Upcoming SlideShare
×

Like this document? Why not share!

# Structured Network Coding and Cooperative Wireless Ad-Hoc ...

## on Apr 13, 2010

• 643 views

### Views

Total Views
643
Views on SlideShare
643
Embed Views
0

Likes
0
7
0

No embeds

### Report content

• Comment goes here.
Are you sure you want to

## Structured Network Coding and Cooperative Wireless Ad-Hoc ...Document Transcript

• LIU et al.: STRUCTURED NETWORK CODING 5 the NC packet transmitted from to has a lower bound as not watching, he/she can only encode a packet using packets follows: received from other peers through CPR without any packets re- ceived directly from WWAN. Without the chance of mixing the packets, the randomness of the components in the native coefﬁ- cient vectors is reduced and thus our previous assumption does (6) not hold. where is the probability that the subspace To better understand the problem, let us consider a scenario spanned by vectors in is a subset of the subspace spanned by where all peers are repairing two streams: and . Assuming the vectors in , which can be calculated as peers randomly select one stream to watch, then for a peer watching stream , half of ’s neighbors are also watching , and they can each send NC packets to with innovative proba- bility . The innovative probability of NC packets sent from (7) the other half of ’s neighbors to , who are watching stream , depends in turn on their neighbors, i.e., two-hop neighbors rs f Proof: We leverage [19, Lemma 2.1], which stated if the of . Again, with probability 1/2, ’s two-hop neighbors are subspace spanned by native coefﬁcient vectors in the transmit- watching and can help via ’s one-hop neighbors. For the Ve o ting peer is not a subset of the subspace spanned by the native rest half two-hop neighbors that watch can also receive some ion coefﬁcient vectors in the receiving peer, then the probability packets of stream during the repairing process, and with these that the subspace dimension increases at the receiving peer, i.e., limited packets they can help as well. ro the innovative probability, is at least . If dimension At this point, we need to consider the common neighbor of is larger than dimension of , then obviously effect where ’s one-hop neighbors can receive identical , and the ﬁrst line of (6) follows. packets from the same two-hop neighbor of . Note we do The second line of (6) follows similar argument, and the key not apply this effect to the two-hop neighbors who watch is to ﬁnd when . Since is a because different common one-hop neighbors may belong to set of basis vectors for , is the same many common neighbor groups and they can receive different eb P as the probability that each basis vector in is also in , packets from those two-hop neighbors during the CPR process, i.e., . Since there are a total of which greatly reduces the effect. However, this is not true for vectors over , the ﬁrst vector selected from has the two-hop neighbors who watch stream and have limited possible choices excluding the zero vector. With packets belonging to . linearly independent vectors, there are different vectors in The common neighbor effect is illustrated in Fig. 4, where subspace . Then the probability that the ﬁrst vector in peers and receive the same packet of stream from is in is where the “ ” in the nu- , which reduces the innovative probability of subsequent NC EE merator and denominator accounts for the zero vector. Simi- packets forwarded to by half. The innovative probability for larly, the probability that the second vector in is also in the two stream scenario can now be estimated as is where the “ ”accounts for vectors . that are linear combinations of the ﬁrst vector. Continue cal- In general, denoting the average number of common neigh- culating the probabilities for the rest of the vectors in and bors as , the average innovative probability for multi-stream multiply all of them, we get the result for the second case. Com- is estimated as bining the two cases, we have (6). Since our derivations are exact and the bound provided in [19, Lemma 2.1] is achievable, the result in Theorem 1 is tight IE and is achievable. Equation (6) shows the innovative probability assuming dimensions of the subspaces and are known. Generally, we deﬁne the probability mass function (PMF) of the (9) dimensions of the subspaces for the average peer as , and we can calculate the lower bound of the average innovative The ﬁrst term in (9) accounts for neighbors watching the same probability, , by a weighted average stream as the receiving peer under consideration, and the second term accounts for neighbors watching different streams. Note that our derivation is limited to two-hop neighbors, which is W (8) conservative. When SNC is considered, the innovative probability is esti- mated similarly as in the UNC case, except we set the batch size to the size of the frame group that is under repair. Note that B. Innovative Probability for Multi-Stream although we can get the simulated innovative probability under When there are multiple streams being repaired simultane- some scenarios ofﬂine, we cannot get it under all cases because ously, our assumption that the components of the native coef- in practice the topology of the network may change and may ﬁcient vectors are randomly generated from is altered. change. In the following, we will use the analytical innovative This is because when a peer forwards a stream that he/she is probability for SNC optimization.
• 6 IEEE TRANSACTIONS ON MULTIMEDIA is calculated as the additional PSNR improvement of using decoded frame for display of frame , plus the PSNR improve- ment of using decoded frame for error concealment of descen- dant frames of frame in the source dependency tree in the event that they are incorrectly decoded, minus the PSNR improvement of using the parent frame of frame (if one exists) for error con- cealment of frame and its descendant frames. is the sum of all in one GOP, i.e., the distortion when no frame is received. is the recovery success probability of frame at peer . Note that in (10) we make the simplifying assumption that the frame recovery probability is independent from each other. itself can be written as rs f (11) Ve o where is the WWAN packet loss rate, and is the proba- bility of frame being recovered at peer through CPR given ion was not initially successfully delivered via WWAN. Fig. 4. Common neighbors in CPR network. n , n , n , and n are common Suppose we are given SNC groups . Frame neighbors of n and n . n , n , and n watches s , and n , n , and n watches ro s . n receives one packet of s during the repair process. can be recovered if innovative packets of SNC types are received, or if innovative packets of SNC types are received, etc. We can V. SNC OPTIMIZATION FRAMEWORK hence write as In this section, we propose a framework to optimize structures eb P and transmissions of network-coded CPR packets at peers so that the expected distortions of streams are minimized. Our pro- posed SNC optimization has two steps. First, the media source (12) deﬁnes a global NC structure to minimize distortion for the av- where is the probability that peer can NC-decode erage peer with average connectivity. Second, at each transmis- SNC type by receiving innovative native or NC sion opportunity a peer selects a stream from and a type packets. Note here we make the simplifying assumption that the EE within the deﬁned NC structure to transmit given its available recoveries of the frame groups are uncorrelated. local state information of its neighbors. We discuss the two steps Using the average innovative probability shown in (8), if a in order. peer sends a NC packet of type with probability , we can approximate as in (13) at the bottom of the page, A. Global NC Structure Deﬁnition where is the number of packets in group . is the expected number of lost packets of type due The media source ﬁrst optimizes an NC structure for each to WWAN broadcast and needed CPR repairs. is the prob- stream for the average peer , assuming that an average peer ability of receiving a particular stream given an active set of can expect packets from neighbors during CPR. Using the streams. In words, (13) ﬁnds the frame group recovery prob- IE DAG source model from Section II-B, the expected distortion ability by looking at the complimentary event that the frame at peer watching stream can be written as group cannot be recovered, i.e., less than innovative packets of SNC types are received. Among the expected received CPR packets, of them are of SNC types and are inno- (10) vative. These packets are useful for to recover frame group . For the rest packets, some of them are of SNC types W (13)
• LIU et al.: STRUCTURED NETWORK CODING 7 but are not innovative; some of them are of SNC types greater WWAN, and 2) NC group status report containing the number than . These packets are not useful for to recover frame group of innovative packets that are received in each NC groups of . . Note that the obtained local neighbor information can be- With our formulation shown in (10) —(13), the SNC opti- come inaccurate (stale) over time. mization at the media source is to ﬁnd the number of frame Using local information, a peer ﬁrst selects a stream among groups , composition of frame groups ’s, and the packet for repair deterministically instead of picking one at transmission probabilities ’s of frame groups so that the random. For a chosen stream, a peer then selects a NC packet average distortion of the GOP is minimized as follows: type to transmit deterministically. This can potentially further improve streaming performance locally beyond the global optimization performed in previous section; for example, if a (14) peer’s neighbors have already fully recovered a certain stream, then the peer will not choose that stream for repair. To solve the optimization problem in (14), a simple exhaus- 2) Local Peer Optimization: Using the local information dis- tive search scheme has been shown to be of exponential com- cussed above, at each transmission opportunity a peer can select rs f plexity [12]. We therefore used an efﬁcient local search algo- the optimal stream for repair and the SNC type that results in the rithm for fast optimization. minimum total distortion among all its neighbors. More specif- Ve o We ﬁrst notice that the search space can be reduced by con- ically, we optimize the following expression: ion sidering the DAG structure described in Section II-B. A frame that precedes frame must surely be as important as frame (15) ro , since without it cannot be correctly decoded. When we assign frames to NC types then, we will assign preceding frames with a smaller or equal NC type than succeeding frames given where and are the stream and the SNC type to be decided the DAG structure. for packet transmission. is the set of SNC types in stream Based on the reduced search space, we perform the local peer has. Similar to (10), , the resulting distortion of search as follows. We ﬁrst assign NC types to the frames neighbor when NC packet of type in stream is transmitted, eb P in topological order according to the DAG structure, so that a is written as frame preceding will have a NC type smaller than . For this NC structure, we exhaustively search the best re- sulting in the smallest distortion using (14). We then ﬁnd the best “merging” of parent and child frames—assigning the same NC (16) type to the merged group— according to the DAG, and search EE for the best for each of the group so that the objective Note here the distortion reduction is for neighbor , and , , is most reduced. We continue until no such beneﬁcial merging and are constants for stream . Since peer has local operation can be found. information from neighbor , we have With our local search scheme, we need to check at most merging operations for frames in each iteration, and there are at most iterations. Hence there are at most merge if frame has been received (17) operations performed, which is signiﬁcantly less than the ex- otherwise. haustive search. In practice, is small, and by restricting the search space of to 0.1—0.9 with 0.1 increment, we can Note that the ﬁrst line in (17) has two meanings: either all the packets in frame of stream are successfully delivered IE bound the optimization in a reasonable amount of time, which facilitates real-time video streaming. through WWAN or they have been repaired through CPR. They are inferred from the native packet reception report and the NC B. SNC Local Peer Optimization group status report, respectively. has similar formula- tion as in the global NC deﬁnition part except here we need to 1) Peers Utilize Local State Information: In the previous decide the stream and packet type for transmission. It is now ap- section, an NC structure was globally optimized for the entire proximated as ad-hoc network assuming an average peer with average con- nectivity. During CPR, however, local state information can be W easily exchanged among neighbors by piggybacking on data packets with minimal overhead. By local we mean only one-hop neighbor information. Speciﬁcally, we assume each NC packet (18) from peer reveals which stream the packet is repairing and which stream is watching [ ]. The NC packet also includes two state reports: 1) native packet reception report identifying Since peers now have neighbor information, is which packets of stream were successfully delivered from updated as in (19) at the bottom of the next page, where
• LIU et al.: STRUCTURED NETWORK CODING 9 Fig. 5. Receiving CPR packet innovative probability. a) Single stream. b) Multi-stream. rs f Ve o ion Fig. 7. PSNR for news and foreman under various CPR data rates. a) news ten ro streams. b) news 20 streams. c) foreman ten streams. d) foreman 20 streams. Fig. 6. CDF of the number of peers repaired during one epoch time. a) CPR BW 4.5 Mbps, S = 10 . b) CPR BW 23 Mbps, S = 20 . individual peer performs local optimization by utilizing partial state information received from neighbors. When a peer has re- ceived enough packets for a certain frame group, the packets eb P low packet loss rate, peers received most of the packets from within that particular frame group can be recovered. With our MBMS. Therefore each transmitted NC packet is a combination SNC frame group optimization, it turned out that when the CPR of a large number of native and NC packets, which makes the bandwidth was low, the SNC optimization returned more NC components of the native coefﬁcient vectors random and the types than when the bandwidth was high. We also noted that the innovative probability close to 1. The difference between the lower the bandwidth was, the smaller the sizes of the ﬁrst few analytical and simulation results was small and was due to the NC groups. This is reasonable because when bandwidth is low, simpliﬁed assumption of uniform distribution on the dimension peers need desperately to decode at least the ﬁrst few frames. EE of subspaces. Dividing the packets into more groups increases the chance that Fig. 5(b) shows the analytical result versus the simulation re- the received packets can be decoded, and therefore peers can at sult under various multi-stream scenarios. Intuitively, with the least decrease some of the distortion with the limited number of increase of the number of video streams, the innovative proba- receiving packets. bility is reduced. We see that the analytical results capture the In the following, we ﬁrst compare the performance of SNC trend of the simulation results very well. to UNC under different CPR data rates using different video se- 2) Multi-Stream Repair With UNC: As discussed in quences. We then show the effectiveness of the local peer opti- Section III, if a peer does not receive a sufﬁcient number of mization and the innovative probability estimation in the SNC IE innovative native or NC packets during CPR to recover all optimization framework. Lastly we explore how the number of WWAN losses, then UNC could not recover any lost packets streams affected the performance. using received NC packets. This undesired phenomenon was SNC Outperforms UNC: Fig. 7(a) and (b) shows the CPR depicted in Fig. 6(a), which shows the CDF of the fraction of data rates versus PSNR plot for when there were ten and peers that recovered all packets through CPR in one epoch time 20 streams, respectively. Fig. 7(c) and (d) shows the CPR data using UNC. There were total active streams, and on rates versus PSNR plot for . We also have the un-re- average 5 peers were watching the same stream. CPR operated paired video quality, the original video quality without any CPR at the typical 802.11b data rate. As shown, only about 80% of repairs, as a performance benchmark. peers recovered their lost packets in one epoch time. Similarly, From Fig. 7 it can be easily observed that SNC outperformed W Fig. 6(b) shows the CDF when there were total active traditional UNC and un-repaired video in all transmission rates. streams, and the CPR bandwidth was increased to 23 Mbps, When there were ten streams provided by MBMS, SNC pro- the typical data rate for 802.11a/g. The result was similar, and vided up to 13.51 dB PSNR improvement for the sequence fewer than 75% of the peers beneﬁted from CPR with UNC. and 19.71 dB PSNR improvement for the sequence 3) Multi-Stream Repair With SNC: We now show the perfor- over un-repaired video when the data rate was larger than 17 mance of SNC for the multi-stream scenario. The complete SNC Mbps. When there were 20 streams, the performance improve- scheme involves a two-step optimization: 1) media source ﬁrst ment over un-repaired video using SNC were up to 10.51 dB searches for the optimal NC structure for each stream separately and 15.37 dB when the data rate was larger than 50 Mbps. using the optimization framework shown in Section V; and 2) For UNC, the peers needed innovative native or NC
• LIU et al.: STRUCTURED NETWORK CODING 11 Recent works [18], [24]–[26] have attempted to jointly opti- [2] G. Cheung, W.-T. Tan, and T. Yoshimura, “Double feedback streaming mize video streaming and NC. [18] discussed a rate-distortion agent for real-time delivery of media over 3G wireless networks,” IEEE Trans. Multimedia, vol. 6, no. 2, pp. 304–314, Apr. 2004. optimized NC scheme on a packet-by-packet basis for a wire- [3] J. Crowcroft and K. Paliwoda, “A multicast transport protocol,” in less router, assuming perfect state knowledge of its neighbors. Proc. ACM SIGCOMM, New York, Aug. 1988. Though the context of our CPR problem is different, our formu- [4] J. Zfzal, T. Stockhammer, T. Gasiba, and W. Xu, “Video streaming over MBMS: A system design approach,” J. Multimedia, vol. 1, no. 5, lation can be viewed as a generalization in that our optimiza- pp. 25–35, Aug. 2006. tion is on the entire GOP, while [18] is performed greedily per [5] P. Sharma, S.-J. Lee, J. Brassil, and K. Shin, “Distributed communi- packet. cation paradigm for wireless community networks,” in Proc. IEEE Int. Conf. Communications, Seoul, Korea, May 2005. Reference [24] utilized the hierarchical NC scheme in the [6] S. Raza, D. Li, C.-N. Chuah, and G. Cheung, “Cooperative peer-to-peer same way for CDN and P2P networks to combat Internet band- repair for wireless multimedia broadcast,” in Proc. IEEE Int. Conf. width ﬂuctuation. Our work is more general in that our source Multimedia and Expo (ICME), Beijing, China, Jul. 2007, pp. 1075–1078. model is a DAG, while the model in [24] is a more restricted [7] L. Li, R. Ramjee, M. Buddhikot, and S. Miller, “Network coding-based dependency chain. Moreover, we provide a NC optimization broadcast in mobile ad-hoc networks,” in Proc. IEEE INFOCOM 2007, framework to better exploit the beneﬁt of SNC. Anchorage, AL, May 2007, pp. 1739–1747. rs f [8] X. Liu, S. Raza, C.-N. Chuah, and G. Cheung, “Network coding based [25] discussed the application of Markov Decision Process cooperative peer-to-peer repair in wireless ad-hoc networks,” in Proc. [16] to NC, in which NC optimization and scheduling are IEEE Int. Conf. Communications (ICC), Beijing, China, May 2008. Ve o centralized at the access point or base station. Like [18] they re- [9] A. Rahmati and L. Zhong, “Context-for-wireless: Context-sensitive en- ergy-efﬁcient wireless data transfer,” in Proc. ACM MobiSys, San Juan, ion quire complete state information assuming reliable ACK/NAK PR, Jun. 2007, pp. 165–178. schemes, which has yet been shown to be scalable to large [10] S. Chandra and A. Vahdat, “Application-speciﬁc network management for energy-aware streaming of popular multimedia formats,” in Proc. ro number of peers. In our work, we instead consider fully dis- USENIX Annu. Conf., Monterey, CA, Jun. 2002, pp. 329–342. tributed peer-to-peer repair without assuming full knowledge [11] T. Pering, Y. Agarwal, R. Gupta, and R. Want, “Coolspots: Reducing of state information of peers. the power consumption of wireless mobile devices with multiple radio Reference [26] discussed applying structure on NC across interfaces,” in Proc. ACM MobiSys, Jun. 2006, pp. 220–232. [12] X. Liu, G. Cheung, and C.-N. Chuah, “Rate-distortion optimized net- multiple generations of video packets, where one generation is work coding for cooperative video stream repair in wireless peer-to- deﬁned at the transport layer irrespective of application-layer peer networks,” in Proc. 1st IEEE Workshop on Mobile Video Delivery, Newport Beach, CA, Jun. 2008. eb P GOP structures. In our work, NC is applied within one GOP, and [13] X. Liu, G. Cheung, and C.-N. Chuah, “Structured network coding and the structure is deﬁned according to the dependency tree among cooperative local peer-to-peer repair for MBMS video streaming,” in the video frames in the GOP. Deﬁning NC structure within a Proc. Int. Workshop on Multimedia Signal Processing, Cairns, Queens- GOP enables us to build a rate-distortion based NC optimiza- land, Australia, Oct. 2008. [14] T. Wiegand, G. Sullivan, G. Bjontegaard, and A. Luthra, “Overview tion framework which ﬁnds the optimal NC structure resulting of the H.264/AVC video coding standard,” IEEE Trans. Circuits Syst. in the smallest expected distortion. To our knowledge, we are Video Technol., vol. 13, no. 7, pp. 560–576, Jul. 2003. also the ﬁrst in the NC literature to use randomization in the im- [15] G. Cheung, W.-T. Tan, and C. Chan, IEEE Trans. Circuits Syst. Video EE Technol., vol. 17, no. 6, pp. 649–662, Jun. 2007. plementation of SNC for video streaming optimization. [16] P. Chou and Z. Miao, “Rate-distortion optimized streaming of packe- tized media,” IEEE Trans. Multimedia, vol. 8, no. 2, pp. 390–404, Apr. 2006. VIII. CONCLUSIONS [17] T. Ho, M. Medard, R. Koetter, D. R. Karger, M. Effros, J. Shi, and B. Leong, “A random linear network coding approach to multicast,” IEEE In this paper, we present a novel, rate-distortion optimized, Trans. Inf. Theory, vol. 52, no. 10, pp. 4413–4430, Oct. 2006. NC-based, cooperative peer-to-peer packet repair solution [18] H. Seferoglu and A. Markopoulou, “Opportunistic network coding for for the multi-stream WWAN video broadcast. We make con- video streaming over wireless,” in Proc. IEEE 16th Int. Packet Video Workshop, Lausanne, Switzerland, Nov. 2007, pp. 191–200. tributions in the following major aspects. First, we propose [19] S. Deb, M. Medard, and C. Choute, “Algebraic gossip: A network a two-step NC structure optimization framework in which coding approach to optimal multiple rumor mongering,” IEEE Trans. IE the video stream repair can be optimized in a rate-distortion Inf. Theory, vol. 52, no. 6, pp. 2486–2507, Jun. 2006. [20] The TML Project Web-Page and Archive. [Online]. Available: http:// manner. Second, we analyze the innovative probability of a iphome.hhi.de/suehring/tml/. receiving NC packet to facilitate accurate NC structure opti- [21] Qualnet. [Online]. Available: http://www.scalable-networks.com/. mization. Lastly, we provide detailed simulations and show [22] R. Ahlswede, N. Cai, S.-Y. R. Li, and R. W. Yeun, “Network informa- tion ﬂow,” IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 1204–1216, Jul. that the video quality can be improved by up to 19.71 dB over 2000. un-repaired video stream and by up to 5.39 dB over video [23] C. Gkantsidis and P. R. Rodriguez, “Network coding for large stream using traditional unstructured network coding. scale content distribution,” in Proc. IEEE Infocom, Mar. 2005, pp. 2235–2245. [24] K. Nguyen, T. Nguyen, and S.-C. Cheung, “Video streaming with net- W REFERENCES work coding,” Springer J. Signal Process. Syst Special Issue: ICME07, Feb. 2008. [1] Technical Speciﬁcation Group Services and System Aspects, Multi- [25] D. Nguyen, T. Nguyen, and X. Yang, “Multimedia wireless transmis- media Broadcast/Multicast Service (MBMS) User Services, Stage 1 sion with network coding,” in Proc. IEEE 16th Int. Packet Video Work- (Release 6) (3GPP TS.26.246 Version 6.3.0, 2006. shop, Lausanne, Switzerland, Nov. 2007, pp. 326–335.
• 12 IEEE TRANSACTIONS ON MULTIMEDIA [26] M. Halloush and H. Radha, “Network coding with multi-generation Gene Cheung (SM’XX) received the B.S. degree mixing: Analysis and applications for video communication,” in Proc. in electrical engineering from Cornell University, IEEE Int. Conf. Communications, May 2008. Ithaca, NY, in 1995 and the M.S. and Ph.D. degrees in electrical engineering and computer science from the University of California, Berkeley, in 1998 and 2000, respectively. In August 2000, he joined Hewlett-Packard Laboratories Japan, Tokyo, where he is currently a Senior Researcher. His research interests in- clude media transport over wireless networks, joint source/network coding for video streaming, and community-based media interaction. Dr. Cheung is currently an Associate Editor of the IEEE TRANSACTIONS ON MULTIMEDIA and a voting member of the IEEE Multimedia Communications Technical Committee. rs f Chen-Nee Chuah (SM’XX) received the B.S. de- gree in electrical engineering from Rutgers Univer- Ve o sity, New Brunswick, NJ, and the M.S. and Ph.D. de- grees in electrical engineering and computer sciences ion Xin Liu (S’XX) AUTHOR: MISSING MEMBER from the University of California, Berkeley. YEARS. received the B.S. degree in electronic and She is currently an Associate Professor in the information engineering and the M.E. degree in Electrical and Computer Engineering Department ro computer engineering from Beijing University of at the University of California, Davis. Her research Posts and Telecommunications, Beijing, China, in interests include Internet measurements, network 2003 and 2005, respectively. In 2006, he received management, and wireless/mobile computing. the M.S. degree in electrical engineering from the Dr. Chuah received the NSF CAREER Award in State University of New York at Buffalo, Buffalo, 2003 and the Outstanding Junior Faculty Award from the UC Davis College of NY. He is pursuing the Ph.D. degree in computer Engineering in 2004. In 2008, she was selected as a Chancellor’s Fellow of UC engineering at the University of California, Davis. Davis. She has served on the executive/technical program committee of several His research interests are wireless networking, co- ACM and IEEE conferences and is currently an Associate Editor for IEEE/ACM eb P operative communications, and network coding. TRANSACTIONS ON NETWORKING. EE IE W