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. ACHIEVEMENT DESCRIPTION
Collision Helps! Algebraic Collision Recovery for Wireless Erasure Networks Medard
IMPACT
NEXT-PHASE GOALS
ACHIEVEMENT DESCRIPTION
STATUS QUO
NEW INSIGHTS
New approach for contention management in wireless networks
Throughput and completion delay improvement without coordination among senders
Alice
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
Tx 1 AP
Bob
Rx 1 X
Tx n
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
Rx 2
Include notes that would be helpful to the reader or someone (other than yourself) who needs to understand the details. Ideally the chart will be useful even without the author to explain the details. Also include references to published papers plus URLs to online versions if available.
Keep in mind that somewhere or other in this chart, each of these questions should be answered:
1. What technical challenge is being undertaken on behalf of the project
2. Why is it hard and what are the open problems
3. How has this problem been addressed in the past
4. What new intellectual tools are being brought to bear on the problem
5. What is the main intermediate achievement
6. How and when does this achievement align with the project roadmap (end-of-phase or end-of-project goal)
7. What are the even long-term objectives and consequences?
8. Which thrusts and SOW tasks does this contribution fit under and why?
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)
Per packet delay: Understand the decoding process at the receivers
Half-duplex constraint: Requires scheduling between transmit and receive state
Collision recovery improves the performance of a MAC with no coordination among senders

3. X Collision BAD!!! REALLY? Approaches to Medium Access Control:
Motivation 3
Alice
Bob AP X
Collision BAD!!!
REALLY?
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!

4. ZigZag Decoding 4
Chunk 1 from user A from 1st copy of collided packet can be decoded successfully
Subtract from 2nd copy to decoded the Chunk 1 of user B
Subtract from 1st copy of collided packet to decode Chunk 2 from user A
Subtract from 2nd 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, Best Paper Award

5. Algebraic Abstraction5
Tx 1 y x Rx
Tx 2 z
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

6. System Model – Problem Formulation6
Tx 1
Rx 2
Tx 2
Rx 3
Rx 1
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
Performance measures:
Delay:
Each sender has one packet
Goal: Characterize the expectation of the Delivery time, TD
Throughput:
Packets arrive at each sender according to independent arrival processes, e.g. Bernoulli process
Goal: Characterize the queue stability region

7. Delivery Time – Single Receiver7
Tx 1
Tx i
Tx n Rx
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

8. Stability Region – Single Receiver8
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 A Rx

9. Delivery Time – Multiple Receiver Case9
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
Tx 1
Rx 2
Tx 2
Rx 3
Rx 1

10. Stability Region – Multiple Receiver Case10
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 Qij 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