1 Joint Smoothing and Source Rate Selection for Guaranteed Service Networks Olivier Verscheure, Pascal Frossard and Jean-Yves Le Boudec To be published in IEEE INFOCOM, Anchorage, Alaska, March 2001. Abstract—We consider the transmission of variable bit rate (VBR) video over a network offering a guaranteed service such as ATM VBR or the guaranteed service of the IETF. The guaranteed service re- quires that the flow accepted by the network has to be conforming with a traffic envelope . In this context, the output of the video en- coder is constrained by the traffic envelope defined at the network entry point, the playback delay budget and the decoding buffer size. In previous works, the constraints are satisfied either by smoothing a fixed coder output, or by modifying the encoding parameters. In this paper we take a combined approach. This allows us to find a joint source rate selection/smoothing solution which minimizes the to- tal average distortion while satisfying constraints on traffic envelope, playback delay and decoding buffer size. Our solution is based on a Viterbi-like algorithm. Our approach is made possible by the repre- sentation of the optimally smoothed output as the time inverse of a shaper output. Experimental results exhibit significant improvements in terms of total average distortion compared to the smoothing of a fixed coder output, under equivalent traffic parameters and decoding constraints. I. I NTRODUCTION We consider the transmission of variable bit rate (VBR) video over a network offering a guaranteed service such as ATM VBR or the guaranteed service of the IETF [1], [2]. The guaranteed service requires that the flow produced by the output device conforms with a traffic envelope , namely over any window of size , the amount of data does not exceed . With the Resource Reservation Proto- col (RSVP), is derived from the T-SPEC field in mes- sages used for setting up the reservation, and is given by , where is the maximum packet size, the peak rate, the sustainable rate and the burst tolerance [3]. The function is also called an arrival curve. In our framework, the video source must thus produce an output conforming with the arrival curve constraint. One approach for achieving this is called rate control [4], [5], [6]. It consists in modifying the encoder output, by acting on the quantization parameters. Rate control is a delicate issue in video coding since it significantly affects the video quality. An alternative approach is to smooth the video stream, using a smoother fed by the encoder [7], [8], [9], Olivier Verscheure is with the IBM T.J. Watson Research Center, New- York, USA. Pascal Frossard was with the Signal Processing Laboratory (LTS) at EPFL, Switzerland. He is now with the IBM T.J. Watson Research Center. Jean-Yves Le Boudec is with the Institute for Computer Communica- tions and Applications (ICA) at EPFL, Switzerland. Contact author: O. Verscheure (ov1@us.ibm.com). [10]. This work combines both approaches. Our scenario is illustrated on Figure 1. A video signal is encoded, and then input into a smoother. The smoother writes the stream into a network for transmission. The smoother also feedbacks the optimal channel rate for the next time interval . We call the total num- ber of bits observed on the encoded flow, starting from time , and the output of the smoother. The smoother output must satisfy the traffic envelope constraint given by some function negotiated with the network, which can be expressed as for all [10]. At the destination, the receiver stores incoming bits into a decoding buffer before passing them to the decoder. The decoder starts reading from the decoding buffer after a de- lay , and then reads the decoding buffer so as to reproduce the original signal, shifted in time. Thus the output of the decoding buffer is equal to , where is equal to plus the transfer time for the first packet of the flow. The delay is called playback delay at the receiver. We assume that the network offers to the flow a guar- anteed service, such as defined for example by the IETF. Call the cumulative function at the output of the net- work. The transformation can be decomposed into a fixed delay, and a variable delay. Without loss of generality, we can reduce to the case where the fixed de- lay is zero, since it does not impact the smoothing method. The variable delay is due to queuing in, for example, guar- anteed rate schedulers. The relationship between and cannot be known exactly by the sending side, because it depends to some extend on traffic conditions; however, the guarantee provided by the network can be formalized by a condition of the form [11], [12], [13], [14]: such that In the condition, is a function, called the network ser- vice curve, which is negotiated during the reservation setup phase. For example, the Internet guaranteed service as- sumes the form where is called the latency and the rate. We consider smoothing strategies that ignore the details of the network, but do know the ser- vice curve . This paper extends our previous work on optimal smoothing [10]. In our previous work, we have demon- strated that there exists an optimal smoothing strategy that simultaneously minimizes the playback delay and the re-