LDPC-Staircase FEC Schemes for FECFRAME

draft-roca-fecframe-ldpc-00

IETF 75 – Stockholm, July 2009

V. Roca – M. Cunche (INRIA)

J. Lacan (ISAE)

In short…

goal

specify the use of LDPC-Staircase codes in fecframe

provides two schemes:

scheme 1: LDPC-Staircase for arbitrary packet flows

scheme 2 is similar to scheme 1 but limited to a single

sequenced flow

NB: in -00, only scheme 1 is specified…

In short… (cont')

Brief overview of LDPC-Staircase codes

these codes :

systematic

close to ideal erasure recovery capabilities

• …if associated to appropriate decoder

• even if they are not ideal codes (idem Raptor, unlike RS)

low complexity software codecs

• e.g., decoding speed in 850Mbps - 1,8 Gbps with k=1,000

source symbols

large block codes

• k=10,000 symbols feasible, while keeping high speed decoding

Brief overview of LDPC-Staircase… (cont')

Source block creation

simple strategy

an ADU block is encoded as a single source block

and basically that's all…

Enc Symbol Len (E) Enc Symbol Len (E) Enc Symbol Len (E)

< ------------------ >< ------------------ >< ------------------ >

+----+----+-----------------------+--------+

|F[0]|L[0]| R[0] | Pad[1] |

+----+----+----------+------------+--------+

|F[1]|L[1]| R[1] |

+----+----+----------+--------------------------------------+----+

|F[2]|L[2]| R[2] |P[2]|

+----+----+----------+--------------------------------------+----+

|F[3]|L[3]| R[3] | P3|

+----+----+------+---+

4th ADU

…

1st ADU

ADU block

What about performances?

depend on:

decoding scheme used

more specifically

the decoder has to solve a system of linear equations

possible with Zyablov Iterative Decoding (ID) scheme

• fast but sub-optimal erasure recovery

or Gaussian Elimination (GE)

• optimal erasure recovery but more costly

…

What about performances… (cont')

...or with a hybrid ID/GE scheme

recommended for most situations

start decoding with ID

• it’s perhaps sufficient…

• if not, it will anyway simplify the system

finish with GE (e.g., if it’s known that no additional

symbol will be received)

• works on the system simplified by ID

• correctly implemented, its complexity is not an issue at all

Erasure recovery resultscompare LDPC-Staircase as per [RFC5170] (with N1=5),

Reed-Solomon over GF(28), Raptor as per [RFC5053](1)

k=1,000 source symbols

average overhead overhead for decoding failure probability ≤ 10-4

LDPC-Staircase 0.63% 2.2% (1022 symbols needed)

Raptor 0.21% 1.4% (1014 symbols needed)

(1) copyright © CNES

"Raptor coding/decoding software"

RS over GF(28)

LDPC-staircase Raptor

object size (bytes)

average

inefficiency

ratio

exce

llent r

esults

!

Decoding complexity results

conditions: k=1,000, code rate 2/3, (LDPC: N1=5)

compare with L. Rizzo's reference RS over GF(28) codec

LDPC-staircase between 30 to 14 times faster than RS

30 times faster on

average (1.8 Gbps) GE needed more

and more often

ID sufficient

sustainable

decoding

speed

(Mbps)

loss

probability(%)

still 14 times

faster

(850 Mbps)

with RS: 60Mbps

LDPC-staircase

RS over GF(28)

References

• “Optimizing the Error Recovery Capabilities of LDPC-

staircase Codes Featuring a Gaussian Elimination

Decoding Scheme”,

SPSC'08, October 2008.

http://hal.inria.fr/inria-00291656/en/

• “Le RFC 5170 en pratique : conception et évaluation d'un

codec AL-FEC LDPC-Staircase hautes performances”,

to appear in CFIP'09, October 2009.

http://hal.inria.fr/inria-00291656/en/

General

performance

analysis…

Additional,

recent

results

(in French)

Next steps

specify scheme 2

limited to a single sequenced flow

specify RTP framing for FEC Repair Packets

in a companion I-D probably

WG Item?

opinion welcome