1. Kai-Chao Yang VCLAB, NTHU 1

2.  Unequal Error Protection Rateless Codes for Scalable Information Delivery in Mobile Networks (INFOCOM 2007)  Rateless codes  UEP for rateless codes  Simulation results  Characterization of Luby Transform codes with small message size for low-latency decoding  LT Code Parameters (ICC 2008) 2

3. Ulaş C. Kozat and Sean A. Ramprashad IEEE INFOCOM 2007 3

4.  Rateless code  Original content  Infinite unique encoding blocks  Overhead  ( K,  ): Under probability (1-  ), receive (1+  ( K,  )) K encoding blocks can recover K message blocks  The same source for all senders  Disregard of heterogeneous receivers and channels  No need to check missing blocks  High coding overhead for small content size   Solution: concatenating many small sized contents to a large content 4

5.  LT Codes  Encoding process  For the i th encoding node, select degree d i by Soliton distribution  Choose d i input nodes  Perform XOR on chosen nodes  Decoding process  Decode degree-one nodes  Remove degree-one edges iteratively … x1x1 x2x2 x3x3 x4x4 x5x5 x6x6 y1y1 y2y2 y3y3 y4y4 y5y5 x1x3x1x3 x2x2 x2x5x2x5 x3x5x6x3x5x6 Degree123… k probability  (1)  (2)  (3) (k)(k) 5

6.  Raptor Codes  Pre-codes + rateless codes  Example  LDPC + LT code  Modified Soliton distribution  Decrease probability of low-degree nodes 6 …

7.  Decoder performance   1 (in raptor codes)  Rapid change  Bad for small k   2 (in LT codes)  Progressive change 7 Degree1234589196466 11 0.0080.4940.1660.0730.0830.0560.0370.0560.0250.003 Degree1234589196466  2 (part)0.2370.4420.1090.0540.0330.0120.0090.0020.000 1000 500 100

8.  Scalable media  Different importance in the same content  e.g.  Software updates  Advertisements  Multimedia (pictures, audio, and video)  Scalable or layered video Media 1Media 2Media 3Media 4 Layer 1Layer 2Layer 3Layer 4 8

9.  Parameters  K 1 : Number of high-priority input nodes  K - K 1 : Number of low-priority input nodes   1 ( N ): ratio of unrecovered nodes for high-priority layer after receiving N blocks   2 ( N ): ratio of unrecovered nodes for low-priority layerafter receiving N blocks  N i * : minimum number of encoding nodes needed to reach  i fidelity  Goal  Minimize N 1 * and N 2 * s.t. N 1 * << N 2 *  N* 9

10.  The receiver download bitstreams separately  Let K 1 =100,  1 *=0.01 and K 2 =500,  2 *=0.1  Overhead  2  Let K =600,  =0.01  Overhead  1.3 Sender … … … … … K1K1 K2K2 Receiver 12 …… 10 Receiving order

11.  Type-1 Codes  Weakness  Change of degree distribution (input nodes)  It is likely that d 1 = 0 for low-degree encoding nodes … … … d 1 = min([(K 1 /K)dk M,K 1 ]d 2 = d-d 1 … K1K1 K2K2 11 N. Rahnavard and F. Fekri, “Finite-length unequal error protection rateless codes: Design and analysis,” in IEEE GLOBECOM 2005.

12.  Type-2 Codes  No change of Raptor codes (Pre-code + LT code)  Let r i = K i /N i  r 1  r 2  … … …………… N1N1 N2N2 N3N3 K1K1 K2K2 K3K3 Standard LT code 12

13.  Pre-code rate  Design goal   1 * <<  2 * << ½ for K 1 << K  Choose pre-coding rate of high priority layer at ½  The difference between  ( K,  1 * ) and  ( K,  2 * ) decides the performance 13

14.  Drawback (extreme case)  Suppose  ( K,  )=  *  K > K*, where  * and K* are constant.  Let K 1 << K and K 2  K. Two layers are recovered simultaneously.  (1+  *)K 1 overhead 14

15.  Core layer: ½  r  1  Enhancement layer: r = 1 15

16.  Type 1 vs. Type 2  K =500 16 Type 1: d 1 = min([(K 1 /K)dk M,K 1 ] d 2 = d-d 1

17. Elizabeth A. Bodine and Michael K. Cheng ICC 2008 17

18.  Robust Soliton Distribution  Ideal Soliton distribution  Robust Soliton distribution  Normalization 18 The expected degree-one encoding nodes

19.  Influence of c (Success rate and operations) 19 k=100k=10

20.  Influence of c and  (Average degree and degree-one nodes) 20

21.  Influence of c (Number of unrecovered input symbols) 21

22.  Minimize the overhead of LT codes  Reduce c  Minimize the decoding delay of LT codes  Increase c 22