ENERGY-AWARE ON-LINE ALGORITHMS FOR IMAGE TRANSMISSION OVER WIRELESS LAN R. Chandramouli
S. Sri Ganesh Veera Kumar and R. N. Uma
Department of E.C.E. Stevens Institute of Technology Email:
[email protected]
Department of Computer Science The University of Texas at Dallas Email: {sriganesh,rnuma}@utdallas.edu
ABSTRACT In this paper, we analyze the performance of on-line image transmission algorithms designed to minimize wastage of battery energy and bandwidth over bursty wireless channels. These algorithms estimate the wireless channel state in an online fashion and adapt accordingly. Theoretical basis for these algorithms are presented using competitive analysis. Computational and transmission energy consumption factors are taken in to account. Experimental results show that some of the proposed algorithms can results in significant performance improvement. I. INTRODUCTION The mobility of a wireless device is limited by its battery life. In addition to limited battery power, the performance of wireless networks is constrained by time-varying channel capacity, bursty and location-dependent channel errors and limited bandwidth. To address the issue of limited battery power, research has focused on low power signal processing circuits and architectures to increase battery life. Alternatively, one can design channel-adaptive transmission algorithms that minimize the wastage of battery power. In this paper, we take the latter approach. The focus of this paper is on transmission control strategies that adapt to the time varying wireless network conditions in an online fashion (on the fly) with a goal towards higher energy efficiency. Such algorithms can employ a number of strategies, for example, employ a channel predictor to obtain information about the state of the wireless channel, blindly estimate the channel state, estimate the probability distribution of the channel state variation, or use non-adaptive and adaptive thresholding schemes to decide when to transmit and when to stop. We consider the last approach here. We analyze the proposed strategies using competitive analysis techniques [1]. This analysis shows how good the proposed link layer transmission control algorithms are compared with the optimal algorithm that has perfect knowledge of the states of the wireless channel for the entire duration of
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the communication. Clearly, the optimal algorithm is not practical. Techniques for estimating/predicting wireless channel states include pilot-symbol aided channel estimation [2], [3], blind estimation [4], [5] and techniques involving periodically probing the channel to detect any changes in the channel state information [6]. It has been observed that pilot symboling can cause up to a 14% loss in capacity [2]. Blind channel estimation schemes usually tend to be computationally expensive causing concern for low power mobile wireless networking. Therefore, an approach that balances the transmission energy consumption with the reception quality would be a good alternative. Since image and video data can sustain certain amount of packet loss, in this paper, we investigate online techniques for transmission that neither use pilot symbols nor perform complex signal processing operations for channel estimation. We consider a two-state Markov chain model for the wireless channel. The states correspond to “GOOD” (G) and “BAD” (B), respectively. When the link is in the G state, the packet error probability is within acceptable levels (usually low) and in the B state the link has an unacceptable packet error rate. For sake of simplicity, in this paper, we assume that the packet error probability in G state is zero and in the B state it is 1. The two state model has a state transition probability matrix given by, PBB PBG (1) PGB PGG where PBB = P (current state is B|previous state is B), etc. If PBB = PGG then it is not difficult to show that the correlation coefficient of this symmetric Markov chain is given by, ρ = PBB − PBG = PGG − PGB .
(2)
which can be viewed as a measure of the burstiness. A higher value of ρ means that the channel is more bursty compared to a smaller ρ. For this two state wireless channel mode we present both non-adaptive and adaptive on-line transmission control strategies. We assume that packet
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losses are solely due to the physical imperfections of the wireless channel, i.e., we neglect other interferences such as multi-user interference, etc., for the sake of simplicity. The rest of this paper is organized as follows. Competitive analysis is introduced in Section II. Section III contains the description of the proposed channel-dependent transmission algorithms and their theoretical results. Section IV details the simulation study and presents the experimental results. Conclusions can be found in Section V. II. COMPETITIVE ANALYSIS
if number of consecutive packets lost ≥ r {stop transmission restart transmission after To time units}. Theorem 1: [8] The deterministic algorithm, Ar is 2competitive. III-B. Adaptive Algorithm
Problems arising in the real world are best formulated as on-line problems. When designing algorithms to solve such problems, the algorithms do not have access to the whole input sequence at once; the input is made available to the algorithm piece by piece. The algorithm needs to make irrevocable decisions with only a partial knowledge of the input. Traditionally, such algorithms are analyzed through an average-case analysis where the distribution of the input sequence is hypothesized and the expected cost is computed. However, a drawback of this scheme is that the distribution of the input sequence is rarely known precisely. Sleator and Tarjan [1] introduced a different method of analyzing on-line algorithms known as competitive analysis. Competitive analysis is a worst-case analysis where the cost of the on-line solutions is compared to the cost of the optimal off-line solution. Though, this approach seems to be pessimistic, it has been widely used to analyze a variety of problems; refer to [7] and the references contained therein. An algorithm A is said to be c-competitive if for all valid input sequences I, costA (I) ≤ c·cost OP T (I), where cost A (I) is the cost incurred by algorithm A on input sequence I and cost OP T (I) is the cost incurred by the optimal off-line algorithm on input sequence I. III. COMPETITIVE ALGORITHMS In this section, we present three different algorithms for solving the channel adaptive image transmission problem: (i) a simple deterministic algorithm that is 2-competitive; (ii) an adaptive algorithm, that “learns” the input sequence and takes action accordingly; and (iii) a randomized algorithm that yields a better competitive ratio than the deterministic algorithm. In this paper, we only state these results as theorems; we refer the reader to [8] for their proofs. III-A. Deterministic Algorithm Let Et be the energy dissipated in transmitting one packet by the mobile unit. Let Ed be the energy dissipated during To time units where To is the time-out period after which the mobile unit will resume transmission. Let d r = E Et where r ≥ 1 without loss of generality. Our on-line algorithm, denoted Ar , is as follows:
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We use a stochastic adaptive learning technique to determine whether or not to transmit based on a probabilistic estimate of the current channel condition. Consider two control actions available to the adaptive algorithms, namely, α1 : transmit a packet and α2 : do not transmit a packet. If the transmitter sends a packet, it waits for a fixed time period to receive an acknowledgement (ACK). If an ACK is received within this period then the action α1 is rewarded (with feed back from receiver, β = 0), if not a time-out occurs and α1 is penalized (β = 1). Then, a modified version of the reward-penalty learning algorithm is used to update the control action probabilities at time n in the set p(n) = {p1 (n), p2 (n)}. Then the transmission decision at time n is chosen according to the probability distribution p(n). This process continues until the probability vector p(n) converges when the state of the channel is predicted accurately one time unit ahead. We assume that the reverse channel or the feedback channel is considered to be error free. The effect of an erroneous feedback channel and feedback delays will be considered in future research. It is also assumed that an ACK is generated for every packet transmitted. Depending on the needs of the situation the feedback and updating can also be done after every few packets with some minor changes to the proposed algorithm. Based on the above learning technique we can describe an algorithm A as follows:
Algorithm Adaptive: For slot n {transmit with probability p1 (n) do not transmit with probability (1−p1 (n)) and restart transmission after To time units}.
Theorem 2: [8] The competitive ratio of the adaptive algorithm is r + 1 in expectation, where r ≥ 1 is defined d as E Et
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(a) Lower (psnr=28.91dB)
Bound
(b) Optimal (psnr=24.41dB)
(c) (psnr=12.88dB)
Oblivious
Fig. 1. Received Lena image according to the various transmission strategies using Lucent’s Orinoco wireless LAN card. Lower Bound corresponds to the best possible performance achievable by optimal. Oblivious corresponds to vanilla transmission that transmits irrespective of current channel condition. The simulation parameters for this set of results is ρ = 0.9, To = 100 and r = 3. The base layer was assumed to be transmitted without any errors. figure
We refer to the above adaptive algorithm as Adaptive (with timeout). We consider another variant of the adaptive algorithm that does not timeout which we refer to as Adaptive (without timeout). III-C. Randomized Algorithm Let σx be an input sequence of channel states, for example, G,G,B,B,B .... Let Ai be the deterministic algorithm of Section III-A with threshold i. The randomized algorithm A chooses algorithm Ai with a probability πi .
Algorithm Randomized: Let Ai be the algorithm Deterministic with threshold i. Choose Ai with probability πi .
Theorem 3: [8] The randomized algorithm has a come . petitive ratio e−1 IV. EXPERIMENTAL RESULTS We evaluate the performance of the algorithms in Section III through simulations. Our simulation model consists of two nodes – one node is the sender and the other the receiver. The channel between the two nodes is simulated as a two-state Markov model. Images are transmitted over this wireless channel. The images were encoded using the Layered-DCT (LDCT) compression algorithm of [9]. Each image was
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subdivided into 16x16 blocks and each block was encoded into 4 layers — layer 0 being the most important base layer and layer 3 the least important highest layer. The blocks were raster-scan ordered. The layering was achieved through the LDCT algorithm. In the LDCT algorithm, the DC coefficients are coded into the base layer (layer 0) as in baseline JPEG and for the AC coefficients, consecutive bit planes are grouped into a layer for a total of three layers. Each layer is run-length coded. We point out that we did not implement the optimizations discussed in [9]. The images were encoded at a rate of 0.64 bits/pixel. Our simulations were done using three parameters: (i) the correlation coefficient of the channel (ρ) as defined in Eq. (2). In our experiments, ρ ∈ {0.3, 0.5, 0.7, 0.9}. (ii) The time-out period To is the period after which the mobile unit will resume transmission. To is varied in multiples of ν, where 1/ν is one packet duration. (iii) The parameter r that is explicitly used in the Deterministic d and Randomized algorithms. r = E Et where r ≥ 1 without loss of generality. The different energy profiles we considered in our experiments are tabulated in Table I. However, due to space limitations we only present our results for one wireless LAN card. We compare the relative performance of the competitive algorithms based on the energy wasted in transmitting one image, the delay incurred, packet loss and PSNR (Peak Signal to Noise Ratio)1 of the received image. Throughout the simulations, we measure time in units of ν where ν is the time taken to transmit one packet which corresponds 1 PSNR
is the ratio of peak signal power to noise power in dB and is (255)2 given by PSNR = 10 log10 . MSE
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(a) Randomized (psnr=18.00dB)
(b) Deterministic (psnr=17.46dB)
(c) Adapt (without timeout) (psnr=13.74dB)
(d) Adapt (with timeout) (psnr=13.07dB)
Fig. 2. Received Lena image according to the various transmission strategies using Lucent’s Orinoco wireless LAN card. The simulation parameters for this set of results is ρ = 0.9, To = 100 and r = 3. The base layer was assumed to be transmitted without any errors. figure Energy Profile Parametric Setting PC 4800 (wireless LAN card) Lucent Orinoco (wireless LAN card) Rockwell WINS (sensor node) Medusa II (sensor node)
To {10ν, 100ν} 6ν 10ν 20ν 100ν 155ν 311ν 5ν 10ν 100ν 5ν 10ν 100ν
r {2, 5, 10} 3 5 10 3 5 10 3 6 54 3 6 51
r
Energy
Delay
100 155 311
3 5 10
6875.60 7281.46 8259.10
25360.00 34379.00 56104.40
Avg. Lost Pkts 554.20 746.60 1028.00
PSNR 17.38 15.74 15.07
Table II. Performance of the Randomized algorithm for Lucent’s Orinoco wireless LAN card under different performance measures for the channel correlation coefficient of ρ = 0.9. table
Table I. The different energy profiles considered in our simulations table to one slot. Our image was encoded into 4096 layers and each layer was packetized into one packet. We evaluated the algorithms Randomized, Deterministic, Adaptive (without timeout) and Adaptive (with timeout). In addition we also present the performance of Optimal and Lower Bound. Optimal “knows” in advance the length of the bad burst and can take actions accordingly. Lower Bound refers to the ideal case where packets are transmitted only in good slots and the wireless card goes to the sleep state in bad slots. For all of the algorithms, we assume the transition energy is negligible. In this paper, due to space considerations, we present only results corresponding to Lucent’s Orinoco wireless LAN card and channel correlation coefficient of ρ = 0.9. However, this is representative of our entire data. From Tables II, III, and V we can see that Randomized and Deterministic give about 1 to 3.5 dB PSNR improvement
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To
r
Energy
Delay
100 155 311
3 5 10
6749.60 6977.35 7203.88
22560.00 27621.00 32655.00
Avg. Lost Pkts 678.60 894.00 1052.40
PSNR 16.48 15.29 14.64
Table III. Performance of the Determinsitic algorithm for Lucent’s Orinoco wireless LAN card under different performance measures for the channel correlation coefficient of ρ = 0.9. table over Adaptive (with timeout). As r and the time-out period increase, packet loss and hence energy wasted decrease. Also, with an increasing r and time-out period, the corresponding delay increases. Hence these competitive algorithms provide a delay vs. energy tradeoff. Figures 1 and 2 gives a visual insight to the relative performance of the various transmission algorithms. From Figure 2 it can be observed that Randomized clearly outperforms the other algorithms. This is the case in all of our simulations. More importantly, the relative performance of the three algorithms Randomized, Deterministic and
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To
r
Energy
Delay
100 155 311
3 5 10
5823.71 5823.71 5823.71
1984.60 1984.60 1984.60
Avg. Lost Pkts 1479.80 1479.80 1479.80
PSNR
To
r
Energy
Delay
13.12 13.12 13.12
100 155 311
3 5 10
7163.60 7596.73 8186.32
31760.00 41385.00 54487.20
Table IV. Performance of the Adaptive (without timeout) algorithm for Lucent’s Orinoco wireless LAN card under different performance measures for the channel correlation coefficient of ρ = 0.9. table To
r
Energy
Delay
100 155 311
3 5 10
13537.40 17445.43 29363.56
173400.00 260245.00 525092.40
Avg. Lost Pkts 1536.00 1458.80 1445.40
Avg. Lost Pkts 82.20 197.20 403.60
PSNR 23.75 21.03 18.43
Table VI. Performance of the Optimal algorithm for Lucent’s Orinoco wireless LAN card under different performance measures for the channel correlation coefficient of ρ = 0.9. table
PSNR
To
r
Energy
Delay
12.89 13.52 13.31
100 155 311
3 5 10
5517.38 5517.38 5517.38
4279.60 4279.60 4279.60
Avg. Lost Pkts 0.00 0.00 0.00
PSNR 28.91 28.91 28.91
Table V. Performance of the Adaptive (with timeout) algorithm for Lucent’s Orinoco wireless LAN card under different performance measures for the channel correlation coefficient of ρ = 0.9. table
Table VII. Performance of the Lower Bound algorithm for Lucent’s Orinoco wireless LAN card under different performance measures for the channel correlation coefficient of ρ = 0.9. table
Adaptive closely match that of their theoretical performance guarantees of 1.58, 2 and (r+1) respectively, where their theoretical performance guarantee is expressed as a ratio of the performance of the algorithm to that of an optimal off-line algorithm.
[4] M.C. Tournier, A. Ferreol, and P. Larzabal, “Low complexity blind space-time identification of propagation parameters,” Proc. ICASSP, vol. 5, pp. 2873 –2876, 1999. [5] L. Tong and S. Perreau, “Multichannel blind identification: From subspace to maximum likelihood methods,” Proc. of the IEEE, vol. 86, no. 10, pp. 1951–1968, Oct. 1998. [6] Michele Zorzi and Ramesh R. Rao, “Error control and energy consumption in communications for nomadic computing,” IEEE Trans. On Computers (Special Issue On Mobile Computing), vol. 46, pp. 279–289, March 1997. [7] A. Borodin and R. El-Yaniv, Online computation and competitive analysis, Cambridge University Press, 1998. [8] R. Chandramouli and R. N. Uma, “To transmit or not to transmit: An investigation using competitive analysis,” Proceedings of the IEEE Wireless Communications and Networking Conference, 2003. [9] E. Amir, S. McCanne, and M. Vetterli, “A layered DCT coder for Internet video,” in Proc. IEEE Int. Conf. Image, Lausanne, Switzerland, 1996.
V. CONCLUSION We have presented several online algorithms for image transmission over bursty wireless channels. These algorithms control the transmission by adapting to the channel state on-the-fly. Theoretical analyses of these algorithms are presented along with experimental results. Experiments show that significant energy savings can be achieved using the proposed techniques within acceptable quality of the received image. ACKNOWLEDGMENT R. Chandramouli was partially supported by NSF ITR CCR-0082064 and NSF CAREER ANIR-0133761. VI. REFERENCES [1] D. D. Sleator and R. E. Tarjan, “Amortized efficiency of list update and paging rules,” Communications of the ACM, vol. 28, no. 2, pp. 202–208, February 1985. [2] J.K. Cavers, “An analysis of pilot-symbol assisted modulation for rayleigh fading channels,” IEEE Trans. on Vehicular Technology, vol. 40, pp. 686–693, Nov. 1991. [3] P. Spasojevic and C.N. Georghiades, “Complementary sequences for isi channel estimation,” IEEE Trans. on Information Theory, vol. 47, no. 3, pp. 1145–1152, March 2001.
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