Information Theory for Mobile Ad-Hoc Networks (ITMANET): The FLoWS Project

Collision Helps!

Algebraic Collision Recovery for Wireless Erasure Networks

Ali ParandehGheibiJoint work with

Jay Kumar Sundararajan, Muriel Medard

• 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

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Motivation3

• 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 BobAPXCollision BAD!!!

REALLY?

ZigZag Decoding4

• 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, 2008. Best Paper Award

Algebraic Abstraction5

• 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

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Tx 1

RxTx 2

System Model – Problem Formulation6

• 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 2Tx 2

Rx 3

Rx 1

Performance measures:

1. Delay:

– Each sender has one packet

– Goal: Characterize the expectation of the Delivery time, TD

2. Throughput:

– Packets arrive at each sender according to independent arrival processes, e.g. Bernoulli process

– Goal: Characterize the queue stability region

• 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 Receiver7

Tx 1

Tx i

Tx n

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Stability Region – Single Receiver8

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• 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

Delivery Time – Multiple Receiver Case9

Tx 1

Rx 2Tx 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 everytime 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

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:

Conclusions11

• 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