Symbol Level Network Coding

By Sachin Katti, Dina Katabi, Hari Balakrishnan,

Muriel MedardSigcomm 2008

Mesh Networks Borrowed the Internet Contract

Conflicts with wireless mesh characteristics

PHY + LL Deliver correct packetsNetwork Forward correct packets to destination

Current contract builds reliability on a link by link basis

Spatial diversity more naturally provides reliability across multiple links

S

R1

R2

D

99% (10-3

BER)

99% (10 -3 BER)

Wireless Naturally Provides Reliability Across Links

0%

0%

Even 1 bit in 1000 incorrect Packet loss of 99%

S

R1

R2

D

99% (10-3

BER)

99% (10 -3 BER)

Wireless Naturally Provides Reliability Across Links

0%

0%

Current contract Link by link reliability 50 transmissions

Loss

Loss

S

R1

R2

D

99% (10-3

BER)

99% (10 -3 BER)

Wireless Naturally Provides Reliability Across Links

0%

0%

Spatial diversity: Even if no correct packets, every bit is likely received correctly at some node

Exploit wireless characteristics 3 transmissions

Current contract 50 tx Low throughputExploit wireless characteristics 3 tx High throughput

Useful with High Quality Links?R1

R2

R3

R4

Sa

Pb

Db

Da

Sb

Pb

Pa

Pa

Pa

Pb

1%

2%

1%

3%

0%

0%

0%

0%

Loss

Loss

Loss

Loss

Useful with High Quality Links?R1

R2

R3

R4

Sa

Pb

Db

Da

Sb

Pb

Pa

Pa

Pa

Pb

1%

2%

1%

3%

0%

0%

0%

0%Current contract Inhibits concurrency

Exploit wireless characteristics Enables high concurrency

Current Contract

Limits throughput, inhibits concurrency

PHY + LL Deliver correct symbols to higher layerNetwork Forward correct symbols to destination

PHY + LL Deliver correct packetsNetwork Forward correct packets to destination

High throughput, high concurrency

New Contract Exploiting Wireless Characteristics

MIXIT• New contract between layers to harness

wireless characteristics• Novel symbol-level network code that

scalably routes correct symbols• High concurrency MAC

How does a Router Identify Correct Symbols?• PHY already estimates a confidence for every

decoded symbol [JB07]• PHY + LL delivers high confidence symbols to

network layer

PHY Confidence

Packet

PHY + LL Deliver correct symbols to higher layerNetwork Forward correct symbols to destination

What Should Each Router Forward?

R1

R2

DSP1P2

P1P2

P1P2

What Should Each Router Forward?

R1

R2

DSP1P2

But overlap in correctly received symbols Potential solutions1)Forward everything Inefficient2)Coordinate Unscalable

P1P2

P1P2

P1P2

P1P2

Forward random combinations of correct symbols

R1

R2

DSP1P2

MIXIT Prevents Duplicates using Symbol Level Network Coding

P1P2

P1P2

1s

…

…R1

R2

D

2s2

1

7s

2s

2

7

…

1s

…

…

2s

Routers create random combinations of correct symbols

2

1

9s

5s

5

9

…

MIXIT Prevents Duplicates using Symbol Level Network Coding

R1

R2

D2

1

7s

2s

…

2

1

9s

5s

…

21 s,sSolve 2

equations

Destination decodes by solving linear equationsRandomness prevents duplicates without co-ordinationRandomness prevents duplicates without co-ordination

MIXIT Prevents Duplicates using Symbol Level Network Coding

1s

…

…R1

R2

D

2s2

1

7s

2s

2

7

…

1s

…

…

2s

Routers create random combinations of correct symbols

15s

5

0

…

MIXIT Prevents Duplicates using Symbol Level Network Coding

R1

R2

D2

1

7s

2s

…

15s …

21 s,sSolve 2

equations

Destination decodes by solving linear equations

Symbol Level Network Coding • No duplicates Efficient • No coordination Scalable

Symbol Level Network Coding • No duplicates Efficient • No coordination Scalable

MIXIT Prevents Duplicates using Symbol Level Network Coding

Destination needs to know which combinations it received

21 9s5s

21 0s5s

21 9s0s

(if both symbols were correct)

(if only s1 was correct)

(if only s2 was correct)

Nothing (if neither symbol was correct)

Destination needs to know which combinations it received Use run length encoding

5

9

Original Packets Coded Packet

0

9

Original Packets Coded Packet

Use run length encoding

Destination needs to know which combinations it received

9

5

Original Packets Coded Packet

Destination needs to know which combinations it received Use run length encoding

0

5

Original Packets Coded Packet

Destination needs to know which combinations it received Use run length encoding

Run length encoding efficiently expresses combinationsRun length encoding efficiently expresses combinations

Destination needs to know which combinations it received Use run length encoding

Routers May Forward Erroneous Bits Despite High Confidence

MIXIT has E2E error correction capability

Symbol-LevelNetwork Coding

ECC Data

MIXIT’s Error Correcting Code (ECC)1. Routers are oblivious to ECC2. Optimal error correction capability3. Rateless

Decode ECCData

PHY + LL Deliver correct symbols to higher layerNetwork Forward correct symbols to destination

Source Destination

High Concurrency MAC

• Each node maintains a map of conflicting transmissions

• Map is based on empirical measurements and built in distributed, online manner

w & x NO!w & u YES!

xu w

Evaluation

• Implementation on GNURadio SDR and USRP• Zigbee (IEEE 802.15.4) link layer• 25 node indoor testbed, random flows• Compared to:

1. Shortest path routing based on ETX2. MORE: Packet-level opportunistic routing

Throughput (Kbps)

CD

F

Throughput increase: 3x over SPR, 2x over MOREThroughput increase: 3x over SPR, 2x over MORE

Throughput Comparison

2.1x3x

Shortest PathMOREMIXIT

Throughput (Kbps)

CD

FWhere do the gains come from?

Shortest PathMOREMIXIT

Take concurrency away from MIXIT

Where do the gains come from?

1.5x

Without concurrency, 1.5x gain over MOREWithout concurrency, 1.5x gain over MOREThroughput (Kbps)

CD

F

Shortest PathMORE

MIXIT withoutconcurrency

Take concurrency away from MIXIT

Where do the gains come from?

Throughput (Kbps)

CD

F

MIXIT

Gains come from both moving to the symbol level and high concurrency

Gains come from both moving to the symbol level and high concurrency

Shortest PathMORE

MIXIT withoutconcurrency

Where do the gains come from?Higher Concurrency?

1.4x

MORE, enhanced with higher concurrency is only 1.4x better

Throughput (Kbps)

CD

F

Where do the gains come from?

Throughput (Kbps)

CD

F 2.1x

1.5x

Higher concurrency MAC fully exploits symbol-level diversity

Higher concurrency MAC fully exploits symbol-level diversity

ConclusionMIXIT• New contract harnesses wireless characteristics• Symbol-level network coding to scalably route

correct symbols• High concurrency• Implementation and evaluation demonstrating 3-4x over shortest path, 2-3x gains over MORE