1. Clustering of Source/Channel Rate Allocations for Receiver-driven Multicast under a Limited Number of Streams Philip A. Chou, Microsoft Research Kannan Ramchandran, UC Berkeley

2. Multicast Sender sends one stream (of packets) into the network; the stream is replicated as necessary in the network to reach interested receivers. Scales to an unlimited number of receivers. Potentially good for Internet radio, TV, etc. RRRR S RR …

3. Problem: Heterogeneity Multicast over a wide area proceeds over a collection of packet erasure channels whose bandwidths and erasure processes are –Essentially unknown [except in broad statistical sense] –Variable from receiver to receiver –Time-varying RRRR S RR … Collection of packet erasure channels

4. Receiver-driven Multicast Sender sends multiple streams into the network, each tailored to a different channel characteristic (in terms of bandwidth or reliability) Each receiver subscribes to the stream that best match its channel characteristic (can switch over time) RRRR S RR …

5. Existing Work Deering (1988): IP Multicast McCanne (1996): Receiver-driven Layered Multicast –Sender sends out each layer in a separate stream –Each receiver subscribes to as many streams as will fit –Addresses bandwidth heterogeneity Tan & Zakhor (1999, 2000): RLM w/FEC Chou et al. (1999, 2000): RLM w/FEC+ARQ –Generalizes RLM to include layered channel codes –Receiver subscribes to optimal collection of source and parity layers (to minimize distortion for available rate) –Addresses both bandwidth & packet loss heterogeneity –Problem: dozens (or even hundreds) of streams

6. Clustering Receivers Questions to be answered: –How large should M be to serve most receivers well? –How can we design the collection of M streams? –How can a receiver decide which of the M streams to use? We will assume streams are all at the same bitrate. Redundancy is provided by FEC. Space of associated channels Distribution over channels 1 source parity 2…M

7. Existing FEC Systems Commercial systems (e.g., Windows Media) use systematic Reed-Solomon code to produce N-K parity packets for every K source packets The parameters (N,K) are chosen to match the packet loss characteristics for the channel source parity 100Kbps K N for more reliable channelsfor less reliable channels

8. Existing FEC Systems Priority Encoding Transmission (PET, Albanese et al., 1996) is similar, but it allows K to change across source layers with different importance. 100Kbps K2K2 K3K3 K1K1 parity source N

9. PET packetization Property: recover layer i iff receive K i packets (out of N) Albanese et al. (1996) use 3 layers (I,P,B), dont optimize Davis & Danskin (1996) optimize K i s for any number of layers for minimum distortion Mohr, Riskin, & Ladner (1999) assume fine grain scalability (e.g., SPIHT) and adjust breakpoints using greedy search Puri & Ramchandran (1999) optimize breakpoints using O(N) algorithm

10. Optimal Stream for a Known Channel Wolog assume N layers, layer i 1,…,N coded with K i =i. Let R=(R 0,R 1,…,R N ) be breakpoint vector, where R 0 0 and R 1,…,R N index the last byte in layers 1,…,N respectively. Let D(R 0 ), D(R 1 ), …, D(R N ) be the corresponding vector of distortions if R 0, R 1,…, R N source bytes are recovered. Let q=(q 0,q 1,…,q N ) be probability mass vector, where q k =Pr{1 st k of N layers recovered}=Pr{k of N packets received}. The effect of any stationary packet erasure channel on the receivers expected distortion is through q=(q 0,q 1,…,q N ). R0R0 R1R1 RNRN R D(R0)D(R0) D(R1)D(R1) D(RN)D(RN) Operational D(R) function

11. Expected Distortion and Rate Expected Distortion is Transmission rate (bytes per GOF) is where k =N/(k(k+1)) for k=1,…,N-1 and N =1. Finding R=(R 0,R 1,…,R N ) that minimizes D(R) s.t. R(R) R* can be found by minimizing D(R)+ R(R) for some using the O(N) algorithm of Puri & Ramchandran.

12. Optimal Stream for a Collection of Channels Let {q } be a collection of channels indexed by Є over which there is a distribution Expected distortion of PET packetization R for channel q is Overall expected distortion (w.r.t. ) is Hence to min D(R) s.t. R(R) R*, find q=q and use P&R.

13. Multiple Optimal Streams for a Collection of Channels Start with M streams with PET packetizations R 1,…,R M. Let m( ) be stream number to which receiver with channel q should subscribe. Optimal m( ) (minimizing overall expected distortion) is m( ) = argmin m D (R m ) = argmin m q,k D(R m,k ), which induces partition cells m ={ :m( )=m}. Optimal PET packetization R m for cell m is which can be solved by the Puri-Ramchandran algorithm. Repeat. 1 2 … M

14. Simulation Setup We simulate collection of iid packet erasure channels with N=40, ~ Beta(1,b), mean =1/(1+b)=.10,.15,.20. We assume D(R)= 2 -2cR, R = #bytes per GOF, R*=7/c. Find clusters with M=1,2,4,8,16,32. Beta(1,1/ -1) distribution

15. Simulation Results

16. Conclusion We have presented a clustering algorithm that finds the set of M streams having source/channel rate allocations (PET packetizations) that optimally covers the space of packet erasure channels under an arbitrary distribution –nearest neighbor performed by N-dim dot product –centroid is performed by O(N) algorithm For typical (?) distribution of channels, 4 streams can gain 4 out of a possible 5 dB (i.e., loses only 1 dB compared to an infinite number of streams).