint scheme in NS-2 for an example network topology shown in Fig. 7. Each user may stream video sequence via both two access networks. For simulation convenience, we don't consider the jitter parameter and just take into account the burst length L B in this simulation.

That is because this work focuses on the rate control combined with JSCC, and our simulation just aims at testing its efficiency.

Each network is simulated as a link with varying available bandwidth and delay, according to the traces collected from the actual access networks using the ABR and RTT measurements2 .

Table II summarizes the statistics of the collected ABR and RTT of each network trace over 200 GOP periods. During transmission, the environments are updated every frame transmission which can cause changes in the rate allocation and network resources; Within a frame transmission interval, the environment is kept constant. It should be noted that all the simulation results in this section have been obtained using 300 runs in order to get statistically meaningful average values.

when the rate exceeds the current optimal transmission rate available for the selected sourcedestination pair, it will drop the subsequent encoded packets. The AIMD-based scheme probes the network for available bandwidth and reduces rate allocation after congestion occurs. Each user s initiates its rate at a specified rate R AIM D s corresponding to the minimum acceptable video quality, and increases its allocation by R s every t seconds unless network congestion is perceived, in which case the allocated rate is dropped by (R n s -R AIM D s )/2 over the congested network n. In the process of simulation, the increase in rate allocation is allocated to all available networks in proportion to the average of each ABR. In addition, congestion over network n is indicated upon detection of the lost packets, or when the observed RT T exceeds a specified threshold, based on the playout deadline of the video stream.

In Fig. 9, we show a performance comparison between our proposed rate allocation scheme and the competing methods, drop-tail and AIMD, in the scenario where packet losses are caused only by channel over-pumping 3 . It should be noted that due to the use of CBR encoding, the video quality is not constant and varies periodically [START_REF] Qu | An Adaptive Motion-Based Unequal Error Protection Approach for Real-Time Video Transport Over Wireless IP Networks[END_REF]. In Fig. 9, the average PSNR using the proposed NDRA algorithm is 35.33 dB while it is 35.01 using AIMD-based method and 34.70 dB for the case of drop-tail. Thus, using the proposed NDRA algorithm can achieve almost 0.32 dB and 0.63 dB performance gains comparing to the AIMD and drop-tail scheme, respectively. From the network profile, illustrated in Table III (the value is averaged over one GOP), we can see that for GOP No.1, No.2, and No.4, the allocated transmission rate using the proposed NDRA method is higher than the fixed 1.50 Mbps. Thus, using rate allocation can fully exploit the reasonable transmission rate resulting in improved performance compared to using a fixed-rate coding scheme. On the other hand, for GOP No.3, it is obvious that the fixed source coding rate is higher than the allocated transmission rate; therefore, packet losses will occur when the transmission buffer is full resulting in the last couple of frames being lost which cause substantial performance degradation. A lost frame is concealed by just copying the previous frame and if several consecutive frames are lost, the degradation will be even more serious since the concealed frames are then used as correctly received frames to conceal the subsequent lost frames. This results in substantial error propagation. For example, in Fig. 9, we can see that there is substantial performance degradation around the 90th frame for the no-rate control case due to channel over-pumping. Furthermore, although the performance degradation caused by the channel over-pumping packet losses has been partially compensated using passive error concealment, the performance is still not as good as using the rate allocation scheme. It should also be noted from Fig. 9 that the performance achieved by the proposed NDRA method is also super to the traditional AIMD-based method. On one hand, although the AIMD-based method is adaptive to the change of the network conditions, the network is so dynamic that a congested node forwarding a few seconds might not be used at all when the source reacts to the congestion. On the other hand, the proposed NDRA method further take advantage of explicit knowledge of the video distortion-rate characteristics, and can achieve more balanced video quality.

Then, to evaluate the performance of the joint scheme, the proposed NDRA+JSCC scheme is benchmarked against other two competitive schemes: 1) NDRA+RS [START_REF] Zhu | Joint Routing and Rate Alloction for Multiple Video Streams in Ad Hoc Wireless Networks[END_REF][START_REF] Tian | Robust and efficient path diversity in application-layer multicast for video streaming[END_REF], in which a fixed RS [START_REF] Zhu | Joint Routing and Rate Alloction for Multiple Video Streams in Ad Hoc Wireless Networks[END_REF][START_REF] Tian | Robust and efficient path diversity in application-layer multicast for video streaming[END_REF] code is used exclusively in the total system; 2) NDRA only, in which no channel coding is employed in the video transmission system. In Fig. 10, we illustrate a plot of the PSNR versus the frame number for the test sequence; the corresponding network profile is illustrated in a higher performance in terms of end-to-end PSNR compared to the no channel coding and the fixed RS [START_REF] Zhu | Joint Routing and Rate Alloction for Multiple Video Streams in Ad Hoc Wireless Networks[END_REF][START_REF] Tian | Robust and efficient path diversity in application-layer multicast for video streaming[END_REF] schemes. From Fig. 10, we can see that although using the RS (15, 9) code can provide protection, a substantial performance loss is observed compared to the proposed JSCC scheme which is so flexible that it can achieve an optimal value according to current condition. Also, although using no channel coding results in the best source coding efficiency, however, there are no error correcting capabilities which can be used to combat transmission errors; therefore, the corresponding performance is considerably worse than the JSCC scheme.

In order to provide a more comprehensive evaluation of the proposed joint scheme, we repeat the results for other video sequences of varying content complexity (see Table V) under the same simulation configuration as the previous experiments. From Table V, it can be observed that the proposed NDRA+JSCC scheme performances are superior to the other competitive methods, which is due to the network-adaptive and error-resilient characteristics of the proposed joint scheme. The previous objective results are based on a quantitative assessment of reconstructed PSNR values. In Fig. 11, we also display some subjective results based on the reconstructed frames taken from the decoded test sequence of the simulation run. From Fig. 11, we can see that the proposed NDRA+JSCC scheme can provide improved subjective performance compared to the other competing schemes.

C. Observations

Based on the selected objective and subjective simulation results described above, several main observations can be drawn: joint adjusting the allocated rate in each network and the channel coding rate for each stream.

The simulation results demonstrate the effectiveness of our proposed joint scheme for multiple video users over multiple heterogeneous wireless networks.

  distribution function giving the probability of the gap length greater than σ -1 g(σ) density function giving the probability of a gap length σ I n s number of coding layer for the user s over network n K n s source coding for the user s over network n in one GOP L packet size LB average burst length N set of heterogeneous wireless networks N = {1, 2, ..., N }, which contains the number of N networks NGOP number of the frames in one GOP N n s number of packets transmitted by user s over network n in one GOP P loss total packet loss rate including the random packet loss and the packet loss caused by late arrival PB average random packet loss rate PBG,PGB denotes the probability from the state B to G and state G to B respectively in the Gilbert model P (n, m) probability of m errors with in a block of n symbols R matrix of the allocated rate R = {R n s }S×N , in which each element R n s corresponds to the allocated rate of user s ∈ S over network n ∈ N R(n, m) probability of m -1 erroneous symbols with the n -1 symbols following an erroneous symbol. S set of users S = {1, 2, ..., S}, which contains the number of S users T delay constraint U set of utility function U = {U n s }S×N , in which each element U n s corresponds to the utility value of user s ∈ S over network n ∈ N

Fig. 1 .

 1 Fig. 1. Illustration of the cross-layer design of the total system.

Fig. 2 .

 2 Fig. 2. Cross-layer information exchange between the network state monitor at the network layer and the video rate controller at the transport layer.

Fig. 3 .

 3 Fig. 3. Architecture of JSCC.

Fig. 4 .

 4 Fig. 4. Separating the 3-D wavelet transform coefficients into four streams.

Fig. 5 .

 5 Fig. 5. The conception of video layer is used in the encoding-decoding procedure.

Fig. 6 .

 6 Fig. 6. Packetization of source-channel bits of different layers for user s in network n.

Fig. 7 .

 7 Fig. 7. Topology used for network simulations.

Fig. 9 .

 9 Fig. 9. Performance comparison between different rate allocation schemes.

Fig. 10 .

 10 Fig.10. Performance comparison between the proposed JSCC scheme with the representative fixed channel coding and without channel coding scheme.

Fig. 11 .

 11 Fig. 11. Subjective comparisons of decoded frames for Susie sequence. (a) NDRA+JSCC; (b) NDRA+RS(15,9); (c) NDRA only (PSNR=33.7 dB, 31.3 dB, 29.7 dB, respectively).

Table IV (

 IV the values are averaged over one GOP). The proposed JSCC scheme clearly achieves

Forward and backward trip delays are both simulated as half of the measured RTT

Here, we assume that no transmission errors occurred

ACKNOWLEDGMENTS

This work was supported in part by the International Project PRA-SI (financed by France and China governments) under Grant No. SI04-03, and the Key Project of Nature Science Foundation of Jiangsu (China) under Grant BK2007729.

B. Performance Evaluation of the Proposed Scheme

At first, we validate the distortion model introduced in Subsection II.A. Fig. 8 shows the rate-PSNR tradeoff when one user streams the HD video sequence City (300 frames) over the simulated two wireless networks which are noted as 802.11b (n=1) and 802.11g (n=2) network, respectively. The corresponding network parameters ABR (Mbps) and RTT (ms) for 802.11b and 802.11g are 4.5, 221 and 16.1, 290, respectively. The model is fit to experimental data for two cases: in the first case, the only losses considered are due to late arrivals; in the second, an additional end-to-end random loss rate of 5% is considered. The bell-shape of the curves illustrates that the highest performance is obtained when the streaming rate achieves the optimal tradeoff between compression quality and self-inflicted congestion. The approximate optimal operating rate computed by numerically solving (13) matches closely with experimental data.

To demonstrate the effectiveness of our proposed NDRA algorithm, we use the representative drop-tail scheme which employs the fixed rate allocation and the Additive-Increase-Multiplicative-Decrease (AIMD)-based rate allocation method which is used by TCP congestion control [START_REF] Altman | Performance analysis of AIMD mechanisms over a multi-state Markovian path[END_REF] for comparison. In order to get a clear picture of how the allocated rate reflects the reconstructed quality, we just use one user streaming over 802.11b network in this simulation.

More specifically, the drop-tail scheme employs a fixed source coding rate R f = 1.50Mbps and • The rate allocation plays an important role in the whole video transmission system. If the operating rate is lower than the optimal transmission rate, performance loss is due to the source coding inefficiency resulting from the use of an unnecessarily lower source coding rate; if the operating rate is higher, performance loss is caused by packet losses due to buffer overflow and network congestion.

• The JSCC actually achieves a higher performance. On one hand, the proposed JSCC approach is so flexible that it achieves an optimal PSNR value according to current condition; on the other hand, it achieves good trade-off between the performance and the source coding efficiency compared to the fixed channel coding schemes.

• The NDRA method combined with JSCC outperforms the competing methods from the objective comparisons.

V. CONCLUDING REMARKS

In this paper, we use distributed and cross-layer design to maximize the perceived video quality by combining rate allocation with joint source channel coding techniques. As detailed in the paper, our proposed joint scheme can adaptively to dynamic network conditions by


Fast MIP Handover Amelioration in Wireless

Networks by Cross-layer Solution Anne Wei, † GouZhi Wei, * Gerard Dupeyrat * and Benoit Geller ‡ * Université Paris XII, 61 avenue du Général de Gaulle, 94030 Créteil, France † Conservatoire National des Arts et Métiers, 292, rue Saint-Martin, 75003,Paris,France ‡ SATIE -ENS Cachan, 61 avenue du Président Wilson, 94235 Cachan Cedex,France Email: anne.wei@cnam.fr

Abstract-Mobile IP allows a mobile node to maintain a continuous connectivity to the Internet when moving from one access point to another. However, due to the link switching operations packets designated to mobile nodes can be delayed or lost during the handover period. This paper presents a twolayer solution to improve the handover performance both at the Link Layer and the Network Layer in the context of Mobile IP over wireless networks. At the Network Layer, we use a new function named Extended Handover Control Function (EHCF) which allow us to delete the DAD operation. At the Link Layer, a neighbor graphical prediction approach (NGP) reduces the probe latency. Moreover, the EHCF can buffer the packets during the handover process in order to decrease the packet loss. With an analytical model and some OPNET simulations, we show in this paper that our solution allows to provide low latency, low packet loss to the standard handover of Mobile IPv6.

Index Terms-Cross layer, Fast Handover and Mobile IPv6

I. INTRODUCTION

T HE need to keep an "everywhere and at any time" connection with Internet has been more and more demanded in recent years with the success of IEEE 802.11 and of IEEE 802.16 wireless networks standards. A growing number of 802.16/802.11 based wireless networks has been deployed as access networks to the Internet. With those access networks, the mobility support has thus become possible. However, the continuous Internet connectivity and the correct routing of packets were not guaranteed when users change their access points to Internet with classical protocols. To resolve these problems, the Mobile IPv4 (MIPv4) and Mobile IPv6 (MIPv6)protocols [START_REF] Perkins | IP Mobility support for IPv4[END_REF], [START_REF] Johnson | Mobility Support in IPv6[END_REF] were respectively published by the Internet Engineering Task Force (IETF). MIPv6 works well when Nomad users connects spontaneously at Internet without a continuous move. If an user continuously change its access points, the high handover latency and the high packet loss provide some troubles to support the continuous connection with MIP.

As described in MIPv6, the handover latency consists of the link latency and the network latency caused both at the Link Layer and Network Layer. According to some studies [START_REF] Kuang | Improving Handoff Performance in Wireless Overlay Networks by Switching between Two-Layer IPv6 and One-Layer IPv6 Addressing[END_REF], [START_REF] Mishra | An Empirical Analysis of the IEEE 802.11 MAC Layer Handover Process[END_REF], it is found that the handover latency normally takes hundreds of milliseconds due to the probe at the Link Layer This work was supported in part by the international project PRA-SIP under Grant SIP04-03. and more one second due to the DAD (Detection Address Duplication) operation at the Network Layer.

Since 2003 [START_REF] Aboda | Fast Handover Issues[END_REF], the main proposals by the IETF and the IEEE are the Hierarchical Mobile IPv6 (HMIPv6) and the Fast Handover for MIPv6 (FHMIPv6). HMIPv6 introduces a Mobility Anchor Point (MAP) who acts somehow like a local Home Agent (HA) for the visiting Mobile Node (MN). The concept of MAP can limit the amount of signaling required outside the MAP's domain at the Link Layer [START_REF] Soliman | Hierarchical Mobile IPv6 mobility management (HMIPv6)[END_REF], [START_REF] Kuang | Improving Handoff Performance in Wireless Overlay Networks by Switching between Two-Layer IPv6 and One-Layer IPv6 Addressing[END_REF]. While FHMIPv6 used location-based fast handover with the Inter-Access Point Protocol (IAPP) at the Link Layer [START_REF] Koodli | Fast Handovers for Mobile IPv6[END_REF], [START_REF]Recommended Practice for Multi-Vendor Access Point Interoperability via an Inter-Access Point Protocol Access Distribution Systems Supporting IEEE 802.11 Operation[END_REF], [START_REF] Pack | A Selective Neighbor Caching Scheme for Fast Handover in IEEE 802.11 Wireless Networks[END_REF]. The network uses a Link Layer trigger to launch either Pre-Registration or Post-Registration handover operations. Besides of these main proposals, there has been also some approaches for providing the lossless handover and minimizing the handover delay [START_REF] Chaouchi | Pre-handover Signaling for QoS Aware Mobility Management[END_REF]- [START_REF] Kashihara | End-to-End Seamless Handover Using Multi-path Transmission Algorithm[END_REF]. In [START_REF] Chaouchi | Pre-handover Signaling for QoS Aware Mobility Management[END_REF], a Pre-Handover Signaling (PHS) protocol is proposed in order to support the triggering of a predictive handover and to allow the network to achieve accurate handover decisions by considering different constraints such as Quality-of-Service (QoS), user profile and mobile node service requirements. In [START_REF] Bi | An Integrated IP-layer Handover Solution for Next Generation IP-based Wireless Network[END_REF], a Hierarchical Network-layer Mobility Management (HNMM) framework is described in which an integrated IP-layer handover solution provides an optimized network connectivity. Also, a Competition based Soft Handover Management (CSHM) protocol [START_REF] Kristiansson | Application-layer Mobility Support for Streaming Real-time Media[END_REF] and a Multi-path Transmission Algorithm (MTA) [START_REF] Kashihara | End-to-End Seamless Handover Using Multi-path Transmission Algorithm[END_REF] have been presented to decrease packet loss during a handover.

The goal of this paper is to optimize the Mobile IPv6 handover procedure both at the Link Layer and the Network Layer. At the Network Layer, we use a new function named Extended Handover Control Function (EHCF) which allow us to delete the DAD operation. At the Link Layer, a neighbor graphical prediction approach reduces the probe latency. Moreover, the EHCF can buffer the packets during the handover process in order to decrease the packet loss.

The remainder of the paper is thus organized as follows: Section II presents both the Neighbor Graphical Prediction (NGP) and the Extended Handover Control Function (EHCF) approaches with the associated operations. Then we describe the cross-layer solution with the NGP and EHCF approaches. Section III deals with the handover performance in terms of handover latency and packet loss. Regarding the standard handover of MIPv6, our numerical results show that our cross-layer solution NGP-EHCF reduces significantly both the latency and the packet loss. Finally, some conclusions are drawn in Section IV.

II. CROSS-LAYER SOLUTION WITH THE NGP AND THE EHCF

A. Handover latency overview

Generally speaking, a handover consists of a Link Layer handover and a Network Layer handover. The Link Layer handover includes a Discovery phase (scanning the channels to discover an available Access Point), an Authentication phase, and a Re-association phase, whereas the Network Layer handover concerns a Router Discovery phase, a Detection Address Duplication (DAD) phase, a Binding Update phase and a Binding Acknowledgement phase respectively. As displayed on Figure 1, the standard MIPv6 handover latency has been estimated to a maximum value of 1620 ms [START_REF] Kuang | Improving Handoff Performance in Wireless Overlay Networks by Switching between Two-Layer IPv6 and One-Layer IPv6 Addressing[END_REF], [START_REF] Mishra | An Empirical Analysis of the IEEE 802.11 MAC Layer Handover Process[END_REF]. This high latency is not acceptable for real time applications such as video and audio. If we analyze each phase during the handover process, we can note that the probe provides a 240-360 ms latency at the Link Layer and the DAD latency costs almost 1000 ms at the Network Layer. During a handover, the Probe phase allows a MN to scan all nearby APs (Access Point) and then to choice it self the best channel for its new connection. The probe latency depends on the number of channels (in the IEEE 802.11 case; the number of channels scanned is about 11). The idea to reduce the number of channels scanned or to predict a good channel is studied in [START_REF] Aboda | Fast Handover Issues[END_REF]- [START_REF] Pack | A Selective Neighbor Caching Scheme for Fast Handover in IEEE 802.11 Wireless Networks[END_REF] indicated in the Section I.

B. Neighbor Graphical Prediction-NGP at the Link Layer

To reduce the number of channels scanned, two approaches (active and passive) have been used. With the active approach, a MN decides which is the channel for the next connection. In this case, the MN chooses the first scanned channel with enough energy without scanning any further channels. On the contrary, with the passive approach, an external server indicates the channels that the MN can scan [START_REF] Huang | A Fast Handover Mechanism for IEEE 802.11 and IAPP Networks[END_REF].

We present a Neighbor Graphical Prediction approach (NGP) being based on a hierarchical network architecture which is illustrated on Figure 2. Directly linked with its ARs/APs/MNs, each EHCF router can collect all transit data coming from each entity.

Assuming that an EHCF router charges 30 APs as shown on Figure 3, the NGP approach allows an EHCF router to The NGP method works as the following: when a MN moves from an AP i (for example, AP i = 21) to another AP j (for example, AP j = 25), it indicates its EHCF router that triggers a handover. According to the graphical map, the EHCF router then launches the NGP-A algorithm to decide which is the next access point for the moving MN (the procedure of the EHCF router is illustrated on Figure 5). The NGP-A algorithm chooses the MN's next access point according to the MN's localization and nearby signal powers. The Reply message (on Figure 5) thus consists of the next SSID, the next channel and the IP temporary address. (for the detailed information about the formats of these messages see [START_REF] Wei | Handover Optimisation using E-HCF Method for the Mobile IPv6 protocol[END_REF]). As a result, the probe latency at the Link Layer can be reduced from 400 ms to 40 ms.

C. Extended Handover Control Function-EHCF at the Network Layer

At the Network Layer, we introduce a local intelligent entity called Extended Handover Control Function (EHCF) which should be capable of controlling its attached Access As shown on Figure 2, linked directly with its ARs, each EHCF router reserves a list of all available IP local addresses. An EHCF router also generates and updates periodically a second list which records the used ARs/APs/IP addresses. By comparing these two lists, the EHCF router can find a potential duplicate IP address (collision) in its domain. Then, this EHCF router can withdraw this potential duplicate IP address or can ask a concerned sub-node to change its IP address. In this way, the EHCF router enables to insure an unique IP address to a MN without DAD.

Furthermore, an EHCF router could exchange both some local information with its ARs/APs/MNs and some external information with other EHCF routers. To realize our EHCF proposal, we propose six new messages: MN Request (MN-Req), MN Reply (MNRep), HCF Request (HCFReq), HCF Reply (HCFRep), Connection Established Information (CEInf) and Handover Finished Confirmation (HFCon) messages (for the detailed information about the formats of these messages see [START_REF] Wei | Handover Optimisation using E-HCF Method for the Mobile IPv6 protocol[END_REF]). In order to minimize the packet loss during a handover, an EHCF router stores packets into a buffer until the MN is really attached to the new IP address. The entire handover procedure is displayed on Figure 6.

1) EHCF Procedure: We first recall that HCFReq/HCFRep messages are used between EHCF routers for extra-domain handovers. Each EHCF router must record and update its database periodically. This database helps to decide an unique new IP configuration in order to adapt for MN movements without the DAD phase during a handover.

As illustrated on Figure 6, the EHCF procedure is composed of the following steps:

• Moving in the network, if the threshold of the received signal strength is overstepped, the MN begins to probe the neighbor AR/AP's information, including the signal strength, some IP addresses, AP's BSSIDs, AR interface addresses and the sub-network prefix. Then the MN sends a MNReq message to its E-HCF original router (via its AR/AP) to report this information. • Receiving the MNReq message, the AR stops to forward all the packets sent to the MN and forwards them to its E-HCF original router in order to avoid the packet loss during the handover procedure. CoA and configure it automatically. • The MN sends a CEInf message to its EHCF original router to confirm its new attachment. • After receiving the CEInf message, the EHCF original router transfers the buffered packets to the MN's new CoA. Then, the EHCF original router sends an HFCon message to end the handover procedure.

• The MN can then exchange Binding Update (BU) and Binding Acknowledgement (BA) messages with its home agent and its correspondent node.

As shown in the E-HCF procedure, a MN can obtain its new CoA before it really attaches to its next AR/AP. Moreover, any DAD latency (about 1000 ms) is avoided. Thus, the EHCF approach allows the reduction of both the traditional handover latency and the packet loss. The handover performance is thus optimized compared to a traditional approach.

III. NGP-EHCF PERFORMANCE ESTIMATION

The NGP-EHCF performance estimation has been evaluated in terms of the total handover latency and of the packet loss with an analytical model. This model allows us to compare our NGP-EHCF handover performance with the standard handover of the MIPv6 protocol.

A. NGP-EHCF Latency Analysis

According to the handover procedure on Figure 3, we cite the following latency notations to estimate the handover latency:

• L EHCF : Total handover latency with the EHCF approach. • L N GP : Latency due to the MN's handover at the Link Layer.

• L M N Req : Latency for a MN to send a MNReq message to its E-HCF original router. The average overall EHCF handover latency L EHCF can be summed as following:

L EHCF = L N GP + L M N Req + L dec + L M N Rep + L CN inf + L conf + L BU/BA (1)
As this L EHCF depends upon the mobile link bandwidth and the computation capacity of each entity in the wireless network, we summarize the parameter values used in our numerical analysis in Table I.

B. Numerical Results of the Total Handover Latency

With the parameters of Table I, we give a latency comparison between the standard handover latency and the NGP-EHCF latency according to equation ( 1). These latencies are functions of the wireless link bandwidth and of the computation capacity. For example, the L M N Req latency can be numerically estimated as following: with a 10 Mb/s computation capacity, a MN needs 57.6 µs to generate a 72-byte MNReq message, whereas, 28.8 µs are required for an Access Router. Putting this 72-byte message on a 9kb/s GSM network, requires about 64 ms, so that the global of L M N Req is about 64 ms.

On Figure 7, the standard MIPv6 handover latencies (upper curve) and the NGP-EHCF handover latencies as function of the number of handovers are displayed. With an IEEE 80.211b wireless network, the average of the NGP-EHCF handover latency is about 200 ms. This average NGP-EHCF handover latency is validated by our simulation results on OPNET illustrated on Figure 8. Using the NGP-EHCF cross-layer solution, the latency reduction from 1620 ms to less 200 ms comes from avoiding the probe process at the Link Layer and the DAD phase at the Network Layer.

C. NGP-EHCF Loss

In terms of packet loss with the NGP-EHCF approach, packets can be stored into a buffer during the handover (see subsection II-C.1). Figure 9 illustrates the comparison of packet loss rates between the NGP-EHCF approach and the MIPv6 standard. The upper curve represents the number of lost packets with the MIPv6 standard (38 packets received out of 100 emitted packets), where the bottom curve with NGP-EHCF approach (68 packets received out of 100 emitted packets). This gives a typical 30% gain with the NGP-EHCF approach. Fig. 9. Comparison of loss rates between the NGP-EHCF approach and the MIPv6 standard by simulation IV. CONCLUSION In order to improve the handover performance for the Mobile IPv6, this paper proposes a cross-layer solution-NGP-EHCF based on a location graph at the Link Layer (NGP) and on a control function at the Network Layer (EHCF). The NGP-EHCF approach allows to collect and store some link and network data in order to anticipate some handover operations. Regarding the classical Mobile IPv6 handover performance, our numerical results validated by simulations show that the NGP-EHCF approach enables to decrease significantly both the total handover latency and the packet loss.

Fig. 1 .

 1 Fig. 1. Standard MIPv6 Latency both at the Link Layer and at the Network Layer

Fig. 2 .

 2 Fig. 2. Architecture of Fast Handover in IEEE 802.11 Wireless Networks(Router is an Access Router; EHCF is an EHCF router)

Fig. 3 .

 3 Fig. 3. 30 APs at one of Paris's Districts

Fig. 4 .Fig. 5 .

 45 Fig. 4. 30 APs Graphical Map correspond to one of Paris's Districts

Fig. 6 .

 6 Fig. 6. EHCF Procedure (EHCF original router is an attached router with an EHCF function; the EHCF distant/remove router is a router with who an EHCF original router can communicate)

•

  Receiving the MNReq message, the E-HCF original router decides to which AR/AP the MN will be associated. The choice of the AR/AP is mostly based on database obtained with periodic exchange messages from an E-HCF router to another (HCFReq and HCFRep messages) or with periodic exchange messages from ARs/APs/MNs. For example, if the number of registered MNs in one AR or AP has reached a limit, the EHCF original router will not attach the MN to this saturated AR or AP. After making the previous decision, the EHCF original router sends to the MN a MNRep message which consists of a new AP's BSSID, an AR interface address, a sub-network prefix and a new IP address.• With the MNRep message, the MN can obtain its new

Fig. 7 .

 7 Fig. 7. NGP-EHCF handover latencies and the standare MIPv6 handover latencies with IEEE802.11b

Fig. 8 .

 8 Fig. 8. NGP-EHCF handover latency by simulation

  dec : Latency necessary to an EHCF router to decide which AR/AP the MN should be attached (including the short delays to send an HCFReq message and to receive an HCFRep message).• L M N Rep : Latency for an E-HCF router to send a MNRep message to the MN. CN inf : Latency necessary for a MN to auto-configure its new CoA. • L conf : Latency due to the fact that an EHCF router sends buffered packets and a HFCon message. • L BU/BA : Binding Update/Binding Acknowledgement latency.

• L • L


Raoufeh Abedini

Bruno Clair
email: bruno.clair@ecofog.gf

Kambiz Pourtahmasi

Françoise Laurans

Olivier Arnould

Cell wall thickening in developing tension wood of artificially bent poplar trees

Keywords: gelatinous layer, secondary wall layer, developing xylem, maturation stress, tree biomechanics

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

The ability of trees to regulate their shape and maintain their trunk vertically is performed thanks to an asymmetrical distribution of mechanical stresses around the tree circumference [START_REF] Archer | Growth stresses and strains in trees[END_REF]. When the axes of hardwood species need a strong reorientation or reaction to weight, a high tensile stress can be produced on the upper side of the leaning stem by the production of the so-called tension wood [START_REF] Fournier | Biomechanical action and biological functions[END_REF]. The cell wall structure of tension wood can exhibit important changes compared with normal wood [START_REF] Onaka | Studies on compression and tension wood[END_REF][START_REF] Ruelle | Morphology, Anatomy and ultrastructure of reaction wood[END_REF]. Normal wood cells are composed of a middle lamella, a thin primary wall and a large secondary wall layer (SL) divided into three sub-layers, called S1, S2 and S3. In numerous species, such as poplar, tension wood is characterized by fibres with a specific morphology and chemical composition due to the development of a so-called gelatinous layer (GL), replacing the S3 and a part of or the whole S2 layer (Saiki andOno 1971, Andersson-Gunneräs et al. 2006). The GL is known to have a high cellulose content [START_REF] Norberg | Physical and chemical properties of the gelatinous layer in tension wood fibre of aspen (Populus tremula L.)[END_REF][START_REF] Côté | A contribution to the ultrastructure of tension wood fibers[END_REF] with microfibrils oriented nearly parallel to the cell axis [START_REF] Fujita | Electron microscopy of microtubules and cellulose microfibrils in secondary wall formation of poplar tension wood fibers[END_REF], Prohdan et al. 1995), embedded in an un-lignified matrix [START_REF] Pilate | Lignification and tension wood[END_REF]) made of numerous specific non-cellulosic polysaccharides [START_REF] Mikshina | Cellulosic Fibers: Role of Matrix Polysaccharides in Structure and Function[END_REF]. At the tissue level, poplar tension wood is also characterized by a reduced number and a lower diameter of vessel elements [START_REF] Jourez | Anatomical characteristics of tension wood and opposite wood in young inclined stems of poplar (Populus euramericana cv 'Ghoy')[END_REF].

Although the GL is the most important structural change of tension wood in most temperate eudicots, numerous tropical species do not produce a GL [START_REF] Okuyama | Growth stresses in tension wood: role of microfibrils and lignification[END_REF][START_REF] Yoshida | Tension wood and growth stress induced by artificial inclination in Liriodendron tulipifera Linn. and Prunus spachiana Kitamura f. ascendens Kitamura[END_REF][START_REF] Clair | Tension wood and opposite wood in 21 tropical rain forest species. 1. Occurrence and efficiency of the G-layer[END_REF][START_REF] Sultana | Wood anatomy of nine Japanese hard wood species forming reaction wood without gelatinous fibers[END_REF]. In tension wood with G-fibres, the GL is recognized as the driving force of tensile stress as its amount is directly related to the mechanical stress level [START_REF] Clair | Relationship between growth stress, mechanical-physical properties, and proportion of fibre with gelatinous layer in chestnut (Castanea sativa Mill.)[END_REF][START_REF] Washusen | The relationship between longitudinal growth strain and the occurrence of gelatinous fibers in 10 and 11-year-old Eucalyptus globulus Labill[END_REF][START_REF] Fang | Growth stresses are highly controlled by the amount of G-layer in Poplar tension wood[END_REF]) and tensile stress in cellulose microfibrils has been identified to occur synchronously with their deposition in the GL during cell maturation [START_REF] Clair | Maturation stress generation in poplar tension wood studied by synchrotron radiation microdiffraction[END_REF]. However, the clear mechanism of tensile stress generation remains unclear, and it is therefore interesting to focus research on the development of the GL of tension wood.

Tension wood is often formed at a higher rate compared with normal wood [START_REF] Andersson-Gunneräs | Biosynthesis of cellulose-enriched tension wood in Populus: global analysis of transcripts and metabolites identifies biochemical and developmental regulators in secondary wall biosynthesis[END_REF]. Growth speed and developmental decisions regarding the cell type formed are determined in the meristematic cambial zone, whereas the formation of the GL takes place later during xylem differentiation [START_REF] Timell | Compression wood in gymnosperms[END_REF]. The perception of the need of reaction is very fast; [START_REF] Jourez | Effet de la durée d'application d'un stimulus gravitationnel sur la formation de bois de tension et de bois opposé dans de jeunes pousses de peuplier (Populus euramericana cv 'Ghoy')[END_REF] observed that reaction is visible several hours after tree inclination but the GL is only visible after 1 to 2 days, depending on the trees. However, the development at a finer scale, and especially the balance between SL and GL production, has never been studied and could be of special interest for the understanding of maturation stress generation. Indeed, several observations have been done on the decrease of the SL thickness when the GL thickness increases (visible but not discussed in [START_REF] Clair | Maturation stress generation in poplar tension wood studied by synchrotron radiation microdiffraction[END_REF][START_REF] Yoshinaga | Lignification in poplar tension wood lignified cell wall layers[END_REF][START_REF] Chang | Deposition and organisation of cell wall polymers during maturation of poplar tension wood by FTIR microspectroscopy[END_REF]. The starting point of this study was therefore to identify whether GL formation could be partially due to a modification of SL during maturation.

In this study, the growth of cell wall layers of tension wood is investigated in poplar grown under artificial conditions. The study focuses on GL formation during the secondary wall formation stage (i.e., excluding the cambial zone and early stages of xylem cell expansion). This study aims to answer the question how GL and SL thickness change during the reaction process. What is the relationship between GL and SL thickening? Does GL formation reduce SL thickness in the tension wood cell wall?

MATERIAL AND METHODS

Material

Poplar saplings (hybrid Populus tremula x P. alba (clone INRA 717-1B4)) were grown in a greenhouse at the INRA centre in Orléans, France. Trees were tilted and attached to a tilted pole in the middle of the growing season on 25 th June, 2012. Then, trees were sampled after one day (T1), three (T3), seven (T7), fourteen (T14) and 25 days (T25) after tilting. Sampling was performed on three trees at each sampling date. Trees were 1.3 m high and had a basal diameter of around 10 to 12 mm at the beginning of the experiment. Small blocks were cut from tension wood sides (upper side) and opposite wood side (lower side) of the basal part of the tilted stems. All samples were dehydrated through ethanol series and embedded in LR white resin (London Resin) according to standard methodology (two exchanges of resin/ethanol mixture for one hour, followed by two exchanges in pure resin for one hour, kept one day at room temperature, then kept overnight in a capsule mould at 65ºC). Thin transverse sections (0.5 µm in thickness) were obtained using a rotary microtome (Leica RM2265) with diamond knife (Diatome Histo). The use of dehydrated and embedded samples may affect the quantitative determination of the cell wall thickness compared to the native state. This sample preparation is expected to produce a slight shrinkage or swelling of the wall. For example, [START_REF] Chang | Solvent polarity and internal stresses control the swelling behavior of green wood during dehydration in organic solution[END_REF] showed that ethanol dehydration produces a macroscopic swelling of 0.2%. However, this preparation is necessary to avoid the observation of the GL in a swollen state due to the border artefact described in [START_REF] Clair | Precautions for the structural analysis of the gelatinous layer in tension wood[END_REF]. This artefact has been shown to swell the GL by around 60% [START_REF] Clair | Precautions for the structural analysis of the gelatinous layer in tension wood[END_REF][START_REF] Fang | Growth stresses are highly controlled by the amount of G-layer in Poplar tension wood[END_REF]. In order to avoid observation of GL in a swollen state, sections were taken at least at 50 µm below the trimming surface of the embedded samples. Sections were mounted in Eukitt TM on glass slides without staining.

Measurement of cell wall thickness

Cell wall layer thickness of wood fibres was measured using the phase contrast mode with a Leica DMLP microscope with immersion oil lenses. Phase contrast is preferable to bright field microscopy when high magnifications (400x, 1000x) are needed especially as the specimen is colourless or the details are so fine that colour does not show up well. Light microscopy allows for the measurement of all the cells along a radial line and an average measurement on each whole cell, which is not possible using TEM technique that requires the deposition of the sections on a grid thus hiding part of the sample. Several images were captured using a digital camera (Leica DFC320) from cambium cells to ring boundary with a sufficient overlap to allow for the repositioning of each image with the previous one in order to accurately measure the distance of each cell to the cambium. Preliminary testing on another sampling (data not shown here) indicated that the thickness of the compound middle lamella (CML) is constant all along the maturation sequence and does not show significant variation with SL and GL thickness changes. Therefore, CML thickness was not measured in this study. Thickness of GL and SL were measured in three radial lines of cells per sample using image analysis software ImageJ (National Institutes of Health, Bethesda, MD, USA). In order to handle the variability of cell wall layer thickness around the cell, and to increase the precision of the measurement, a mean cell wall thickness was calculated according to the method proposed by [START_REF] Yoshinaga | Lignification in poplar tension wood lignified cell wall layers[END_REF]. External contours of the GL, SL and lumen were plotted manually from images (Fig. 1) and the average thickness was calculated according to following formula: GL mean thickness = 2 × AGL/(PGL + PLumen), and SL mean thickness = 2 × ASL/(PSL + PGL), where AGL is the area of GL, ASL the area of SL, PGL the external perimeter of GL, PSL the external perimeter of SL and PLumen the lumen perimeter. Finally, the mean cell diameter was evaluated as D = PSL/π. This method integrates the whole fibre and thus allows for a better precision in the thickness measurement than when performed only in some points. A reproducibility test, made by measuring 30 times the same wall thickness, yielded a confidence interval at 95% of 0.015 µm.

Each measured cell was later recognized by its distance to the cambium both in µm and in number of the cells (when a vessel interrupted the radial line, the number of cells was counted on the adjacent radial line), its cell dimensions (equivalent mean diameter) and its mean cell wall thicknesses (SL and GL). As mentioned in [START_REF] Fang | Growth stresses are highly controlled by the amount of G-layer in Poplar tension wood[END_REF], GL thickness is positively related to the cell diameter (the higher the fibre diameter, the thicker the GL) due to the reduced wall thickness near the end of the fibres, as shown by [START_REF] Okumura | Thickness variation of the G-layer along a mature and a differentiating tension wood fiber in Populus euramericana[END_REF]. Therefore, in order to make the progressive changes in the wall thickness comparable from fibre to fibre, thicknesses are presented as relative thicknesses by dividing them by the mean cell diameter.

RESULTS

As it is not possible to follow the thickening of a single cell, several cells in a single radial line from cambium to mature wood are considered as a good proxy of the maturing cell all along this study. On each sample, the 3 radial lines measured were very similar to each other, only disturbed by the presence of vessels. Therefore, for the sake of clarity, only one radial line is presented in our graphs, for a given sample.

Stimulus duration before GL formation

The presence of fibres with a GL (G-fibre) was not detectable one day after tilting. 3 days after tilting, GL was observable only in 1 tree among the 3 sampled trees. One week after tilting, all trees exhibit a GL in almost all of the tension wood fibres.

Identifying the tilting date in sections

To better understand the cell wall thickness changes in response to the gravitropic stimulus, it is necessary to identify which cells were produced before and after tilting. This date is clearly identifiable thanks to the appearance of the GL at the tilting date followed by a strong decrease in SL thickness. In the transition zone, SL is first as thick as before tilting but with a thin GL (Fig. 2d); then SL thickness gradually decreases. Whereas SL has a thickness of around 1.56 µm before the tilting date (average of all samples), it is reduced to around 0.6 µm when the GL thickness remains stable. One can consider that the gradual change in SL thickness is due to the sudden change in the signal that modified the function of the cell, stopping the development of the SL to start the deposition of a GL. Therefore, cells with SL of intermediate thickness correspond to cells that already differentiated but were not mature at the tilting date, whereas cells with a thinner SL and a thick GL were differentiated after the tilting date.

Growth rate

Growth rate is obtained by counting the number of cells and the distance from the tilting position to the cambium. Growth rates are given in Table 1. The number of cells formed per day slightly increased after 7 days to 14 days after tilting, and then decreased strongly during the last period.

Table 1. Radial growth rates, expressed as the number of cells formed during a tilting period, and as the mean distance of the cell produced during this period. Each value is an average of three radial lines measured for each tree. Gray background corresponds to the average of the three trees sampled at a given date. * indicates that the growth rate was estimated according to the previous period.

Period of growth (days)

Tree

Mean number of cells per day Mean distance per day (µm) 0-7 SL thickness before tilting Table 2 summaries the mean values and the significance of relationships between changes in thickness and distance to the cambium for each measured sample. The average thickness of SL before tilting (Fig. 2 stage e) was measured on all the trees sampled at T7, T14 and T25 with a mean value of 1.56 µm (standard deviation (SD): 0.13) and a mean relative thickness of 0.097 (SD: 0.004). However, this thickness is not constant as it increases from ring boundary to tilt position (Fig. 2 stage e). This increase was statistically significant in 7 samples out of 9 (Table 2). In the two samples where the correlation was not significant, some GL are observed before tilting (as in Fig. 2 stage e). The presence of GL can largely affect the SL thickness and explain the disturbed relationship. The presence of GL in upright trees is commonly observed and can be considered as a normal behaviour considering the need for the tree to stay up-right. Some other trees presented a thin GL before tilting, which weakly affected the present relationship (Fig. 2). Table 2: Mean value of the measured thickness and statistical analysis of the change in thickness versus distance to the cambium (DC) in the different stages presented on Fig. 2. r: correlation coefficients calculated of the relative thickness vs. distance from cambium. SLTh and GLTh: respectively SL and GL thickness (in µm). Slopes were measured using the "real" thickness to illustrate the thickening in µm/mm. Grey background indicates that measurements were not performed as it was meaningless to measure a mature GLTh when it cannot be certified that GL reached its final thickness. Seven days after tilting, SLTh after tilting (stage b+c) was too small to compute the correlation between SL thickness and distance to the cambium. Change in SL thickness after tilting After the tilting date, SL has a rather constant thickness in mature wood (i.e., except in the differentiating zone near the cambium), around 2.6 times thinner than before tilting. A careful investigation of SL thickness in this stable zone shows however that SL thickness slightly increases when the distance to the cambium decreases with a significant negative correlation between SL thickness and distance from cambium (Table 2). This negative correlation is significant in trees sampled at T14 and T25. In trees sampled after 7 days, the relationship is meaningless as the stable zone is too short.

Kinetics of GL deposition vs. SL thickening

In most of the recorded radial lines, GL thickening occurs synchronously or soon after completion of the SL thickening. Three radial lines (out of the 27 measured ones) presented a peculiar behaviour as the GL deposition started slightly before the end of SL thickening, so that SL and GL thickness continue to increase simultaneously (Fig. 3). The late increase in the thickness of SL is only observed after a long time of tilting (T25). Moreover, it has to be noticed that the GL is generally not observable or measurable in its early stage of deposition, as attested by the absence of measured thickness between 0 and 0.3 µm (Fig. 3). This induces an overestimation of SL in this portion as attested by the steep decrease in SL thickness at the position where the first GL is detected in Fig. 3 where an empirical correction is proposed. It can therefore be supposed that GL deposition starts slightly earlier than what is recorded in some other samples and therefore this behaviour could be more common than the few cases observed.

After the end of its thickening, final GL thickness was found to be 2.5 µm (SD: 0.17) on average. This value takes into account only radial lines from trees sampled at T14 and T25 as it is difficult to be sure that the GL thickening period was finished for trees sampled at T7 and before.

Fig. 3: detailed view of sample T25-1 where the GL (squares) deposition starts before the end of SL (circles) thickening. Lower dotted line is an empirical extrapolation to correct the lack of GL measurement when its thickness is too thin. This lack induces an over-estimation of SL in this portion as attested by the steep decrease in SL thickness at the position where the first GL is detected. The upper dotted line thus proposes a corrected trend of SL thickness in this area taking the linear extrapolation of the GL thickness into account.

The GL thickening period is considered to be the distance between the first occurrence of GL in young cells near the cambium to where they reached a constant thickness (stage b in Fig. 2). GL thickening period varies from 570 to 982 µm (Fig. 4), with, as a general trend, a longer period for trees sampled at T25 compared to trees sampled at T14 (Fig. 4). No general trend can be detected for the relationship between mean GL thickness (or relative thickness) and GL thickening period (Fig. 4).

GL and SL growth rates

Table 2 gives the slope of the SL and GL thickening vs. the distance to cambium. This slope can be expressed as an increase in the wall thickness in µm by distance to the cambium in mm. It gives an estimate of the growth rate at the cell wall level under the assumption of a constant cell division speed. Although the validity of this assumption is uncertain, it is interesting to compare these stages of cell wall building in a single tree and even more in a single radial line of cells. In 8 of the 9 measured trees, the slope of the SL thickening was lower than the slope of GL thickening, whatever the growth rate in the considered period as presented in Table 1.

Cell wall thickening in opposite wood during tension wood formation

The marking of the tilting position in opposite wood (OW) side is much less clear than in tension wood (TW) as there is no GL development or steep decrease in SL. Moreover, TW and OW have different growth rates; it is therefore problematic to compare the cell wall thickening on both side of the stem from their distance to the cambium, as cells are not produced at the same date. Therefore, tilting position was determined assuming a similar growth rate all around the stem before tilting. In order to compare cell wall thickness at the same date in TW and OW, the remaining cells produced after tilting (from the tilting position to the cambium) are then assumed to grow at different but proportional speed on both sides.

Before tilting, cell wall thickness of OW fibres shows a similar trend as observed in TW side (Fig. 5 stage e) as, at that time, trees were upright and no differences are expected on both sides. After tilting (stage b+c), the trend observed before tilting is disturbed in all trees. In several trees, an increase of the SL thickness is observed consecutively to the tilting. However, no general trend was present for all trees.

In T25 samples, average SL thickness in OW after tilting (stage b+c) was 1.78 µm whereas it was 1.64 µm before tilting. This should be compared to the total cell wall thickness on the TW side, which measured 3.01 µm after the GL had been formed.

DISCUSSION

The present study allows us to reconstruct the general developmental pattern of fibre cell wall layers in tilted trees before and after tilting as presented in Fig. 6. Developing cells and mature cells are two main stages in this diagram. The developing fibres part contained young cells in which cell wall thickening is in progress with first the deposition of CML (not presented) followed by the formation of SL and GL.

Measurements of wood cell wall thickness before tilting show the progressive increase of SL during the growing season. An increase in cell wall thickness is commonly observed in softwoods (e.g., Mork 1928[START_REF] Denne | Definition of latewood according to Mork (1928)[END_REF]) and the change in wall thickness at the ring transition is also reported for hardwoods (IAWA Committee, 1989) but, we were unable to find reference reporting quantitative measurements of changes in fibre wall thickness during the growing season. It may be noticed that the seasonal SL thickness change in our poplar samples is very slight compared to what is observed in softwood, such as Abies alba, Picea abies or Pinus sylvestris, where a factor of more than 2.5 is observed for the tracheids wall thickness change during a season [START_REF] Cuny | Kinetics of tracheid development explain conifer tree-ring structure[END_REF].

Interestingly, this trend of increasing SL thickness remains true in tension wood with the presence of GL. This observation, always observed in our sampling, confirms some earlier unrecorded observations [START_REF] Clair | Maturation stress generation in poplar tension wood studied by synchrotron radiation microdiffraction[END_REF][START_REF] Yoshinaga | Lignification in poplar tension wood lignified cell wall layers[END_REF][START_REF] Chang | Deposition and organisation of cell wall polymers during maturation of poplar tension wood by FTIR microspectroscopy[END_REF]) and proves that this increase is not linked to the development of the GL but is a common trend throughout the growing season both in normal wood and tension wood in poplar trees. The GL thickness remains nearly constant in mature wood. This stability may be attributed to the constant stimulus as the stem is attached to a pole. However, the secondary layer increases significantly during the growing season. This would indicate that, whatever the needs for uprighting, poplar trees cannot allocate all of their resources to the production of the GL and some trade-off is needed to ensure its sustainability all along the season. 3-Fibres that were in the cambial zone at tilting time, these cells have a thin SL and constantly thick GL (Fig. 2,6: c). This interpretation of the timing of cell wall deposition assumes that a signal is received soon after the tilting. [START_REF] Jourez | Effet de la durée d'application d'un stimulus gravitationnel sur la formation de bois de tension et de bois opposé dans de jeunes pousses de peuplier (Populus euramericana cv 'Ghoy')[END_REF] have shown that a stimulus is perceived in poplar after only few hours, however modifications of the wood cell wall was more visible in opposite wood than in tension wood, thanks to a dedicated protocol using double tilting. A G-layer was observed in their study from 6 h to 48 h after tilting, depending on the trees. In our sampling, the reaction may have been slightly slower as GL was visible in one of the trees cut after 3 days and all of the trees sampled after 7 days of tilting. Concerning the modification of the cell during maturation to adapt to the new mechanical needs of the plant, it is interesting to note that this behaviour is much more reactive in poplar than what was observed by [START_REF] Yoshizawa | Formation and structure of compression wood tracheids induced by repeated inclination in Taxus cuspidata[END_REF] in softwood. In their study on artificially tilted Taxus cuspidata, they have shown that only small modifications in cell wall structure occur in tracheids that were already in the enlargement or thickening zones when the stimulus starts. We could therefore propose that this ability to transform fibres already formed is an efficient way to react to tilting and may allow poplar trees to be more efficient to react with tension wood formation than T. cuspidata with compression wood formation .

SL thickness decreased markedly from normal wood to tension wood confirming that in tension wood, GL replaces part of the S2 layers [START_REF] Saiki | Cell wall organization of gelatinous fibers in tension wood[END_REF]. Total thickness also increased compared to normal wood cells before tilting and opposite wood cells that were formed after tilting. This shows that the GL is thicker than the replaced layer that exist in normal fibres, as already observed by [START_REF] Fang | Transverse shrinkage in G-fibers as a function of cell wall layering and growth strain[END_REF].

Timing of GL versus SL deposition

In most of the samples, GL formation start after SL reached its maximum thickness. It means that SL thickening was completed before GL formation. However, in some samples, especially 25 days after tilting, SL thickness seems to increase even after the start of GL formation. This would mean that the SL is able to continue thickening when GL deposition already started. The building of the GL before the end of SL thickening is surprising as layers are supposed to be deposited one after one. Considering the presupposed assumption of the study that several cells along a radial line are considered as a single cell during maturation one could suspect a misinterpretation. In order to verify it, let us consider a second interpretation: as soon as the GL starts to be observable, the SL may be supposed to have reached its final thickness. As we observed an increasing SL thickness after GL deposition, the pattern of thickening would indicate a decrease in SL thickness from ring to cambium. This pattern has never been observed in our samples; reversely the opposite pattern was statistically significant in all our samples. Moreover, at the end of the growing season, near the ring boundary, SL tends to be thicker with no more GL (data not shown from other samples) as previously shown by [START_REF] Jourez | Effet de la durée d'application d'un stimulus gravitationnel sur la formation de bois de tension et de bois opposé dans de jeunes pousses de peuplier (Populus euramericana cv 'Ghoy')[END_REF]. Thus, even if surprising, our observations indicate that in some samples, the SL continues its thickening after GL started to be deposited. This observation can be discussed in the light of what has been observed by [START_REF] Yoshinaga | Lignification in poplar tension wood lignified cell wall layers[END_REF]. These authors observed a continuation of the lignification of the SL after the start of the GL deposition. They suggest that monolignols may be transported through the developing GL during the lignification of the SL or propose an alternative hypothesis of an external synthesis in the rays. Our observation of an increase in SL thickness could be the result of the swelling of the wall during this lignification process.

GL thickening period

Our results indicate that GL thickening distance (i.e., the number of cells from the beginning of GL deposition to the end of GL thickening) is higher in trees sampled after 25 days than in trees sampled after 14 days (Fig. 4). This observation can be interpreted in two ways: the time to mature is longer or the cell production is faster (higher growth rate). According to the computation of the number of cells produced after tilting and the distance of the tilting position to the cambium (Table 1), growth rate was more than 3 times higher during the period from 7 to 14 days than during the period from 14 to 25 days. It is therefore clear that this increase in GL thickening period refers to a longer maturation process. Tension wood is reported to have a longer maturation process than normal wood [START_REF] Bollhöner | Xylem cell death: emerging understanding of regulation and Function[END_REF]. However, the reason for this great change in maturation time remains enigmatic. No relationship was observed between the time of thickening and the final GL thickness. This indicates that thickness is not directly linked to the time of maturation.

The slope of the GL or SL thickening vs. distance to the cambium can be interpreted as thickening speed of the layers and be expressed as µm/mm. This allows us to compare cell wall layer thickening under the assumption of a constant cell division speed. It is therefore not possible to compare layers thickening at different dates or to compare TW to OW, but it remains reasonable to compare SL and GL thickening in a single TW sample. GL appears to grow faster than SL, i.e., 1.9 and 1.4 times faster in T7 and T14 respectively. At T25, around the same thickening speed was measured on average in the 3 trees in SL and GL because in one of the trees, the slope was lower for GL than for SL. This could be attributed to limited resources such as a decrease in light or temperature between T14 and T25 that affect cell division and growth rate for that tree in T25. Regarding the faster growth rate of GL compared to SL, it may be speculated that this would be a consequence of its lower carbon cost due to the lack of lignin [START_REF] Pilate | Lignification and tension wood[END_REF]) and the high mesoporosity [START_REF] Clair | Characterization of a gel in the cell wall to elucidate the paradoxical shrinkage of tension wood[END_REF]) in the GL. This would allow a faster production of thick GL, which has been recognized to be the driving force of the maturation stress generation [START_REF] Fang | Growth stresses are highly controlled by the amount of G-layer in Poplar tension wood[END_REF][START_REF] Clair | Maturation stress generation in poplar tension wood studied by synchrotron radiation microdiffraction[END_REF]. Following this idea, the lack of lignin in GL would be a strategy for a fast recovery when reaction is needed. It will be interesting in the future to test this hypothesis, especially comparing species producing TW with a GL to species where the GL is absent in TW.

Figure 1 .

 1 Figure 1. Detail of an optical image used for the measurement of cell walls parameters with ImageJ software. Scale bare = 5 µm

  Figure 2. GL and SL relative thickness change from the cambium to the ring boundary in a tree sampled 25 days after tilting. --a: SL thickening, --b: GL thickening, --c: GL constant thickness, --d: tilting, --e: before tilting. Squares: GL, circles: SL. Dotted line: left: end of SL thickening, center left: end of G thickening, center right: end of the transition, right: tilting date.

Fig. 4 :

 4 Fig.4: relationship between the mean GL thickness (plotted as relative thickness) and the GL thickening period. Squares: T14, triangles: T25. Different shades represent different trees.

Figure 5 .

 5 Figure 5. SL thickness variation in opposite wood (OW) of the sample T25-2 from the cambium to the ring boundary. The different stages of TW cell wall development as defined in Fig. 2 are indicated in the top of this figure to emphasise the change in OW due to tilting (at d).

Figure 6 .

 6 Figure 6. Schematic of the development pattern of fibre cell wall layers in a tilted tree producing GL. Thick line: GL, thin line: SL. --TZ: transition zone is the zone where already differentiated fibres change in function and develop a GL later.Transition zone at the tilting dateAround the tilting position different type of fibres are observable: 1-Fibres without GL in normal wood zone, considered to have already finished their maturation before tilting, in these cells the tilting has no effect on their cell wall thickness (Figs. 2, 6: e); 2-Fibres with decreasing SL thickness and increasing GL thickness in the transition zone (tilting), these cells already started their SL thickening before tilting then received the reaction signal and changed in function during their development, halting their SL formation in a rather thick state to start a GL at the end of the maturation (Fig.2, 6: d). 3-Fibres that were in the cambial zone at tilting time, these cells have a thin SL and constantly thick GL (Fig.2, 6: c). This interpretation of the timing of cell wall deposition assumes that a signal is received soon after the tilting.[START_REF] Jourez | Effet de la durée d'application d'un stimulus gravitationnel sur la formation de bois de tension et de bois opposé dans de jeunes pousses de peuplier (Populus euramericana cv 'Ghoy')[END_REF] have shown that a stimulus is perceived in poplar after only few hours, however modifications of the wood cell wall was more visible in opposite wood than in tension wood, thanks to a dedicated protocol using double tilting. A G-layer was observed in their study from 6 h to 48 h after tilting, depending on the trees. In our sampling, the reaction may have been slightly slower as GL was visible in one of the trees cut after 3 days and all of the trees sampled after 7 days of tilting.

ACKNOWLEDGMENTS

Special thanks are due to Prof. Joseph Gril (LMGC, CNRS, Université de Montpellier). This study received the support of the SCAC (Service de Coopération et d'Action Culturelle) of French embassy in Tehran and the Iranian center of Excellency on applied management of fast growing wooden species. Part of this work was performed in the framework of the project "StressInTrees" funded by the French National Research Agency (ANR-12-BS09-0004).