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 mspecify the use of LDPC-Staircase codes in fecframe provides two schemes: mscheme 1: LDPC-Staircase for arbitrary packet flows mscheme 2 is similar to scheme 1 but limited to a single sequenced flow NB: in -00, only scheme 1 is specified…

In short… (cont') the current I-D relies on: V. Roca, C. Neumann, D. Furodet, "Low Density Parity Check (LDPC) Staircase and Triangle Forward Error Correction (FEC) Schemes", RMT WG, RFC 5170 (Standards Track/Proposed Standard), June mopen-source, LGPL+, reference codec available at:

Brief overview of LDPC-Staircase codes these codes : msystematic mclose to ideal erasure recovery capabilities …if associated to appropriate decoder even if they are not ideal codes (idem Raptor, unlike RS)  mlow complexity software codecs e.g., decoding speed in 850Mbps - 1,8 Gbps with k=1,000 source symbols mlarge block codes k=10,000 symbols feasible, while keeping high speed decoding

Brief overview of LDPC-Staircase… (cont') well suited to fecframe target applications ma good choice when dealing with high bitrate flows, or when a large number of flows must be globally protected ma good choice when low complexity software decoding is a MUST

Source block creation simple strategy man ADU block is encoded as a single source block mand 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| th ADU … 1 st ADU ADU block

What about performances? depend on: m decoding scheme used more specifically m the decoder has to solve a system of linear equations m possible with Zyablov Iterative Decoding (ID) scheme fast but sub-optimal erasure recovery m or Gaussian Elimination (GE) optimal erasure recovery but more costly m …

What about performances… (cont')...or with a hybrid ID/GE scheme m recommended for most situations m start decoding with ID it’s perhaps sufficient… if not, it will anyway simplify the system m 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 results mcompare LDPC-Staircase as per [RFC5170] (with N1=5), Reed-Solomon over GF(2 8 ), Raptor as per [RFC5053] (1) k=1,000 source symbols average overheadoverhead for decoding failure probability ≤ LDPC-Staircase0.63%2.2% (1022 symbols needed) Raptor0.21%1.4% (1014 symbols needed) (1)copyright © CNES "Raptor coding/decoding software" RS over GF(2 8 ) LDPC-staircaseRaptor object size (bytes) average inefficiency ratio excellent results!

Decoding complexity results conditions: k=1,000, code rate 2/3, (LDPC: N1=5) mcompare with L. Rizzo's reference RS over GF(2 8 ) codec mLDPC-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(2 8 )

References “Optimizing the Error Recovery Capabilities of LDPC- staircase Codes Featuring a Gaussian Elimination Decoding Scheme”, SPSC'08, October “Le RFC 5170 en pratique : conception et évaluation d'un codec AL-FEC LDPC-Staircase hautes performances”, to appear in CFIP'09, October General performance analysis… Additional, recent results (in French)

Next steps specify scheme 2 mlimited to a single sequenced flow specify RTP framing for FEC Repair Packets min a companion I-D probably WG Item? mopinion welcome