1. Wireless Mesh Networks
XORs in the Air
A. Zubow
“XORs in The Air: Practical Wireless Network Coding”, Sachin Katti, Hariharan Rahul,
Wenjun Hu, Dina Katabi, Muriel M´edard, Jon Crowcroft,

2. Introduction - COPE New Architecture For Wireless Mesh Networks
Routers Forward & Code (Mix) Packets
Intelligent Mixing Improves Throughput
Prior Work = Theoretical & Multicast
This Study = Practical & Unicast
COPE = Inter-flow Network Coding
MORE = Intra-flow Network Coding

3. COPE Substantially improves throughput
‘Coding Shim’ between IP and MAC Layers
Finds coding opportunities
Benefits by sending multiple packets in single transmission (wireless broadcast)

4. COPE: Simple Example Bob & Alice Current approach = 4 transmissions
COPE = 3 transmissions
Thus allowing for increased throughput
Coding+MAC

5. COPE: Even Bigger Savings
Previous example: obvious throughput gains
COPE exploits shared nature of wireless medium (broadcast)
Nodes overhear transmissions
Store these packets for short time
Sends data out telling what it has heard
This data is used for opportunistic coding

6. Opportunistic Coding
Each node uses knowledge of what it’s neighbors have (which packets)
This information allows for source to send XOR’ed packets intelligently
It knows who will be able to decode the encoded packet
Allows for more than two flows
Allows for multiple packets to be coded

7. COPE = 2 Key Principles
COPE exploits broadcast nature of wireless channel
COPE employs network coding
Packets are mixed before transmission
COPE addresses:
Unicast traffic
Dynamic & bursty flows
Other practical issues regarding implementation

8. Summarized Findings Network coding can improve wireless throughput
When congested with mainly UDP flows throughput gains 3 - 4x
For mesh networks connected to Internet via AP gains depend on total download / upload AP
w/o hidden terminals TCP throughput increases about 38%

9. Background (Theory) Famous Butterfly Example:
All Links Can Send One Message Per Unit of Time
Sources Want to Hit Both Receivers
Coding (Again) Increases Overall Throughput

10. Background (cont.) Ahlswede et al. pioneered network coding
Routers that mix information allow communication to achieve multicast capacity
Li et al. found for multicast linear codes sufficient to achieve max capacity bounds

11. COPE Overview
COPE terms:

12. COPE Overview 3 Main Techniques Opportunistic Listening
Opportunistic Coding
Learning Neighbor State

13. COPE Overview: Opportunistic Listening
Wireless is a broadcast medium
Many chances for nodes to overhear
COPE sets all nodes as promiscuous
They store overheard packets for time (T)
Default T = .5 seconds
Also: reception reports are sent out
These are tacked onto normal output
Includes seq. number of stored packets

14. COPE Overview: Opportunistic Coding
Q.: Which packets do we combine to achieve maximum throughput?
A.: Send as many (native packets) as possible while ensuring nexthop has enough info to decode.

15. COPE Overview: Opportunistic Coding
Always seeking largest N that satisfies above rule

16. COPE Overview: Learning Neighbor State
Each node announces its stored packets in reception reports
Sometimes reports don’t get through
Congestion or in times of light traffic
To solve this problem: educated guess
Estimation of probability that neighbor has packet based on delivery probability

17. COPE’s Gains How Beneficial is COPE?
Throughput improvement depends on:
Coding opportunities
Traffic patterns

18. COPE’s Gains: Coding Gain
# transmissions w/o coding to the minimum # transmissions w/ Coding
Remember Alice & Bob?
Coding gain = 4/3 = 1.33

19. COPE’s Gains: Coding Gain
Maximum Achievable Coding Gain?
For arbitrary topologies - open question
Authors prove:
With listening certain topologies benefit

20. COPE’s Gain: Coding Gain
Interesting to note:
Previous slide talks about theoretical gain
In practice gains are lower due to:
Coding opportunities
Packet header overhead
Medium losses
COPE coding gains are not lost when medium is fully utilized.

21. COPE’s Gain: Coding+MAC Gain
Interaction between coding & MAC
Beneficial results
Example Bob & Alice
MAC divides bandwidth between 3
w/o coding router sends 2 x more
Makes router a bottleneck
COPE allows routers queue to drain fast
Coding + MAC gain of Alice & Bob = 2

22. COPE’s Gain: Coding+MAC Gain
Authors Prove:

23. Making It Work - Packet Coding Algorithm
Packets are never delayed
If there is nothing to code with, send anyway
Preference to XOR with similar lengths
Small packet XOR with large = less bandwidth
If one must XOR different lengths - pad
Never code packets to same next hop

24. Making It Work - Packet Coding Algorithm
Searching for appropriate packets to code is efficient
FIFO output queue:
De-queue, small or large?, Look at appropriate queues (only heads to avoid reordering)
Worst case - 2M packets (M=# neighbors)
Packet reordering bad (TCP thinks congestion)
Doesn’t happen much but if so they are put in order before transport layer

25. Making It Work - Packet Coding Algorithm
Finally relay nodes all estimate probability that neighbor has packet prior to sending
PD must stay higher than threshold G (G = 0.8 default)
If equation is above G each nexthop has probability G of being able to decode next packet

26. Making It Work - Packet Decoding
Fairly Simple
Each node maintains a packet pool
Searches hash table keyed on packet ID
XORs native packets with coded packets
Gets packet meant for it (node)

27. Making It Work - Pseudo-Broadcast
Has Two MAC Modes:
Unicast
Broadcast
Packets Are Ack-ed
Exponential Backoff
Un-Reliable
No Backoff

28. Making It Work - Pseudo-Broadcast
Piggy backs unicast
Link-layer destination set to one intended node
XOR header added
Other nodes can overhear transmission
If receiving node is nexthop - continue
Else store packet in buffer
More reliable than pure broadcast
Packets have several tries to get to destination
Snooping nodes get more chances to update their buffers

29. Making It Work - Hop-by-Hop ACKs and Retransmissions
(Again) Encoded packets require all nexthops to acknowledge receipt of native packet
Packets headed many places & only link layer designated hop returns synchronous ACK
COPE may guess node has enough info to decode when it really does not

30. Making It Work - Hop-by-Hop ACKs and Retransmissions
When a node sends an encoded packet it schedules a retransmission event for each encoded native packet
If any packet is not Ack-ed within some threshold (time) that native packet is encoded and re-sent later
Nexthops receive packets and ACK immediately upon decoding via header (or control packets which are also used for reception reports)

31. Making It Work - TCP Packet Reordering
Asynchronous ACKs can cause packet reordering
TCP may see this as congestion
COPE has ordering agent
For each TCP flow host
Maintains packet buffer
Records last TCP sequence number
Will not pass on packets to transport layer until no hole exists or timer times out

32. Implementation Details: Packet Format
COPE inserts variable length coding header
Only shaded fields below required

33. Implementation Details: Packet Format
First Block: Metadata for decoding
ENCODED_NUM: # Encoded
For each packet PKT_ID (Dest. IP & Seq. #)
MAC of nexthop (for each native packet)
Reception Reports
REPORT_NUM: # of Reports
SRC_IP: Source of reported rackets
Last_PKT: last packet heard from source
Bit map of recently heard packets

34. Implementation Details: Packet Format
Asynchronous ACKs
Cumulative ACKs on per neighbor basis
Local sequence numbers established
ACK headers start with # of ACKs
Each ACK starts with MAC of neighbor
Next each ACK has pointer to end of cumulative ACKs
Finally, bit map shows missing packets

35. Implementation Details: Control Flow

36. Experimental Results 20 Node wireless testbed Results:
When many random UDP flows:
Throughput 3 - 4x increase
Traffic does not use congestion control:
Throughput improves - exceeding coding gain
Mesh network -> internet via gateway
Throughput improvement between %
w/o hidden terminals TCP’s gain agrees with expected coding gain

37. Experimental Results: Testbed
20 Node wireless network
Two floors connected by open lounge
Offices, passages, etc.
Paths btw 1 & 6 hops
Loss rate btw %
6 Mb/s

38. Experimental Results: Testbed
Nodes ran Linux / used Click toolkit
Testbed used Srcr routing protocol
Djikstra’s shortest path algorithm
Each node had card w/ omni-directional antenna
ad hoc mode w/ RTS / CTS disabled
udpgen & ttcp used to generate traffic
Long-live flows & attempt to match internet traffic

39. Metrics Network throughput Throughput gain
E2E throughput
Throughput gain
Ratio of measured network throughputs with and without COPE
What else might have been interesting?

40. COPE in Gadget Topologies
Toy topologies
Very small loss rate & no hidden terminals (40 different runs)
Long-lived TCP flows
Close to expected (minus overhead)

41. COPE in Gadget Topologies
Above results show that w/ congestion control results lean towards coding gain rather than Coding+MAC
When many long-lived flows (TCP) bottleneck senders backoff (to avoid drop)
This leaves only coding gains

42. COPE in Gadget Topologies
Repeat of Above w/ UDP
Coding+MAC Gains (Better Than TCP)
Coding Allows Downstream Routers to Avoid Dropping Packets Already Having Consumed Bandwidth
Worcester Polytechnic Institute

43. COPE in an Ad Hoc Network
TCP
TCP flows arrive w/ poisson process
Pick sender & receiver randomly
Traffic models Internet
No significant improvement (2-3%)
Hidden terminals are culprit
Many retransmissions
bottlenecks never build up
Therefore no coding gains (or opportunities)
Would TCP do better w/o collisions?

44. COPE in an Ad Hoc Network
Compressed topology
Within carrier sense range
Artificially impose original loss rates
Hidden terminals = no more
At peak 38% gain over no coding

45. COPE in an Ad Hoc Network
UDP (back to large scale testbed)
Random sender / receiver
File size follows Internet studies
500 experiments…

46. COPE in an Ad Hoc Network
Scare coding opp. at low demands
demand up / congestion up / gain up

47. COPE in an Ad Hoc Network
Low demand - reports arrive to late
Demand goes up - bottlenecks form - longer wait times - nodes get more reports
Demands get higher - high loss rates of reception reports - guessing relied upon

48. COPE in an Ad Hoc Network
@ peak gain point (5.6 Mb/s)
On average 3 packets coded together
Packets drained from bottlenecks faster
Throughput gains x

49. COPE in a Mesh Access Network
Growing interest in accessing Internet via multi-hop network with one (or more) gateways
Nodes divided into 4 sets (1 is gateway)
UDP flows
Fluctuate upload / download traffic
Gain goes up as upload traffic up

50. COPE in Mesh Access Network

51. Fairness Channel from source to bottleneck matters
Capture effect (If Alice’s channel is bad then Bob might push more traffic)
If Alice moves slowly away?
Coding opp. down, throughput down, fairness down
w/o coding throughput goes Up
Coding aligns fairness & efficiency

52. Fairness

53. Discussion Target: stationary wireless mesh networks
Memory needed to store packets
Need more than delay bandwidth product
Need omni-directional antenna
Current design does not consider power

54. Conclusions Coding is an old theme
COPE assists many random UDP flows best
No congestion control is a good thing
No hidden terminals is good as well (even for TCP)
Mesh networks connected to Internet via AP - COPE shows gains from %
Many extensions - sensor networks? cellular?

55. Resources Sachin Katti, Hariharan Rahul, Wenjun Hu, Dina Katabi,
Muriel Medard, Jon Crowcroft, MIT CSAIL & University of Cambridge
Daniel Courcy- Worcester Polytechnic Institute