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 packetsASSUMPTIONS 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

xy

z

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 nRx

Stability Region – Single Receiver8

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

Delivery Time – Multiple Receiver Case9

Tx 1

Rx 2Tx 2

Rx 3

Rx 1Delivery 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