A CROSS-LAYER APPROACH FOR ENERGY EFFICIENT TRANSMISSION OF PROGRESSIVELY CODED IMAGES OVER WIRELESS CHANNELS Cristina Costa
Create-Net - Via Solteri 38, Trento, Italy
[email protected]
Fabrizio Granelli
University of Trento - Via Sommarive 14, Trento, Italy
[email protected]
ABSTRACT Mobility, made available by today’s communication networks, imposes several limitations in the design of multimedia applications, due to high error rates, reduced bandwidth, strong variability, and mobile terminals lifetime. This paper investigates the use of an energy constrained cross-layer approach for the transmission of progressively coded images over packet-based wireless channels. We propose an optimum power allocation algorithm to enable unequal error protection of a preencoded image. Simulations are performed modeling transmission over a Rayleigh fading channel. The investigation focuses on JPEG2000, but it is applicable to other progressively coded bitstreams as well. Our experimental results demonstrate that it is possible to achieve a relevant performance enhancement with the proposed approach over uniform error protection. The optimal solution can also serve as a guideline for developing less computationally intensive empiric approaches. I. INTRODUCTION In addition to limited reliability and reduced bandwidth, power consumption is becoming an increasingly important problem in mobile wireless networks. Moreover, services and users are becoming more demanding, and the need to transmit multimedia data is growing. However, high error rates, limited bandwidth, and low energy budget make the deliverery of high quality multimedia difficult at best. These problems are particularly true for new emerging network topologies, such as sensor networks or WLANbased access networks. In this paper, we consider the problem of energy constrained image transmission over a wireless packet network. We provide a solution to the problem of achieving maximum end-to-end image quality using a cross layer approach that optimally distributes the energy budget among the packets by enabling interaction between the application and the link / physical layers. Progressive coding tools, like those implemented in JPEG2000 [3], can help in the delivery of multimedia data, since they provide a very flexible approach in terms
0-7803-9134-9/05/$20.00 ©2005 IEEE
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Aggelos K. Katsaggelos
Northwestern University Evanston, IL, USA
[email protected]
of rate control. These methods achieve a fine granular SNR scalability, since the bitstream can accommodate different spatial/quality resolutions depending on the amount of data being transmitted and decoded. This characteristic can be exploited to achieve robust transmission of pre-encoded images over noisy channels, since it allows for the indentification of groups of data with different importance for the decoding procedure. Indeed, instead of using equal error protection (EEP) schemes that assign the same amount of protection to all the parts of the bitstream, it is possible to use schemes that prioritize the information, giving more importance, hence more protection, to the critical parts of the coded bitstream. This kind of approach is commonly known as unequal error protection (UEP) approach. The concept of applying UEP to the transmission of progressively coded images is not new, and has been often implemented using source coding schemes [5]-[7] (the literature on the topic is quite large and we therefore only mention a few references closely related to our work.) Our preliminary work [9] demonstrated the effectiveness of the power control based approach for transmitting video streams. The present paper extends such concepts to the transmission of wavelet-compressed images using JPEG2000, therefore extending its validity. Experimental tests underline a significant increase of the quality of the reconstructed image as compared with an EEP scheme that allocates the same amount of energy to each transmitted packet. The paper is organized as follows: in section 2, the powerbased UEP strategy is described for a generic progressively coded bitstream. Section 3 reviews the quality layer concept, supported by the JPEG2000 standard, and used in our implementation. Experimental evidence of the effectiveness of the proposed approach is provided in section 4, and section 5 draws our conclusions. II. CROSS-LAYER ENERGY-EFFICIENT UEP The idea behind cross-layer approaches is to jointly consider error protection strategies at various network layers, in order to improve the transmission efficiency in terms of protection, bandwidth and resource consumption.
In the proposed approach, we assume that the transmission power can be changed for each packet, thus varying the amount of protection of the packet itself. This is made possible by enabling information exchange between the application layer (image encoder) and the link and physical layers (responsible for data packetization and power allocation). Unequal error protection can then be achieved by tuning the power allocated to each packet transmission [13]. Based on this hypothesis, the following sections provide details of the proposed strategy. A. Progressive image transmission Progressive coding can be implemented by wavelet-based coding algorithms, like SPHIT [1] and EBCOT [2], or bitplane coding. Some of such tools are included in recent image and video coding standards such as JPEG2000 [3], MPEG-4 VTC, and FGS MPEG-4 [5]. In progressive image coding, the bitstream is constructed in such a way that it can be truncated and partially decoded, obtaining a lower resolution reconstruction of the image. If we consider a set of truncation points, we obtain a set of different coding layers where correct decoding of a layer depends on the correct reception of all previous layers. Using this feature, a packet-based progressive image transmission can be organized in such a way as to assign every layer to an independent packet. Consequently, the correct reception of a packet affects the use of the information contained in all the subsequent packets. For the sake of simplicity, we assume that the first packet, containing the image header, is always received correctly. This can be possibly achieved by implementing an ARQ scheme. Under this hypothesis, the average distortion D of the reconstructed image can be expressed as follows:
D = D0 − E [∆ ] = D0 −
L
∏ (1 − ρ )⋅ ∆ , l
l =1 i =1
i
l
(1)
where D0 is the distortion associated with the first layer only (contained in the first packet), L is the total number of transmitted packets, ρl is the loss probability for the l-th packet (or layer), and ∆l is the distortion reduction associated with the l-th layer. Since lower layers have greater importance than higher ones, the transmission of some packets will be more critical than others. Therefore, this multi-layer approach can be successfully associated with an UEP scheme. B. Problem formulation The proposed approach aims at solving the problem of how to transmit an image with minimum end-to-end distortion, given a limited energy budget. The problem can be formulated as follows:
min D s.t. E tot = Pl
L l =1
B l ⋅ Pl , R
(2)
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where R is the bitrate, and Bl, Pl are the size and the power assigned to the l-th packet, respectively. Using Lagrange multipliers, (2) can be converted into the following equivalent unconstrained problem:
minJ = min D0 − Pl
Pl
L
l
∏(1 − ρ ) ⋅ ∆ + λ i
l =1 i =1
l
Bl ⋅ Pl R l =1 L
,
(3) where λ is the Lagrange multiplier that needs to be chosen so that the constraint in Eq. (2) is satisfied. Since the average transmission power used by a modulation scheme directly affects the probability of packet loss, we define the function g as the relationship between the loss probability ρl of the l-th packet and the power Pl: ρ l = g (Pl ) (4) This relationship is assumed to be known at the transmitter and it depends on the characteristics of the physical layer. In paragraph 2.3, we use a classical analytic model, but other channel models and/or empirical evaluations can be employed as well. The minimization problem can be solved by computing the first derivative of the cost function J with respect to PL, and by rearranging the equations. The following expression is obtained: −1 −1 L L ∂ρ j (5) ∂ρ L B ⋅ (1 − ρ ) = ⋅ (1 − ρ ) ⋅ L ⋅ (1 − ρ )−1 ⋅ ∆ l −1 + 1 ∂Pj
j
∂PL
L
Bj
∏
l = j +1 h = l
h
∆L
In paragraph 2.3, we will see how (5) can be used to calculate the relationship between the power assigned to the various packets and the optimal solution. With a similar approach it is possible to solve the dual problem also, i.e., how to transmit the image by minimizing the transmission energy, subject to a minimum distortion constraint. In the optimal solution resulting in this case the power assignment must obey the same relationship as in (5).
C. Channel model definition We consider transmitting in an erasure channel where the data are first grouped in packets and then transmitted. In this framework, the packet is either delivered free of errors or dropped by the system. We consider a narrow-band slowly-fading channel with additive white Gaussian noise. The adopted model derives from a study on capacity versus outage of Ozarow, Shamai, and Wyner [10], according to which: −k N ⋅W Pj ρ j = 1− e ; k= 0 ⋅ (2 R W − 1) (7) E [H ] where W is the channel bandwidth, N0W the noise power, R the bitrate, and E[H] the expected channel state (we consider a Rayleigh fading channel, H being the channel’s fading, fixed for each packet). Typical values for new
(a)
(b)
(c)
Fig.1. PSNR Gain in dB vs. N0⋅W/E[H] (interference plus noise) for packets of 100 bytes (a), 250 bytes (b) and 500 bytes (c): average over 3,000 experiments; 100 QL distributed between 0.001 bpp and 0.1 bpp
generation wireless standards [11] are N0W/E[H] = 6 W, R = 225, and W = 5MHz. The bit budget is given by T·R, where T is the transmission time and R the bitrate. By using the channel model in (7), it is possible to rewrite the expression in (5) as:
(P ) = (P ) 2
j
2
L
⋅
BL ⋅ Bj
L
L
∏e
l = j +1 i = l
+ k
Pi
⋅
∆ l −1 +1 . ∆L
(8)
Equation (8) describes in a closed form the relationship among the values of power assigned to the various packets, when optimal power allocation is to be achieved. In particular, once the power of the last packet PL is assigned, it is possible to recursively calculate the power Pj (j=1,…,L-1) to be assigned to all the remaining packets and the total energy consumption. In order to solve the minimization problem, it is sufficient to find the value of PL that satisfies the energy budget. In the dual problem, the same relationship is used to find the minimum energy necessary to obtain the desired distortion. III. QUALITY SCALABILITY IN JPEG2000 The above described method was applied to image transmission exploiting the Quality Layers (QL) implemented by the wavelet transform based JPEG2000 compression standard [3]. In JPEG2000 baseline, the several wavelet sub-bands generated during compression are divided, for coding purposes, into several smaller blocks called codeblocks. Embedded bitstream coding is achieved by independently quantizing and bitplane-encoding each codeblock. When the decoder detects an error, it typically discards all successive data related to the codeblock where the error has occurred, thus producing a lower quality version of the decoded data related to that codeblock, as if it were encoded using a coarser quantisation parameter. In order to improve the rate distortion curve that allows embedded scalability, in JPEG2000 it is possible to create,
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at the encoding time, a certain number of Quality Layers (QL). The user can decide how many QLs to implement and at which coding rates. Each QL progressively accommodates data contributions from the codeblocks Data is chosen so that the distortion at each QL is minimized. Using this approach, each time a QL is added to the bitstream, the distortion of the obtained decoded image is reduced in the rate-distortion sense in an optimal way. If the number of layers is large enough, the distortion associated with the bitstream truncated at a random point will be close to the optimal one, achieving a near optimum progressively coded bitstream. IV. SIMULATIONS RESULTS In this section we present the results obtained using a test set of high resolution monochromatic images: woman, bike, café, and water. The image compression tool adopted in these experiments is the kakadu v4.1 implementation of JPEG2000 standard [12]. For the sake of simplicity, in this work we consider the image coded as a single tile. The number of encoded QLs is set to 100, with bitrates distributed between 0.001 bpp and 0.1 bpp. Each QL (or part of it) is assigned for transmission to an independent packet. Results achieved by optimal UEP are compared with an equal power allocation scheme with the same total energy budget. In the experiments an energy budget of 2 Joules is employed, and results are averaged over 3.000 experiments. In Fig.1 (a, b, c), the PSNR gain is reported for increasing noise values (expressed as interference plus noise power, N0W/E[H]) and different packet sizes. As the total energy budget increases, the difference between the two methods becomes less significant. The point at which the curve starts decreasing depends on the type of the encoded image, how difficult it is to compress it and its size (Table 1). When the total quality of the decoded image is high, the difference between UEP and EEP can be more relevant, since the optimal UEP automatically chooses an
appropriate truncation point, avoiding transmitting data that do not significantly contribute to image quality. The data obtained through optimal power allocation allows us to evaluate how much it is possible to improve the performance of the system in terms of energy consumption. As an example, the channel gains obtained by choosing the parameter k of the channel model equal to 1 and a packet size equal to 100 bytes (Table 1) show that it is possible to achieve a significant improvement in the final distortion with a wise use of the energy budget.
woman bike cafe water
TABLE 1 – DECODED IMAGE PSNR Size PSNR PSNR (pixel X pixel) Optimal UEP EEP 2048x2560 26.77 25.33 2048x2560 22.54 20.13 2048x2560 19.08 17.39 1465x1999 44.47 42.88
PSNR Gain
1.44 2.41 1.69 1.60
The rate-distortion data used in the optimization procedure can be obtained in the following two ways: (i) by truncating the bitstream at different points or (ii) directly using the R-D data generated by the JPEG2000 encoder. Indeed, during the creation of the QLs, a set of layer datalength and distortion-length slopes is generated and these can be used to calculate the approximate distortion reduction introduced by a QL. For comparison purposes in Fig. 2 the resulting optimal power allocation per packets is reported: plotted data are obtained using both directly calculated data and encoder statistics. It can be observed that the two curves are nearly identical. For implementation purposes, then, it is possible to use the R-D data directly obtained from the encoder, therefore avoiding collecting R-D data from a time and resource consuming measurement process.
obtained are encouraging, demonstrating that, in the case of progressively coded images, the use of unequal power can significantly improve the quality perceived by the user. The algorithm was implemented in the framework of the JPEG2000 standard, but it can also be applied to generic bitstreams containing progressively encoded data or RoI information as well. The proposed solution can be used both as an upper bound during the design of empirical methods or directly for transmitting data. In this last case it is possible to use an R-D model instead of the measured data, in order to speed up the assigned power calculation and save precious resources. Moreover, the rate-distortion optimization phase can be adapted to quality measures other than the MSE without loosing the general validity of the proposed approach. This will allow introducing adaptivity criteria based on visually meaningful distortion measures, taking into account contrast sensitivity and/or visual masking. REFERENCES [1] [2] [3] [4] [5] [6] [7]
[8] [9] [10] [11] Fig.2: Assigned Power vs. Packet Number
[12]
V. CONCLUSIONS
[13]
The problem of optimal power allocation for image transmission over wireless packet networks was addressed and a new algorithm was proposed. The results we
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