Error Control for Real-Time Streaming Applications

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1 Error Control for Real-Time Streaming Applications Ashish Khisti Department of Electrical and Computer Engineering University of Toronto Joint work with: Ahmed Badr (Toronto), Wai-Tian Tan (Cisco), Xiaoqing Zhu (Cisco), John Apostolopoulos (Cisco)

2 Multimedia Streaming - Overview Source Stream Latency Receiver Interrup;on Network Receiver 2 Latency Interrup;on Streaming Server Receiver 3 Applications Application Bit-Rate (Mbps) MSDU (B) Delay (ms) PLR Video Conf. 2 Mbps ms 10 4 Interactive Gaming 1 Mbps ms 10 4 Video Streaming 4 Mbps s / 35

3 Streaming Audio time(ms) s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 3/ 35

4 Streaming Audio 0Source Stream time(ms) s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 Playback Stream T=100ms s 0 s 1 s 2 3/ 35

5 Streaming Audio 0 Source Stream time(ms) s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 Playback Stream T=100ms s 0 s 1 s 2 3/ 35

6 Streaming Audio Source Stream s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 Encoded Stream 0 Source s time(ms) 0 Stream s 1 s 2 s 3 s 4 s 5 s 6 s ps 0 p s 1 p s 2 p s 3 p s 4 p s 5 p s 6 p s 7 s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 Playback Stream Playback Stream s 0 s 1 s 2 s 0 s 1 s 2 T=100ms T=100ms (n, k) Streaming Code Source Packet: s i F k q, Parity Packet: p i F n k q ( ) si Channel Packet: x i = F n q Rate R = k n. p i 3/ 35

7 Block Length and Error Correction Source Stream s 0 s 1 s 2 s 3 s 4 s 5 (3,2) FEC s 0 s 1 p 1 s 2 s 3 p 2 s 4 s 5 p 3 s 6 s 7 p 4 (6,4) FEC s 0 s 1 s 2 s 3 p 1 p 2 s 4 s 5 s 6 s 7 p 3 p 4 Smaller Block Length = Smaller Delay Longer Block Length = Better Error Correction Channel Dynamics affect Delay 4/ 35

8 Block Length and Error Correction Source Stream Source Stream s 0 s 0 1 s 1 2 s 2 3 s 3 4 s (3,2) FEC (3,2) FEC s 0 s 1 p 1 s 2 s 3 p 2 s 4 s 0 s 1 p 1 s 2 s 3 p 2 s 4 s (6,4) FEC 0 s 3 (6,4) FEC s 0 s 0 1 s 1 2 s p p 1 2 s s 5 s 5 p 3 p 3 s 6 s 6 s 7 s 7 p 4 p 4 s 5 5 s 6 6 s 7 7 p 3 3 p 4 4 s 0 s 3 Smaller Block Length = Smaller Delay Longer Block Length = Better Error Correction Channel Dynamics affect Delay 4/ 35

9 Block Length and Error Correction Source Stream Source Stream s 0 s 0 1 s 1 2 s 2 3 s 3 4 s (3,2) FEC (3,2) FEC s 0 s 1 p 1 s 2 s 3 p 2 s 4 s 0 s 1 p 1 s 2 s 3 p 2 s 4 s?? 0 s 3 (6,4) FEC (6,4) FEC s 0 s 0 1 s 1 2 s 2 3 p 3 1 p 1 2 s s 5 s 5 p 3 p 3 s 6 s 6 s 7 s 7 p 4 p 4 s 5 5 s 6 6 s 7 7 p 3 3 p 4 4 s 0 s 31 Smaller Block Length = Smaller Delay Longer Block Length = Better Error Correction Channel Dynamics affect Delay 4/ 35

10 Non-Block Codes Block Codes Convolutional/Streaming Codes 5/ 35

11 Real-Time Communication System 6/ 35

12 Real-Time Communication System 6/ 35

13 Real-Time Communication System 6/ 35

14 Real-Time Communication System 6/ 35

15 Real-Time Communication System 6/ 35

16 Real-Time Communication System 6/ 35

17 Real-Time Communication System 6/ 35

18 Real-Time Communication System 6/ 35

19 Real-Time Communication System 6/ 35

20 Real-Time Communication System 6/ 35

21 Real-Time Communication System 6/ 35

22 Real-Time Communication System 6/ 35

23 Proposed Channel Model 1- Good Bad 1- Bad State Good State Bad State Gilbert-Elliott Model Practical Channels introduce both burst and isolated losses. Gilbert-Elliott Channel Models Our Contribution: Error Control Codes for Real-Time Streaming over Channels with Burst and Isolated Erasures. 7/ 35

24 Baseline Approach: Random Linear Codes k n s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 x i p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p i = s i 1 H s i M H M, Erasure Codes: H i F k n k q Random Linear Codes Convolutional-MDS Codes (Gabidulin 88, G.-Luerssen 06 ) p 4 H 4 H 3 H 2 H 1 s 0 p 5 p 6 = H 5 H 4 H 3 H 2 s 1 0 H 5 H 4 H 3 s 2 p H 5 H 4 s 3 }{{} full rank 8/ 35

25 Baseline Approach: Random Linear Codes k n s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 x i p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p i = s i 1 H s i M H M, Erasure Codes: H i F k n k q Random Linear Codes Convolutional-MDS Codes (Gabidulin 88, G.-Luerssen 06 ) p 4 H 4 H 3 H 2 H 1 s 0 p 5 p 6 = H 5 H 4 H 3 H 2 s 1 0 H 5 H 4 H 3 s 2 p H 5 H 4 s 3 }{{} full rank 8/ 35

26 Baseline Approach: Random Linear Codes k n s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 x i p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p i = s i 1 H s i M H M, Erasure Codes: H i F k n k q Random Linear Codes Convolutional-MDS Codes (Gabidulin 88, G.-Luerssen 06 ) p 4 H 4 H 3 H 2 H 1 s 0 p 5 p 6 = H 5 H 4 H 3 H 2 s 1 0 H 5 H 4 H 3 s 2 p H 5 H 4 s 3 }{{} full rank 8/ 35

27 Baseline Approach: Random Linear Codes k n s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 x i p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p i = s i 1 H s i M H M, Erasure Codes: H i F k n k q Random Linear Codes Convolutional-MDS Codes (Gabidulin 88, G.-Luerssen 06 ) p 4 H 4 H 3 H 2 H 1 s 0 p 5 p 6 = H 5 H 4 H 3 H 2 s 1 0 H 5 H 4 H 3 s 2 p H 5 H 4 s 3 }{{} full rank 8/ 35

28 Baseline Approach: Random Linear Codes k n s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 x i p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p i = s i 1 H s i M H M, Erasure Codes: H i F k n k q Random Linear Codes Convolutional-MDS Codes (Gabidulin 88, G.-Luerssen 06 ) p 4 H 4 H 3 H 2 H 1 s 0 p 5 p 6 = H 5 H 4 H 3 H 2 s 1 0 H 5 H 4 H 3 s 2 p H 5 H 4 s 3 }{{} full rank 8/ 35

29 Baseline Approach: Random Linear Codes k n s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 x i p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p i = s i 1 H s i M H M, Erasure Codes: H i F k n k q Random Linear Codes Convolutional-MDS Codes (Gabidulin 88, G.-Luerssen 06 ) p 4 H 4 H 3 H 2 H 1 s 0 p 5 p 6 = H 5 H 4 H 3 H 2 s 1 0 H 5 H 4 H 3 s 2 p H 5 H 4 s 3 }{{} full rank 8/ 35

30 Baseline Approach: Random Linear Codes k n s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 x i p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p i = s i 1 H s i M H M, Erasure Codes: Recover s 0, s 1, s 2, s 3 H i F k n k q Random Linear Codes Convolutional-MDS Codes (Gabidulin 88, G.-Luerssen 06 ) p 4 H 4 H 3 H 2 H 1 s 0 p 5 p 6 = H 5 H 4 H 3 H 2 s 1 0 H 5 H 4 H 3 s 2 p H 5 H 4 s 3 }{{} full rank 8/ 35

31 Baseline Approach: Random Linear Codes k n s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 x i p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 Take Away Points: Recover s 0, s 1, s 2, s 3 Recovery Condition: # of erased symbols < # of received parity equations. Adaptive to Erasure Pattern Weak Burst Correction (R=1/2 =, T 2B) 8/ 35

32 Layered Coding Scheme B = 4, T = 8, R = T T +B = 2 3 Rate 1/2 Baseline Erasure Codes, T = 7 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 v 8 v 9 v 10 v 11 p 8 p 9 p 10 p 11 x i v 0,v 1,v 2,v 3 9/ 35

33 Layered Coding Scheme B = 4, T = 8, R = T T +B = 2 3 Rate 1/2 Baseline Erasure Codes, T = 7 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 v 8 v 9 v 10 v 11 p 8 p 9 p 10 p 11 x i Rate 1/2 Repetition Code, T = 8 v 0,v 1,v 2,v 3 u 0 u 1 u 2 u 3 u 4 u 5 u 6 u 7 u -8 u -7 u -6 u -5 u -4 u -3 u -2 u -1 u 8 u 9 u 10 u 11 u 0 u 1 u 2 u 3 x i u 0 u 1 u 2 u 3 9/ 35

34 Layered Coding Scheme B = 4, T = 8, R = T T +B = 2 3 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 v u u 0 u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 u 9 u 10 u 11 u -8 u -7 u -6 u -5 u -4 u -3 u -2 u -1 u 0 u 1 u 2 u 3 u u 10/ 35

35 Layered Coding Scheme B = 4, T = 8, R = T T +B = 2 3 u 0 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 u -8 u 1 u -7 u 2 u -6 u 3 u -5 u 4 u -4 u 5 u -3 u 6 u -2 u 7 u -1 u 8 u 0 u 9 u 1 u 10 u 2 u 11 p 11 u 3 u v u u R= u+v 3u+v = / 35

36 Layered Coding Scheme B = 4, T = 8, R = T T +B = 2 3 s i u 0 u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 u 9 u 10 u 11 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 +u -8 +u -7 +u -6 +u -5 +u -3 +u -2 +u -1 +u 0 +u 1 +u 2 +u 3 +u -4 u v u x i R= u+v 2 u+v = / 35

37 Layered Coding Scheme B = 4, T = 8, R = T T +B = 2 3 s i u 0 u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 u 9 u 10 u 11 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 +u -8 +u -7 +u -6 +u -5 +u -3 +u -2 +u -1 +u 0 +u 1 +u 2 +u 3 +u -4 u v u x i R= u v 2 u v Encoding: 1 Source Splitting: s i = (u i, v i ), u i F B q, v i F T B q 2 Erasure Code on v i : Generate v i (v i, p i ) where p i F B q is obtained from a RLC. 3 Repetition Code on u i : Repeat the u i symbols with a shift of T 4 Merging: Combine the repeated u i s with the p i s 5 Rate: R = T T +B 10/ 35

38 Layered Coding Scheme B = 4, T = 8, R = T T +B = 2 3 s i u 0 u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 u 9 u 10 u 11 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 +u -8 +u -7 +u -6 +u -5 +u -3 +u -2 +u -1 +u 0 +u 1 +u 2 +u 3 +u -4 u v u x i R= u+v 2 u+v = 2 3 v 0,v 1,v 2,v 3 Encoding: 1 Source Splitting: s i = (u i, v i ), u i F B q, v i F T B q 2 Erasure Code on v i : Generate v i (v i, p i ) where p i F B q is obtained from a RLC. 3 Repetition Code on u i : Repeat the u i symbols with a shift of T 4 Merging: Combine the repeated u i s with the p i s 5 Rate: R = T T +B 10/ 35

39 Layered Coding Scheme B = 4, T = 8, R = T T +B = 2 3 s i u 0 u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 u 9 u 10 u 11 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 +u -8 +u -7 +u -6 +u -5 +u -3 +u -2 +u -1 +u 0 +u 1 +u 2 +u 3 +u -4 u v u x i R= u v 2 u v v 0,v 1,v 2,v 3 u 0 u 1 u 2 u 3 Encoding: 1 Source Splitting: s i = (u i, v i ), u i F B q, v i F T B q 2 Erasure Code on v i : Generate v i (v i, p i ) where p i F B q is obtained from a RLC. 3 Repetition Code on u i : Repeat the u i symbols with a shift of T 4 Merging: Combine the repeated u i s with the p i s 5 Rate: R = T T +B 10/ 35

40 Layered Coding Scheme B = 4, T = 8, R = T T +B = 2 3 s i u 0 u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 u 9 u 10 u 11 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 +u -8 +u -7 +u -6 +u -5 +u -3 +u -2 +u -1 +u 0 +u 1 +u 2 +u 3 +u -4 u v u x i R= u+v 2 u+v = 2 3 v 0,v 1,v 2,v 3 u 0 u 1 u 2 u 3 Encoding: s 0 s 1 s 2 s 3 1 Source Splitting: s i = (u i, v i ), u i F B q, v i F T B q 2 Erasure Code on v i : Generate v i (v i, p i ) where p i F B q is obtained from a RLC. 3 Repetition Code on u i : Repeat the u i symbols with a shift of T 4 Merging: Combine the repeated u i s with the p i s 5 Rate: R = T T +B 10/ 35

41 Layered Coding Scheme B = 4, T = 8, R = s i T T +B = 2 3 v u 0 p v 0 v u 1 p v 1 v u 2 p v 2 v u 3 p v 3 v u 4 p v 4 v u 5 p v 5 v u 6 p v 6 v u 7 7 p v 7 7 v u 8 p v 8 v u 9 p v 9 v u 10 p v 10 v u 11 p v 11 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 +u -8 +u -7 +u -6 +u -5 +u -4 +u -3 +u -2 +u -1 +u 0 +u 1 +u 2 +u 3 u -8 u -7 u -6 u -5 +u u -4-4 u -3 u 0 u 1 R= u u+v u v 2 u 3 u 4 u 5 u 6 u u+v 1 2 v u v 0,v 1,v 2,v 3 u 0 u 1 u 2 u 2 = u -8 u -7 u -6 u -5 u -4 u -3 u -2 u -1 u 0 u 1 u 2 Encoding: u -2 u -1 u 0 u 1 u 2 u 3 u 3 s 0 s 1 s 2 s 3 uv vu u u u u x i 1 Source Splitting: s i = (u i, v i ), u i F B q, v i F T B q 2 Erasure Code on v i : Generate v i (v i, p i ) where p i F B q is obtained from a RLC. 3 Repetition Code on u i : Repeat the u i symbols with a shift of T 4 Merging: Combine the repeated u i s with the p i s 5 Rate: R = T T +B 10/ 35

Convolutional Codes s i =(s i,1,...,s i,k ) Source Symbol: s i (n,k,m) Convolu-onal Code x i =(x i,1,...,x i,n ) Channel Symbol: x i x i = s i G 0 + s i 1 G 1 +.

42 Convolutional Codes s i =(s i,1,...,s i,k ) Source Symbol: s i (n,k,m) Convolu-onal Code x i =(x i,1,...,x i,n ) Channel Symbol: x i x i = s i G 0 + s i 1 G s i m G m, G j F k n q Column Distance: d T : G 0 G 1... G T [ ] 0 G 0... G T 1 d T = min ŵt s0... s T [s 0,...,s T ]..... s G 0 ŵt( ): Hamming weight (Packet Level). 11/ 35

43 Convolutional Codes Column-Distance (Costello 1969): Trellis Path with the following properties: Diverges from the all-zero state at t = 0 Min. Weight in the interval [0, T ] States Column Distance in [0,3] 11/ 35

44 Strongly-MDS Convolutional Codes H. Gluesing-Luerssen, J. Rosenthal and R. Smarandache (IT-2006) States Column Distance in [0,3] Generalized Singleton Bound: d T (1 R)(T + 1) + 1. Counterpart of MDS Block Codes Systematic Codes: x i = (s i, p i ), where p i F n k q 12/ 35

45 Column Distance & Error Correction - Packet Erasures Sliding Window Erasure Channel of Type I: C I (N, W ) In any sliding window of length W there are no more than N erasures (N,W) = (3,6) A Convolutional Code with column distance d T recovers every source packet with delay of T if: W T + 1 d T N / 35

46 Column Distance & Error Correction - Packet Erasures Sliding Window Erasure Channel of Type I: C I (N, W ) In any sliding window of length W there are no more than N erasures (N,W) = (3,6) W = 6 N = 2 A Convolutional Code with column distance d T recovers every source packet with delay of T if: W T + 1 d T N / 35

47 Column Distance & Error Correction - Packet Erasures Sliding Window Erasure Channel of Type I: C I (N, W ) In any sliding window of length W there are no more than N erasures (N,W) = (3,6) W = W 6= 6 N = N 2= 2 A Convolutional Code with column distance d T recovers every source packet with delay of T if: W T + 1 d T N / 35

48 Column Distance & Error Correction - Packet Erasures Sliding Window Erasure Channel of Type I: C I (N, W ) In any sliding window of length W there are no more than N erasures (N,W) = (3,6) W = W 6= W 6= 6 N = N 2= N 2= 2 A Convolutional Code with column distance d T recovers every source packet with delay of T if: W T + 1 d T N / 35

49 Column Distance & Error Correction - Packet Erasures Sliding Window Erasure Channel of Type I: C I (N, W ) In any sliding window of length W there are no more than N erasures (N,W) = (3,6) W = W 6= W 6= W 6= 6 N = N 2= N 2= N 2= 3 A Convolutional Code with column distance d T recovers every source packet with delay of T if: W T + 1 d T N / 35

50 (Packet-Level) Distance and Span Properties Packet Level Column Distance: d T G 0 G 1... G T [ ] 0 G 0... G T 1 d T = min wt s0... s T [s 0,...,s T ]..... s G 0 Packet-Level Column Span: c T G 0 G 1... G T [ ] 0 G 0... G T 1 c T = min span s0... s T [s 0,...,s T ]..... s G 0 14/ 35

51 Column-Span c T = min [s 0,...,s T ] s 0 0 G 0 G 1... G T [ ] 0 G 0... G T 1 span s0... s T G 0 x[0] x[1] x[2] x[3] x[4] x[5] } {{ } j + 1 = 6 c j = c 5 = 6... x [0,T ] = [ x[0], x[1],..., x[t ] ] Column-Span: c T d T c T min {span(x [0:T ] s[0] 0} x C ( min 1, 1 R ) T + 1 R 15/ 35

52 Column Span & Error Correction - Packet Erasures Sliding Window Erasure Channel of Type II: C II (B, W ) In any sliding window of length W there is a single erasure burst of length B (B,W) = (3,5) B 1 =2 W-1 B 2 =3 W-1 B 3 =1 A Convolutional Code with column distance c T recovers every source packet with delay of T if: W T + 1 c T B / 35

53 Column-Distance & Column-Span Tradeoff Badr-Patil-Khisti-Tan-Apostolopoulos (T-IT 2017) Theorem Consider a C(N, B, W ) channel with delay T and W T + 1. A streaming code is feasible over this channel if and only if it satisfies: d T N + 1 and c T B + 1 (N,B,W) = (2,3,6) W = 6 N = 2 17/ 35

54 Column-Distance & Column-Span Tradeoff Badr-Patil-Khisti-Tan-Apostolopoulos (T-IT 2017) Theorem Consider a C(N, B, W ) channel with delay T and W T + 1. A streaming code is feasible over this channel if and only if it satisfies: d T N + 1 and c T B + 1 (N,B,W) = (2,3,6) W = W 6= 6 N = N 2= 2 17/ 35

55 Column-Distance & Column-Span Tradeoff Badr-Patil-Khisti-Tan-Apostolopoulos (T-IT 2017) Theorem Consider a C(N, B, W ) channel with delay T and W T + 1. A streaming code is feasible over this channel if and only if it satisfies: d T N + 1 and c T B + 1 (N,B,W) = (2,3,6) W = W 6= W 6= 6 N = N 2= N 2= 2 17/ 35

56 Column-Distance & Column-Span Tradeoff Badr-Patil-Khisti-Tan-Apostolopoulos (T-IT 2017) Theorem Consider a C(N, B, W ) channel with delay T and W T + 1. A streaming code is feasible over this channel if and only if it satisfies: d T N + 1 and c T B + 1 (N,B,W) = (2,3,6) W = W 6= W 6= W 6= 6 N = N 2= N 2= B 2= 3 17/ 35

57 Column-Distance & Column-Span Tradeoff Badr-Patil-Khisti-Tan-Apostolopoulos (T-IT 2017) Theorem Consider a C(N, B, W ) channel with delay T and W T + 1. A streaming code is feasible over this channel if and only if it satisfies: d T N + 1 and c T B + 1 (N,B,W) = (2,3,6) W = W 6= W 6= W 6= W 6= 6 N = N 2= N 2= B 2= B 3= 3 17/ 35

58 Column-Distance & Column-Span Tradeoff Badr-Patil-Khisti-Tan-Apostolopoulos (T-IT 2017) Theorem Consider a C(N, B, W ) channel with delay T and W T + 1. A streaming code is feasible over this channel if and only if it satisfies: d T N + 1 and c T B + 1 Theorem For any rate R convolutional code and any T 0 the Column-Distance d T and Column-Span c T satisfy the following: ( R 1 R ) c T + d T T R Any (c T, d T ) pair with c T d T is achievable over a sufficiently large field provided that: ( ) R c T + d T T R 1 R 18/ 35

59 MiDAS Construction Layered Code Design u 0 u 1 u 2 u 3 u 4 u 5 u 6 u 7 u 8 u 9 u 10 u 11 v 0 v 1 v 2 v 3 v 4 v 5 v 6 v 7 v 8 v 9 v 10 v 11 p 0 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 p 9 p 10 p 11 u +u -8 +u -7 +u -6 +u -5 +u -4 +u -3 +u -2 +u -1 +u 0 +u 1 +u 2 +u 3 q 1 q 2 q 3 q 4 q 5 q 6 q 7 q 8 q 9 q 10 q 11 l q 0 u v x i Burst-Erasure Streaming Code: (u i, v i, p i + u i T ) Erasure Code: q i = M t=1 u i t H u t, q i F l q Concatenation: (u i, v i, p i + u i T, q i ) Attains the lower bound R = T T + B + l 19/ 35

60 Simulation Results Gilbert-Elliott Channel (α, β) = (5 10 4, 0.5), T = 12 and R 0.5 Gilbert Elliott Channel Good State: Pr(loss) = ε Bad State: Pr(loss) = 1 1- Good Bad Gilbert Elliott Channel - (α,β,n,ǫb) = (0.0005,0.4,2,1) Probability of Occurence Burst Length 20/ 35

61 Simulation Results Gilbert-Elliott Channel (α, β) = (5 10 4, 0.5), T = 12 and R Gilbert Elliott Channel (, ) = (5E 4,0.5), T = Loss Probability x 10 3 Code N B Code N B RLC 6 6 MiDAS 2 9 Burst-Erasure / 35

62 Multicast Streaming Codes Badr-Khisti-Martinian (JSAC 2011) Badr-Khisti-Lui (IT Trans. 2015) Burst Erasure Broadcast Channel Src. Stream Encoder X[i] B 1 Decoder 1 Delay = T 1 B 2 Decoder 2 Delay = T 2 Motivation Common Source Stream, Multiple Receivers B 1 < B 2 Receiver 1 : Good Channel State Receiver 2: Weaker Channel State Delay adapts to Channel State 21/ 35

63 Multicast Streaming Codes Badr-Khisti-Martinian (JSAC 2011) Badr-Khisti-Lui (IT Trans. 2015) Burst Erasure Broadcast Channel Src. Stream Encoder X[i] B 1 Decoder 1 Delay = T 1 B 2 Decoder 2 Delay = T 2 Column-Span A streaming code is feasible on the (B 1, T 1, B 2, T 2 ) multicast channel if and only if: c T1 B c T2 B / 35

64 Diversity Embedded Streaming Codes: DE-SCo Badr-Khisti-Martinian (JSAC, March 2011) Burst Erasure Broadcast Channel Src. Stream Encoder X[i] B 1 Decoder 1 Delay = T 1 B 2 Decoder 2 Delay = T 2 Theorem There exists a {(B 1, T 1 ), (B 2, T 2 )} multicast streaming code of rate R = T 1 T 1 +B 1 provided T 2 T 2 B 2 B 1 T 1 +B 1. T 2 is the minimum such threshold. 22/ 35

65 Multicast Streaming Capacity Badr-Khisti-Lui (IT Trans. 2015) Assume w.l.o.g. B 2 B 1 T 2 B T = T1 B1 B1 Region A Capacity T2 T + B 2 2 B C B 1 + B 2 E (B 1, B 2 ) DE-SCo B 2 D T 2 =T 1 +B 1 T 2 =T 1 SCo A T 1 B C D E T1 T + B 2 1 T1 T + B 1 1 Partial Characterization 1 T2 B1 T B + B / 35

66 Multiple Multiplexed Streams Badr-Lui-Khisti-Tan-Zhu-Apostolopoulos (T-IT (Submitted), Netcod 2016) Encoder Burst Erasure Channel Decoder 1 Decoder 2 Source Streams: s 1 [t] F k 1 q s 2 [t] F k 2 q Encoder: x[t] = f t (s 1 [0], s 2 [0],..., s 1 [t], s 2 [t]) F n q R 1 = k 1 /n and R 2 = k 2 /n Burst Erasure Channel (B): x[t] y[t] Stream 1: ŝ 1 [t] = γ 1,t (y[0],..., y[t + T 1 ]) Stream 2: ŝ 2 [t] = γ 2,t (y[0],..., y[t + T 2 ]) Assume T 2 > T 1 (wlog) 24/ 35

67 Multiple Multiplexed Streams Badr-Lui-Khisti-Tan-Zhu-Apostolopoulos (T-IT (Submitted), Netcod 2016) Encoder Burst Erasure Channel Decoder 1 Decoder 2 Capacity Region A rate pair (R 1, R 2 ) is achievable if there is a streaming code with R 1 = k 1 /n and R 2 = k 2 /n over some F q such that: Each source packet in stream 1 is recovered with a delay of T 1 Each source packet in stream 2 is recovered with a delay of T 2 The union of all achievable rate pairs (R 1, R 2 ) is the capacity region. 24/ 35

68 Capacity Region T 2 T 1 + 2B R 1 T 1 T 1 +B T 1 T 2 +B 0 T 2 T 1 T 2 +B T 2 T 2 +B R 2 R 1 + R 2 T 2 T 2 + B, (T 1 + B)R 1 + T 1 R 2 T 1 25/ 35

69 Network Streaming Mahmood-Badr-Khisti (IT-Trans 2016) Channel Input: x t (F q M ) n (Extension Field) Channel Matrix: A t F n n q (Base Field) Chanel Output y t = x t A t Delay constraint T ŝ t = f t (y 0,..., y t+t ) 26/ 35

70 Network Streaming Mahmood-Badr-Khisti (IT-Trans 2016) Column Sum Rank: Theorem d R (T, C) = min (x 0,...,x T ) C s 0 0 T rank φ(x t ) Within the interval [0, T ] the source symbol s 0 is recoverable at time t = T if and only if t=0 T rankdef A j < d R (T, C) j=0 Construction of Maximum-Sum-Rank (MSR) convolutional codes. 27/ 35

71 Other Extensions Field Size Constraints: Diagonally Interleaved Codes (Badr-Khisti-Tan-Apostolopoulos 2014) Mismatched Streaming Codes (Patil-Badr-Khisti-Tan Asilomar 2013) Partial Recovery Streaming Codes (Badr-Khisti-Tan-Apostolopoulos JSTSP 2014) Multiple Erasure Bursts (Li-Khisti-Girod Asilomar 2011) - Interleaved Low-Delay Codes Multiple Links (Lui-Badr-Khisti CWIT 2011) - Layered coding for burst erasure channels Other Works Martinian and Sundberg (2004) Leong-Ho (ISIT 2012), Leong-Qureshi-Ho (ISIT 2013), N. Adler and Y. Cassuto (ISIT 2015) 28/ 35

72 Dual-Delay Streaming Codes Badr-Khisti-Zhu-Tan-Apostopolous (Infocom 2017) Short-Memory RLC Code Repetition Code with longer Memory Source Stream s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s 11 s 12 Encoded Stream s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s 11 s 12 q 0 q 1 q 2 q 3 q 4 q 5 q 6 q 7 q 8 q 9 q 10 q 11 q 12 q i = s i 1 + s i 2 + s i 10 29/ 35

73 Dual-Delay Streaming Codes Badr-Khisti-Zhu-Tan-Apostopolous (Infocom 2017) Short-Memory RLC Code Repetition Code with longer Memory Source Stream s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s 11 s 12 Encoded Stream s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s 11 s 12 q 0 q 1 q 2 q 3 q 4 q 5 q 6 q 7 q 8 q 9 q 10 q 11 q 12 q i = s i 1 + s i 2 + s i 10 29/ 35

74 Dual-Delay Streaming Codes Badr-Khisti-Zhu-Tan-Apostopolous (Infocom 2017) Short-Memory RLC Code Repetition Code with longer Memory Source Stream s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s 11 s 12 Encoded Stream s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s 11 s 12 q 0 q 1 q 2 q 3 q 4 q 5 q 6 q 7 q 8 q 9 q 10 q 11 q 12 Ignored Parity s 0 s 1 s 2 q 10 = s 8 + s }{{} 9 +s 0 not erased 29/ 35

75 Dual-Delay Streaming Codes Badr-Khisti-Zhu-Tan-Apostopolous (Infocom 2017) Short-Memory RLC Code Repetition Code with longer Memory Source Stream s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s 11 s 12 Encoded Stream s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9 s 10 s 11 s 12 q 0 q 1 q 2 q 3 q 4 q 5 q 6 q 7 q 8 q 9 q 10 q 11 q 12 Ignored Parity s 0 s 1 s 2 Short Bursts B = 1, 2, delay T = 2B, like RLC Longer Bursts B [3, 8], delay T = 10, Like Repetition Code B > 8, partial recovery with T > 10 RLC Threshold B = 5 29/ 35

76 Gilbert Elliott Channel Model Erasure Sequence 1- Good Bad 1- Delay (Pkts) Bad State Good State Gilbert-Elliott Model Tb Tg Excess Delay in Bad State time Chanel-Adaptive Delay Good State: T g = 3 packets Bad State: T b = 12 packets Comparisons Baseline (RLC) Codes Non-Adaptive Streaming Codes Adaptive (Dual-Delay) Streaming Codes 30/ 35

77 Simulation Result Gilbert-Elliott Channel (α, β) = (5 10 4, 0.4) and R 0.5 Gilbert Elliott Channel Good State: Pr(loss) = ε Bad State: Pr(loss) = 1 1- Good Bad Gilbert Elliott Channel - (α,β,n,ǫb) = (0.0005,0.4,2,1) Probability of Occurence Burst Length 31/ 35

78 Simulation Result Gilbert-Elliott Channel (α, β) = (5 10 4, 0.4) and R Gilbert Channel - (α,β) = (0.0005,0.4) 10-2 Uncoded mmds Code MS Code Horizon Code Packet Loss Rate (Tg = 3,Tb = 12) Erasure Probability in Good State (ǫ) Black Line: Random Linear Codes Red Line: Non-Adaptive Burst Erasure Codes Blue Line: Proposed Codes 31/ 35

79 Real-World Traces These are million packets We divide them into windows of 5 minutes (15000 packets) total of 1,250 windows. Delay T = 5. B 3 B [4, 20] PLR 1% PLR > 1% windows with very long bursts were not considered. 32/ 35

80 Real-World Traces-II 33/ 35

81 Demo 34/ 35

82 Conclusions Error Control Coding for Multimedia Streaming Real-Time Communication over Channels with Burst and Isolated Erasures Other Directions: Sequential Recovery Baseline Schemes are not ideal New Coding Schemes and Performance Gains Channel Dispersion in Streaming Setup (joint work with S. Lee and V. Tan) Source Coding in a streaming setup 35/ 35

(Structured) Coding for Real-Time Streaming Communication

(Structured) Coding for Real-Time Streaming Communication Ashish Khisti Department of Electrical and Computer Engineering University of Toronto Joint work with: Ahmed Badr (Toronto), Farrokh Etezadi (Toronto),