raptor codes

RAPTOR CODESJosé Lopes (please call me Sá)

@zemanelsa

About me• Braga

• MSc in Information Security (FCUL)• Researcher@LaSIGE

• Motorcycles

• MSc Thesis• RaptorQ implementation• Breaking & Securing RQ

What you should take from this talk?

Theory:• What are fountain codes?• What properties they have?• How can they be used?

You should think about:• Where can I use them?• How can my applications benefit from them?• New ideas that work with this mindset

FEC - Forward Error Correction• Used to recover from errors occurred during transmission• Sender encodes the message in a redundant way

• using an error-correcting code (ECC)

• Redundancy allows the receiver to detect errors• and often to correct these errors without retransmission

• Corrects errors without a reverse channel to request retransmission of data• but at the cost of a fixed, higher forward channel bandwidth

• Usually applied in situations where retransmissions are costly or impossible (e.g., multicast)

• Added to mass storage devices to enable recovery of corrupted data (e.g., RAID)

Erasure codes

• Error correcting code• Transforms a message of k symbols into a longer message with n symbols

• The original message can be recovered from a subset (k’) of the n symbols

• (Code rate) r = k/n proportion of the data-stream that is useful

• (Reception efficiency) k’/k

Fountain codes• Rateless erasure code• Endless supply of encoded symbols• Recover original data with any K encoded symbols (with

high probability)

DigitalK

Receiver(bucket)

Fountain

Use case: point-to-multipoint• For a large number of receivers TCP does not

scale• every receiver requires a separate data stream• sender needs to keep track of what arrives at each

receiver

• UDP can be used• scales effortlessly • best effort: loss rate ↑ degraded experience⇒

• Difficult to provide a scalable broadcast service on the Internet• it would be interesting to have reliability whilst

retaining UDP’s efficiency

S

R2

R1

R4 R3

LT code (the first fountain code!)

• Based on two random generators• One generates how many XORs should be made• The other generates (the IDs of) which symbols will be XORed

• 5%-10% extra symbols are usually needed

S : source symbol E : encoding symbol (+ is the XOR operation)

E0 = S2 + S4 + S5 E1 = S0 + S1 + S2 E2 = S0 + S3 E3 = S2

E4 = S0 + S5 E5 = S2 + S5 E6 = S1 + S3 + S4 + S5

S0 S5S4S3S2S1

E0 E1 E2 E3 E4 E5 E6

Raptor codes (finally!)

• Faster encoding/decoding algorithms• Pre-code• Steep overhead-failure probability curve

RaptorQ:• Systematic• Faster• Steeper

HOW CAN WE USE THIS!?!?

Data

Partition into Source Blocks

Source block i

RaptorQDecoder

Source block i

Data

Reconstruct the data

Put in packets &transmit through the network

Received Symbols ( ≥ K)

Some packets are lost in the network

RaptorQ Encoder

Source Symbols (K)

RepairGenerator

Repair Symbols (R)

Encoding Symbols

Can be used as overhead (extra symbols)

SENDER RECEIVER

How awesome is RaptorQ? Pretty awesome...

• Incredibly low probabilities of failure (for accidental faults)

K (number of source symbols)

0 Overhead [·10-3] 1 Overhead [·10-5] 2 Overhead [·10-7]

Loss 10 26 101 10 26 101 10 26 101

10% 0 5.4 5.7 0 0 3.8 0 0 2.5

20% 0 4.0 4.8 0 2.3 2.4 0 0 0.5

50% 0 3.9 4.9 0 1.6 2.5 0 0.9 1.2

60% 4.8 4.1 4.9 0 1.5 2.2 0 0 2.1

85% 0 12.7 4.7 0 0.8 2.4 0 0 1.3

Who’s using Raptor codes?

Where to now?

• José Lopes, “Communication with RaptorQ Erasure Codes in

Malicious Environments”, MSc thesis

• José Lopes and Nuno Neves, “Stopping a Rapid Tornado with a

Puff” (soon to be IEEE S&P)

• The OpenRQ Library (www.lasige.di.fc.ul.pt/openrq)

• Amin Shokrollahi, "Raptor codes”, IEEE Transactions on

Information Theory 52.6 (2006): 2551-2567.

• Amin Shokrollahi and Michael Luby, “Raptor Codes” Now

Publishers Inc 2011

• IETF RFC6330

RAPTOR CODESJosé Lopes (please call me Sá)

@zemanelsa

Thank you! Any questions?