UEP Rateless Codes and LT Parameters

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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 ParametersKai-Chao YangVCLAB, NTHUOutline
  • 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)
  • Unequal Error Protection Rateless Codes for Scalable Information Delivery in Mobile NetworksUlaş C. Kozat and Sean A. RamprashadIEEE INFOCOM 2007Rateless 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
  • 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
  • x1x2x3x4x5x6…y1y2y3y4y5x2x1x3x2x5x3x5x6Rateless Codes
  • Raptor Codes
  • Pre-codes + rateless codes
  • Example
  • LDPC + LT code
  • Modified Soliton distribution
  • Decrease probability of low-degree nodes
  • …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 100Scalable Media
  • 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 4Layer 1Layer 2Layer 3Layer 4UEP 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*
  • 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
  • K1K2……Sender………Receiving order12……ReceiverUEP 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
  • K1K2……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.UEP at the Rateless Encoding Stage
  • Type-2 Codes
  • No change of Raptor codes (Pre-code + LT code)
  • Let ri = Ki/Ni
  • r1 r2  …
  • N1N2N3K1K2K3………………Standard LT codeUEP 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
  • 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+*)KoverheadSimulation Results
  • Core layer: ½  r 1
  • Enhancement layer: r = 1
  • Simulation Results
  • Type 1 vs. Type 2
  • K=500
  • Type 1:d1 = min([(K1/K)dkM,K1]d2 = d-d1Characterization of Luby Transform codes with small message size for low-latency decodingElizabeth A. Bodine and Michael K. ChengICC 2008LT Code Parameters
  • Robust Soliton Distribution
  • Ideal Soliton distribution
  • Robust Soliton distribution
  • Normalization
  • The expected degree-one encoding nodesLT Code Parameters
  • Influence of c (Success rate and operations)
  • k=100k=10LT Code Parameters
  • Influence of c and (Average degree and degree-one nodes)
  • LT Code Parameters
  • Influence of c (Number of unrecovered input symbols)
  • Conclusions
  • Minimize the overhead of LT codes
  • Reduce c
  • Minimize the decoding delay of LT codes
  • Increase c
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