So you think you can FEC?
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1 So you think you can FEC? Mikhail Misha Fludkov (fludkov) Pexip R&D Erlend Earl Graff (egraff) Pexip R&D 8 th GStreamer Conference 21 October 2017 Prague, Czech Republic
2 Outline Introduction to FEC Designing a FEC decoder element FEC algorithms XOR-based FEC Reed-Solomon FEC DEMO!
3 Bird s eye view on FEC #18 #17 #16 #15 #1 #13 #12 #11 #10 #9 #8 #7 #6 #5 # #3 #2 #1 #0 RTP video or audio packets (VP8, H26, OPUS, etc) FEC packets with redundant data
4 Bird s eye view on FEC #18 #17 #16 #15 #1 #13 #12 #11 #10 #9 #8 #7 #6 #5 # #3 #2 #1 #0
5 FEC standards zoo RED - Redundant Audio Data (RFC 2198) ULPFEC based standards: ULPFEC Generic Forward Error Correction (RFC 5109) ULPFEC (WebRTC) X-ULPFECUC (Skype) FLEX FEC - Flexible Forward Error Correction
6 GStreamer element for packet recovery #6 #5 # #3 #2 #1 #0 FECDec # #3 #2 #1 #0
7 Where to hook it up? Before or after jitterbuffer? here? or here? FECDec GstRtpBin FECDec
8 Where to hook it up? #6 #5 # GstRtpBin # FECDec #3 #2 #1 #0 # Lost event with seq-num #
9 What if it works and recovers packets! Yaaay! send_rtcp_src #6 #5 #3 #2 #1 #0 FECDec GstRtpBin # lost packet was recovered and pushed here
10 Where to hook it up to? Flex FEC case recv_rtp_src_100 #1 #0 #1 #0 #1 #0 #1 #0 GstRtpBin recv_rtp_src_200 #1 #0 recv_rtp_src_300 #1 #0 audio packet with ssrc 100 video packet with ssrc 200 Flex FEC packet with ssrc 300
11 Doing it the right way recv_rtp_src_100 PexFecDec RtpStorage GstRtpBin recv_rtp_src_200 PexFecDec recv_rtp_src_300 PexFecDec # get_packets_for_recovery(ssrc300, seq_num) #6 #5 #3 #2 #0
12 Yet another what if #18 #17 #16 #15 #1 #13 #12 #11 #10 #9 #8 #7 #6 #5 # #3 #2 #1 #0
13 FEC Algorithms XOR-based FEC Reed-Solomon FEC
14 XOR-based FEC
15 XOR-based FEC D1 D2 D3 D R1 R2
16 XOR-based FEC D1 D2 D3 D R1 D1 D2 R2 D1 D2 D3 D
17 XOR-based FEC D1 D2 D3 D R1 D1 D2 R2 D1 D2 D3 D
18 XOR-based FEC D1 x D R1 D1 x R2 D1 x D
19 XOR-based FEC D1 x y D R1 D1 x R2 D1 x y D
20 XOR-based FEC D1 x y D R1 R2 D1 D1 x x y D D1 x R1 y D1 x D R2 R1
21 XOR-based FEC D1 x y D R1 D1 x x D1 R1 R2 D1 x y D y R1 D R2
22 XOR-based FEC D1 D2 D3 D R1 D1 D2 R2 D1 D2 D3 D
23 XOR-based FEC D1 D2 D3 D R1 D1 D2 R2 D1 D2 D3 D
24 XOR-based FEC D1 D2 x R1 D1 D2 R2 D1 D2 x
25 XOR-based FEC D1 D2 x y R1 D1 D2 R2 D1 D2 x y
26 Reed-Solomon codes R-S encoder k data symbols t parity symbols Irving S. Reed and Gustave Solomon R-S erasure decoder Either Detect up to t errors Detect and correct up to t Τ2 Correct up to t erasures errors k symbols (data and/or parity) k original data symbols
27 Reed-Solomon codes Data packets Redundancy packets
28 Reed-Solomon codes d c a d 3d Data packets ee c9 95 a1 9d 21 a3 b a5 aa 16 f b 70 7f b c6 bd e8 cb 02 bf 8c 5d a d7 8b 73 0f 61 5 bf bc d7 cd aa 22 d9 a f6 8 8a 1 c 0a c3 ca f d5 ff d6 a5 f3 e3 5d d3 2 3f 2 a8 1b f c8 cb d e 85 2d d6 Redundancy packets 85 9a b2 76 8f 1 c ee d3 5b fd e0 b0 d a d1 82 b2 dd 0c
29 Reed-Solomon codes 55 Data packets ee 5d 90 Redundancy packets 85
30 Reed-Solomon codes 7 Data packets c9 a 09 Redundancy packets 9a
31 Reed-Solomon codes 56 Data packets 95 d7 d6 Redundancy packets b2
32 Reed-Solomon codes d c a d 3d Data packets ee c9 95 a1 9d 21 a3 b a5 aa 16 f b 70 7f b c6 bd e8 cb 02 bf 8c 5d a d7 8b 73 0f 61 5 bf bc d7 cd aa 22 d9 a f6 8 8a 1 c 0a c3 ca f d5 ff d6 a5 f3 e3 5d d3 2 3f 2 a8 1b f c8 cb d e 85 2d d6 Redundancy packets 85 9a b2 76 8f 1 c ee d3 5b fd e0 b0 d a d1 82 b2 dd 0c
33 Reed-Solomon codes
34 Reed-Solomon codes encoding
35 Reed-Solomon codes encoding 100 Encoding coefficients
36 Reed-Solomon codes encoding 100 Encoding coefficients
37 Reed-Solomon codes encoding 100 Encoding coefficients
38 Reed-Solomon codes encoding 100 Encoding coefficients
39 Reed-Solomon codes encoding 100 Encoding coefficients
40 Reed-Solomon codes encoding 100 Encoding coefficients
41 Reed-Solomon codes encoding 100 Encoding coefficients
42 Reed-Solomon codes encoding 100 Encoding coefficients
43 Reed-Solomon codes encoding 100 Encoding coefficients
44 Reed-Solomon codes encoding 100 Encoding coefficients
45 Reed-Solomon codes decoding 100 Encoding coefficients
46 Reed-Solomon codes decoding 100 Encoding coefficients
47 Reed-Solomon codes decoding 100 Encoding coefficients x x x
48 Reed-Solomon codes decoding 100 Encoding coefficients x y x y 670 x y
49 Reed-Solomon codes decoding 100 Encoding coefficients x y x y x y x 3y x 2y 670
50 Reed-Solomon codes decoding 100 Encoding coefficients x y x y x y x 3y x 2y
51 Reed-Solomon codes decoding 100 Encoding coefficients x y x y x y x 3y x 2y
52 Reed-Solomon codes decoding 100 Encoding coefficients x y x y x y x 3y 130 5x 2y 270
53 Reed-Solomon codes decoding 100 Encoding coefficients x y x y x y x 3y 130 5x 2y 270 3x y 10
54 Reed-Solomon codes decoding 100 Encoding coefficients x y x y x y x 3y 130 5x 2y 270 y 3x 10
55 Reed-Solomon codes decoding 100 Encoding coefficients x y x y x y x 3y 130 5x 2y 270 y 3x 10 2x 3 3x x 9x x 550 x 50
56 Reed-Solomon codes summary Encoding Linear combination (matrix multiplication) Decoding Solving linear equation system (matrix inversion and multiplication)
57 But
58 Linear combinations in R R R R
59 Linear combinations not in R? ,255 0,255 0,255
60 Linear combinations not in R? ,255 0,255 0,255 0,255
61 Fields Set of elements and Given a Ϝ and b Ϝ, then a b Ϝ a b Ϝ R and Q infinite fields Finite fields
62 Fields Z 7Z 0,1,2,3,,5,6 is addition modulo 7 is multiplication modulo 7
63 Fields Multiplication table for Z Τ7Z
64 Fields Multiplication table for Z Τ7Z mod 7
65 Fields Multiplication table for Z Τ7Z mod 7
66 Fields Finite fields p q elements Solving linear equation systems works! Reed-Solomon: typically 2 q elements GF 2 8 0,255
67 Linear MDS codes over Z Τ7Z encoding 1 2 3
68 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
69 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
70 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
71 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
72 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
73 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
74 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
75 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
76 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
77 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
78 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
79 Linear MDS codes over Z Τ7Z encoding 1 Encoding coefficients
80 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients
81 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients
82 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients x x x 1 5 2
83 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients x y 5 2 x y 6 x y
84 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients x y x y x y x 3y 5x 2y 6
85 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients x y x y x y x 3y 2 3 5x 2y 6 3
86 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients x y x y x y x 3y 2 3 5x 2y 6 3
87 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients x y x y x y x 3y 2 5x 2y 6 3
88 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients x y x y x y x 3y 6 5x 2y 2
89 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients x y x y x y x 3y 6 5x 2y 2 0x 5y 1
90 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients x y x y x y x 3y 6 5x 2y 2 5y 1
91 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients Multiplication table for Z Τ7Z x y x y x y x 3y 6 5x 2y 2 5y
92 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients Multiplication table for Z Τ7Z x y x y x y x 3y 6 5x 2y 2 5y
93 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients Multiplication table for Z Τ7Z x y x y x y x 3y 6 5x 2y 2 3 5y
94 Linear MDS codes over Z Τ7Z decoding 1 Encoding coefficients Multiplication table for Z Τ7Z x y x y x y x 3y 6 5x 2y 2 y
95 FEC it up! GStreamer elements RED encoder and decoder ULPFEC decoder (XOR and Reed-Solomon) RTPStorage element Reed-Solomon encoder and decoder Only GF 2 8 Matrix operations Cauchy-RS fast matrix inversion SIMD optimizations 1 1 Anvin, H. P. The mathematics of RAID
96 DEMO THYME
97 Benchmarks Reed-Solomon encoding
98 Benchmarks Reed-Solomon decoding
99 Questions? (Do you think we can FEC?)
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