1. Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project Collision Helps! Algebraic Collision Recovery for Wireless Erasure Networks Ali ParandehGheibi Joint work with Jay Kumar Sundararajan, Muriel Medard

2. New approach for contention management in wireless networks Throughput and completion delay improvement without coordination among senders Collision Helps! Algebraic Collision Recovery for Wireless Erasure Networks Medard Collision Recovery e.g. ZigZag decoding Algebraic representation of the collisions Combine finite-field network coding with analog network coding (in the form of collisions) Collision recovery improves the performance of a MAC with no coordination among senders MAIN ACHIEVEMENT: 1. Delivery time: Slotted Aloha: nlog(n) Centralized Scheduling: n/(1-p) Collision Recovery: n+O(1) 2. Stability Region: Achieve the cut-set bound HOW IT WORKS: Exploit the diversity gain of the links to different senders by allowing more simultaneous transmissions Priority-based acknowledgement mechanism Each sender broadcasts a random linear combination of the packets in its queue ACK seen packets instead of decoded packets ASSUMPTIONS AND LIMITATIONS: High SNR regime Perfect feedback channel available for ACKs Interference management in wireless networks: Simultaneous transmissions are are considered lost (collision) in most MAC protocols Collisions are normally avoided using centralized scheduling or Aloha-type mechanisms Per packet delay: Understand the decoding process at the receivers Half-duplex constraint: Requires scheduling between transmit and receive state IMPACT NEXT-PHASE GOALS ACHIEVEMENT DESCRIPTION STATUS QUO NEW INSIGHTS Alice Bob AP X Tx 1 Tx n Rx 1 Rx 2

3. Motivation 3 Approaches to Medium Access Control: –Centralized scheduling –Random access –Back-off mechanism –Distributed collision avoidance e.g. CSMA/CA Collided packets may still be decodable! Alice Bob AP X Collision BAD!!! REALLY?

4. ZigZag Decoding 4 Chunk 1 from user A from 1 st copy of collided packet can be decoded successfully –Subtract from 2 nd copy to decoded the Chunk 1 of user B Subtract from 1 st copy of collided packet to decode Chunk 2 from user A –Subtract from 2 nd copy of collided packet to decode Chunk 2 from user B [1] Shyamnath Gollakota and Dina Katabi, "ZigZag Decoding: Combating Hidden Terminals in Wireless Networks," ACM SIGCOMM, 2008. Best Paper Award"ZigZag Decoding: Combating Hidden Terminals in Wireless Networks,"

5. Algebraic Abstraction 5 Every collision is a “new” linear equation involving collided packets as unknowns Assumption: If packets involved in a reception have not all been decoded, then the reception is considered to be innovative Decoding n packets requires n receptions involving only those packets Generalization: Network Coding with Collision Recovery –Send linear combination of the packets at the transmitter –Treat each reception as a new linear equation of the original packets xy z Tx 1 Rx Tx 2

6. System Model – Problem Formulation 6 Time is slotted Packet erasures i.i.d. across links and over time Perfect feedback channel is available for acknowledgements (ACKs) Each sender’s packets to be delivered reliably to all of its neighbor receivers Tx 1 Rx 2 Tx 2 Rx 3 Rx 1 Performance measures: 1.Delay: –Each sender has one packet –Goal: Characterize the expectation of the Delivery time, T D 2.Throughput: –Packets arrive at each sender according to independent arrival processes, e.g. Bernoulli process –Goal: Characterize the queue stability region

7. Centralized Scheduling: Sequentially assign the channel to senders Random Access: Each sender transmits with probability q Collision Recovery: Every sender keeps transmitting until ACKed Collision Recovery with Random Access: Collisions of up to C packets are recoverable where Delivery Time – Single Receiver 7 Tx 1 Tx i Tx n Rx

8. Stability Region – Single Receiver 8 Rx A Centralized Scheduling: –Scheduler allocates the channel to the sender with the longest queue –May schedule a queue when its channel is in erasure –Without prior channel knowledge, cannot beat the simplex Collision Recovery: –Observation: Upon a successful reception, can acknowledge any of the connected senders –Key idea: By choosing whom to acknowledge, we can preferentially “serve” any of the connected queues –Priority-based policy achieves any corner point of the region

9. Delivery Time – Multiple Receiver Case 9 Tx 1 Rx 2 Tx 2 Rx 3 Rx 1 Delivery time of receiver j = Neighbor set of receiver j = Centralized Scheduling: –It is not always feasible to activate one sender for each receiver in every time slot Collision Recovery: –Each sender keeps sending its packet until acknowledge by all of the neighbor senders –Each receiver acknowledges any of the packets involved in each reception (collision) that have not been already acknowledged

10. Stability Region – Multiple Receiver Case 10 Code-ACK policy: - Transmission mechanism: Each sender transmits a random linear combination of its queue content at every time slot - Acknowledgement mechanism: Each receiver j acknowledges the last seen packet of one of the senders in given by the priority-based policy Cut-set bound: For each receiver j Theorem: Code-ACK policy stabilizes the queues for any set of arrival rates satisfying the cut-set bound. Proof sketch: -Virtual queue Q ij for each sender-receiver pair, (i,j), containing the packets at sender i not yet ACKed by receiver j -Stability of each virtual queue by stability of priority-based policy -Stability of physical queues by:

11. Conclusions 11 Collision Recovery: a new approach to contention management Algebraic abstraction to treat collisions as linear equations of packets Generalized collision recovery for coded packets Collision recovery achieves smaller delivery time compared to centralized scheduling Collision recovery at the receivers combined with random linear network coding at the transmitters achieves larger stability region compared to centralized scheduling Priority-based acknowledgement policy stabilizes the entire rate region given by the cut-set bound without queue-length information Collision recovery approach eliminates the need for coordination among contending sender and leads to fully distributed algorithms implemented over a wireless network