Wireless Network Coding with partial Overhearing information

Transcription

1 Wireless network coding with partial overhearing information Georgios S. Paschos Massachusetts Institute of Technology (MIT) Joint work with: C. Fragkiadakis University of Thessaly, Greece L. Georgiadis Aristotle University of Thessaloniki, Greece L. Tassiulas University of Thessaly, Greece

2 Wireless network coding use intersession network coding to exploit the wireless broadcast [Katti et al. Sigcomm 06 (COPE)] Benefits: reduces the required transmissions power consumption ) more throughput, less The benefits apply to more scenarios using overhearing (side information) Issue: Reporting overhearing might not be desirable In this talk: How to control the system without these reports Transmitting XORs blindly and using feedback is very efficient

3 Overhearing example source source relay destination destination

4 Overhearing example source source relay overhearing destination destination

5 Overhearing example source source relay destination destination

6 Overhearing example source source relay overhearing destination destination

7 Overhearing example source source relay destination destination

8 Overhearing example source source relay + + Observations 1. Both receivers can decode 2. 3 txs instead of 4 (4/3 gain) 3. Overhearing erasures: How does the relay know if packets were overheard? destination destination

9 Learning Side information: Two cases ACK NACK ACK + NACK! Nodes report each overhearing (send ACK) Relay learns which packets were overheard No ACKs Relay XORs blindly If there is a decoding failure the receiver sends NACK Compare the two in terms of throughput and overhead

10 The model Focus on downlink Study relay transmissions Downlink channel model Destination 1 receives perfectly if at most are transmitted (similar for dest. 2) for both receivers to receive use min{r 1,r 2 } r 1 packets 1 2 p 1 p relay 2 r 2 r 1 Random arrival of packets Packets arrive at the relay and with a probability at the pairing receiver (overhearing) Stability at the relay: the backlogs don t grow unbounded The problem: Find the stability regions of ACK and NACK systems Provide efficient transmission policies that use XOR Compare the number of feedback reports in the two approaches

11 1 Wireless Network Coding with partial Overhearing information 2-user Throughput regions ACK: outer bound (using arbitrary coding) 2 ACK: region of a XOR policy NACK: outer bound (using XORs) NACK: region of a XOR policy without knowledge about the channel We will show: ACK: =, capacity region and simple policy NACK: =, code-constrained region and simple policy - Determine the loss - Show cases where all four are the same!

12 ACK Separate packets into good (overheard), bad Assume we are given k 1,k 2 packets- (study policies that evacuate these) Transmissions can be: {g 1,g 2,b 1,b 2,g 1 +g 2, } input queues b overhearing buffers g ACK Proposed Policy: Transmit g 1 +g 2 until one type is not available (empty queue) Then use {g 1,g 2,b 1,b 2 } Lower Bound on evacuation time: We establish a matching bound (assuming general coding func.) Use stability via evacuation tool [Georgiadis et al. ITW 12 ] Capacity region of ACK (achieved with XORs) min{p 1 1,p 2 2 } r 1 r 2 max{r 1,r 2 } apple 1

13 NACK - scheme Each packet is initially unknown. Add u queue All packets arrive in this queue Stationary decision: to XOR or not to XOR? input queues overhearing buffers After a XOR decoding failure a packet can either be bad or good good if one packet is NACKed bad if both packets are NACKed The policies choose actions from the set: {u 1,u 2,b 1,b 2,g 1,g 2, u 1 +u 2, u 1 +g 2, g 1 +u 2, g 1 +g 2,...} We establish a lower bound (on evacuation time) assuming XORs

14 NACK policy erasure prob. of (fast) flow Proposed policy: If Then send u 1, u 2 (no coding) else 1. u 1 +g 2 or g 1 +u 2 2. u 1 +u 2 3. b 1 or b 2 or other singletons f 2 arg max i=1,2 r i input queues overhearing buffers Result: This policy matches in evacuation performance the XOR bound Code-constrained stability region plugin r 1 = r 2 or p f =1 Stat. condition

15 NACK policy operation same rates Rules u 1 +g 2 or g 1 +u ` 2 u 1 +u 2 3. b 1 or b 2 or other singletons Transmissions Time: u 1 +u 2 2. u 1 +u 2 3. u 1 +u 2 4. u 1 +g 2 5. u 1 +u 2 6. u 1 +u 2 7. b 1 The ACK policy needs 7 slots, too!

16 NACK policy operation different rates Consider packets of equal length Different rates: red is fast, blue is slow Plain forwarding of 2 packet takes: NACK: Blind XORs 4 cases 1. Both packets overheard performance gain 2. The red/fast packet overheard no harm 3. The blue/slow packet overheard harming 4. Both packets not overheard harming reception time or

17 Throughput: ACK beats NACK Throughput ratio NACK/ACK Parameters: 1 = 2 r 2 =3 p 2 =0.9

18 Overhead: NACK beats ACK W NACK W ACK W: rate of feedback messages

19 Take home messages We give a characterization of the tradeoff of ACK/NACK schemes ACK Capacity region and NACK code-constrained region Simple stabilizing policies that use XORs Loss of throughput as function of (p, r, λ) XORing blindly and NACKing is a good alternative to ACKs (when probabilities are high) Much less control messages Small (or no) loss of throughput

20 QUESTIONS?

21 Previous results For the ACK (deterministic) case Same rates: index coding Same rates: linear coding [C.-C. Wang] Different rates: Backpressure-type policy, XOR constraint region [1] ACK For the NACK (stochastic) case Undecoded packets are dropped: [1] 2-users? In practice, many user coding opportunity rarely arise (geometrical bounds, physical model bounds, experiments) Choosing combinations from larger sets is complex NACK! + [1] G. S. Paschos, L. Georgiadis and L. Tassiulas, Scheduling with pairwise XORing of packets

22 Learning side-information Explicit ACKs [COPE] Each node announces each overhearing A great number of control messages Piggybacking not possible if no reverse flow (added delay, lost throughput) Feedback via NACKs [COPE, NCRAWL-Broustis et al.] Router XORs blindly, and feedback messages are used only for retransmissions How efficient can this be? Optimal control the system under this scheme? Use intrasession network coding [I 2 NC-Seferoglou et al., CORE-Krigslund et al.] Immediate decodability Decoding complexity

23 ACK & NACK capacity region No network coding ACK & NACK capacity [1] r 1 = r 2 p 1 =0.7 p 2 =0.8

24 Methodology evacuation times k A: system with arrivals B: system for evacuation System B: k At time 0, packets at the input no further arrivals : is the minimum evacuation time T (k) Consider the quantity System A is stable iff 1 T ( t) t for large t An (asymptotically) minimum evacuation policy in B can be mapped to a throughput optimal policy in A

25 Methodology evacuation times (cntd) k A: system with arrivals B: system for evacuation Strategy for both ACK, NACK: Study system B Find lower bounds on the evacuation time of any policy Propose an evacuation policy: compare the asymptotic performance If they match, we have: The proposed policy is an asymptotically minimum evacuation policy on B System A stability region A throughput optimal policy on A (that is based on the decisions of evacuation policy on B)

26 A simple example Example with deterministic service rate k 4pkt/slot T (k) 10 T (k) = k 4 ) ˆT ( )= lim t!1 t 4 t = 4 40 k Thm: ) apple 4