An Inherently Loss-Less and Bandwidth-Efficient Periodic Broadcast Scheme for VBR Video Ioanis Nikolaidis Computing Science Department Universityof Alberta Edmonton, Canada
[email protected] 1.
Allan Hu Computing Science Department University of Alberta Edmonton, Canada
[email protected]
Fulu Li OpenlP Environment Nortel NetworksCorp. Ottawa, Canada
[email protected]
INTRODUCTION
frames of the i-th segment. Then N = ~ = 1 ]S~[. Thus, the total bandwidth necessary, B, to transmit a specific video is B = ~i=1 U bi. Given a playout latency w and the frame sequence fi the question is how to partition the frame sequence to K segments and how to determine the per-channel bandwidth bi in order to minimize B. We note that for a given video the bandwidth B is both the necessary server bandwidth and the necessary client bandwidth, that is, the client and server bandwidth demands are coupled. In order to guarantee the startup latency w, the first segment must be broadcast at a bandwidth bz = ~ e stol f~ The first segment will be completely consumed at timepoint w + (]Sll/FF), hence the bandwidth of the second segment
Many recent proposals for the support of Video-on-Demand (VoD) use a form of periodic broadcast scheduling and assume Constant Bit-Rate (CBR) encoded videos [1, 2, 3, 4, 6, 7, 10]. The few existing proposals [5, 9] for support of the more efficient Variable Bit-Rate (VBI:t) video encoding schemes, employ forms of lossy multiplexing. Thus they can be used for VBR video but at the cost of data losses. In this paper we address the issue of the VBR encoded video broadcast and we propose an inherently Loss-Less and Bandwidth-Efficient (LLBE) scheme. Given ample client storage, LLBE can satisfy any a-priori prescribed per-video startup latency, w. In LLBE, the bandwidth necessary for the transmission and downloading of a video is minimized through an optimization process. We also note that minimization of the server bandwidth can be stated as a shortest path problem and solved in polynomial time.
must be b2 = ~+(IS~/F)" In the general case:
~ e s , fJ
b~ = .
i--1
w + ~ = 1 Is~l
2.
THE LLBE S C H E M E
i=1,...
,K
(1)
F
LLBE operates by partitioning the entire video into K smaller successive and non-overlapping segments. Each segment, Si, is continuously broadcast on a separate channel. Each channel is assigned a different bandwidth, bi. The client set-top box starts downloading the frames of all the segments of a specific video immediately upon "tuning-in". As soon as the first segment is completely downloaded, the uninterrupted playont of the video can begin. The same approach has been used in other proposed schemes as well [2, 7]. Because of the schedule construction employed in LLBE, subsequent segments are guaranteed to be completely downloaded by the client just prior to their consumption.
The loss-less nature of LLBE is evident since the aggregation of the bandwidth required for all the K segments, is constant and equal to B. Thus, the optimization objective is to minimize B by deciding how to assign the S~'s (the b~ will be determined as a side-effect of selecting the S~ according to equation 1). Essentially, we wish to determine an ordered sequence of K integers (the "boundaries" between the segments) in the range 1 to N - 1 that minimizes B. It turns out that the optimization problem is in fact a shortest path problem on a directed acyclic graph. Let us consider the collection of frames from the i - t h to the (j - 1)-st frame (inclusive). We define C~d, the bandwidth "cost" of grouping together in a segment the frames from i to (j - 1).
Assume that the consumption rate of each video is F frames per second. The frame sequence of each video is fully known a priori. Let f~, i = 1, ..., N, stand for the number of bits in the i-th frame of the video, where N denotes the totai number of frames. Let S~ denote the set of successive
j-1
Thus, Cij = ~ w + ~ Based on C~j we can define a graph " with N + 1 vertices and edges from i to j. The edges are defined only for N + i _> j > i _> 1. The edge weights are C~j. The equivalent optimization problem is to find a path from vertex 1 to vertex N + 1 which consists of at most K edges and which minimizes the cost of the path (i.e., shortest path). It is appealing to apply the Bellman-Ford algorithm by stopping after the ( K - 1)-st iteration. However for realistic values of N (in the order of hundreds of thousands), even the cost matrix cannot fit in main memory. Instead, the edge costs are calculated on-demand, by A j--At precalculating the partial sums, Ai. That is, C~,j = ~,+~
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116
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K(segments) Figure 1: O p t i m a l server b a n d w i d t h , B, for t h r e e s a m p l e v i d e o s t r e a m s (source [8]) vs. K, (w = where space.
Ai
= ~ j =i-t , [j.
The Ai vector requires only
O(N)
LLBE
An important feature of LLBE, is the ability to reduce the required bandwidth by increasing the number of partitioned segments, K. The point is demonstrated in the example of Figure 1. It is also evident that for K ~ c~, an asymptotic bandwidth demand exists for a given playout latency w. The exact asymptotic bandwidth demand is highly dependent on the content of the video, that is on the frame sizes of the particular video sequence. Moreover, using the same algorithm we have determined two more interesting properties of LLBE. First, for a sufficiently large frame sequence (therefore large N) and for a large K: bi+t ~ bi
(2)
after a certain i. The property indicates that the latter segments, which correspond to channels of smaller bandwidth are roughly equal in terms of the per-channel bandwidth. To complement this property, we have also observed that: E /ES~+t
'fJ ~ .B E "fJ
(3)
jES~
that is, the traffic v o l u m e in latter s e g m e n t s increases in all exponential m a n n e r (j9 > i). A short c o m p a r i s o n s with p r e ~ o u s l y p r o p o s e d s c h e m e s for VBI:t traffic is also s h o w n
in Figure 2 and demonstrates the bandwidth ei:ficiency of LLBE. We must underline however that the bandwidth efficiency comes at the cost of a large client storage capacity.
3.
Scheme
REFERENCES
[1] Aggarwal, C., Wolf, J., Yu, P., "A permutation-based pyramid broadcasting scheme for video-on-demand systems," In Proc. IEEE Int'l Conf. on Multimedia Systems '96. [2] Hu, A., Nikolaidis, I., van Beek, P., "On the Design of Efficient Video-on-Demand Broadcast Schemes," In Proc. of MASCOTS '99, pp. 262-269.
VBR-B [5] TAF [9]
Loss Rate 0.000 0.153 0.104
60see).
~B 33.587 86.958 60.722
Figure 2: D a t a loss rate a n d total required bandw i d t h (in M b i t s / s e c ) for t h r e e V B R b r o a d c a s t i n g s c h e m e s for a collection o f 10 v i d e o s (source [8]). ( K = 7, w = 16.5sec, losses r e p o r t e d for Hnk bandw i d t h o f 33.6 Mbits/sec) [3] Hua, K., Sheu, S., "Skyscraper Broadcasting: A New Broadcasting Scheme for Metropolitan Video-on-Demand Systems," In Proc. of SIGCOMM '97, pp. 89-100. [4] Juhn, L., Tseng, L., "Harmonic Broadcasting for Video-on-Demand Service," IEEE Trans. on Broadcasting, vol. 43, no. 3, pp. 268-27'1. [5] Li, F., Nikolaidis, I., "Trace-Adaptlve Fragmentation for Periodic Broadcast of VBR Video," In Proc. of NOSSDAV '99, pp. 253-264. [6] Paris, J., Carter, S., Long, D., "Efficient Broadcasting Protocols for Video on Demand," In Proc. of MASCOTS '98, pp. 127-132. [7] Paris, J., Carter, S., Long, D., "A Low Bandwidth Broadcasting Protocol for Video on Demand," In Proc. ot IEEE ICCCN 1998. [8] Rose, O., "Statistical Properties of MPEG Video Traffic and Their Impact on Traffic Modelling in ATM Systems," TR 101, U. of Wuerzburg, Germany, Feb. 1995. [9] SapaciUa, D., Ross, K., Reiaslein, M., "Periodic Broadcasing with VBl~-Encoded Video," In Froc. of IEEE Infoeom '99, pp. 464---471. [10] Viswanathan, S., Imielinski, T., "Metropolitan Area Video-onDemand Service Using Pyramid Broadcasting," Multimedia Systems, vol. 4, no. 4, pp. 197-208.
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