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UEP Rateless Codes and LT Parameters

UEP Rateless Codes and LT Parameters. Kai-Chao Yang VCLAB, NTHU. Outline. Unequal Error Protection Rateless Codes for Scalable Information Delivery in Mobile Networks (INFOCOM 2007) Rateless codes UEP for rateless codes Simulation results

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UEP Rateless Codes and LT Parameters

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  1. UEP Rateless Codes and LT Parameters Kai-Chao Yang VCLAB, NTHU

  2. Outline • 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)

  3. Unequal Error Protection Rateless Codes for Scalable Information Delivery in Mobile Networks Ulaş C. Kozat and Sean A. Ramprashad IEEE INFOCOM 2007

  4. Rateless Codes • 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

  5. Rateless Codes • LT Codes • Encoding process • For the ith encoding node, select degree di by Soliton distribution • Choose di input nodes • Perform XOR on chosen nodes • Decoding process • Decode degree-one nodes • Remove degree-one edges iteratively x1 x2 x3 x4 x5 x6 … y1 y2 y3 y4 y5 x2 x1x3 x2x5 x3x5x6

  6. Rateless Codes • Raptor Codes • Pre-codes + rateless codes • Example • LDPC + LT code • Modified Soliton distribution • Decrease probability of low-degree nodes …

  7. The Impact of Input Size • Decoder performance • 1 (in raptor codes) • Rapid change • Bad for small k • 2 (in LT codes) • Progressive change 1000 500 100

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

  9. UEP for Rateless Codes • Parameters • K1: Number of high-priority input nodes • K-K1: 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 • Ni*: minimum number of encoding nodes needed to reach i fidelity • Goal • Minimize N1* and N2* s.t. N1*<<N2*N*

  10. Brute-Force UEP • The receiver download bitstreams separately • Let K1=100, 1*=0.01 and K2=500, 2*=0.1 • Overhead  2 • Let K =600, =0.01 • Overhead  1.3 K1 K2 … … Sender … … … Receiving order 1 2 … … Receiver

  11. UEP at the Rateless Encoding Stage • Type-1 Codes • Weakness • Change of degree distribution (input nodes) • It is likely that d1 = 0 for low-degree encoding nodes K1 K2 … … d1 = min([(K1/K)dkM,K1] d2 = d-d1 … … N. Rahnavard and F. Fekri, “Finite-length unequal error protection rateless codes: Design and analysis,” in IEEE GLOBECOM 2005.

  12. UEP at the Rateless Encoding Stage • Type-2 Codes • No change of Raptor codes (Pre-code + LT code) • Let ri = Ki/Ni • r1 r2  … N1 N2 N3 K1 K2 K3 … … … … … … Standard LT code

  13. UEP at the Rateless Encoding Stage • Pre-code rate • Design goal • 1* << 2* << ½ for K1 << K • Choose pre-coding rate of high priority layer at ½ • The difference between (K, 1*) and (K, 2*) decides the performance

  14. UEP at the Rateless Codes • Drawback (extreme case) • Suppose (K,)= *  K > K*, where * and K* are constant. • Let K1<<K and K2K. Two layers are recovered simultaneously.  1 (1+*)K overhead

  15. Simulation Results • Core layer: ½  r 1 • Enhancement layer: r = 1

  16. Simulation Results • Type 1 vs. Type 2 • K=500 Type 1: d1 = min([(K1/K)dkM,K1] d2 = d-d1

  17. Characterization of Luby Transform codes with small message size for low-latency decoding Elizabeth A. Bodine and Michael K. Cheng ICC 2008

  18. LT Code Parameters • Robust Soliton Distribution • Ideal Soliton distribution • Robust Soliton distribution • Normalization The expected degree-one encoding nodes

  19. LT Code Parameters • Influence of c (Success rate and operations) k=100 k=10

  20. LT Code Parameters • Influence of c and (Average degree and degree-one nodes)

  21. LT Code Parameters • Influence of c (Number of unrecovered input symbols)

  22. Conclusions • Minimize the overhead of LT codes • Reduce c • Minimize the decoding delay of LT codes • Increase c

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