Kai-Chao Yang

VCLAB, NTHU

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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)

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Ulaş C. Kozat and Sean A. Ramprashad

IEEE INFOCOM 2007

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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

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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

x1 x

3

x2

x2 x

5

x3 x

5 x

6

Degree 1 2 3 … k

probability

(1)

(2) (3)

(k)

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Raptor Codes Pre-codes + rateless codes

Example LDPC + LT code Modified Soliton distribution

Decrease probability of low-degree nodes

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…

Decoder performance 1 (in raptor codes)

Rapid change Bad for small k

2 (in LT codes) Progressive change

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Degree 1 2 3 4 5 8 9 19 64 66

1 0.008 0.494 0.166 0.073 0.083 0.056 0.037 0.056 0.025 0.003

Degree 1 2 3 4 5 8 9 19 64 66

2 (part) 0.237 0.442 0.109 0.054 0.033 0.012 0.009 0.002 0.000 0.000

1000 500 100

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

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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*

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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

Sender…

… …

…

…

K1 K2

Receiver

1 2

… …

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Receiving order

Type-1 Codes

Weakness Change of degree distribution (input nodes) It is likely that d1 = 0 for low-degree encoding

nodes

…

… …d1 = min([(K1/K)dkM,K1] d2 = d-d1

…K1 K2

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N. Rahnavard and F. Fekri, “Finite-length unequal error protection rateless codes: Design and analysis,” in IEEE GLOBECOM 2005.

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

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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

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Drawback (extreme case) Suppose (K,)= * K > K*, where * and K*

are constant.

Let K1<<K and K2K. Two layers are recovered simultaneously.

(1+*)K

1

overhead

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Core layer: ½ r 1 Enhancement layer: r = 1

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Type 1 vs. Type 2 K=500

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Type 1:d1 = min([(K1/K)dkM,K1]d2 = d-d1

Elizabeth A. Bodine and Michael K. Cheng

ICC 2008

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Robust Soliton Distribution Ideal Soliton distribution

Robust Soliton distribution

Normalization

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kiii

iki

,...,2)]1(/[1

1/1)(

kRki

RkikRR

RkiikR

i

kkcR

,...,1/0

//)/ln(

1/,...,1)/(

)(

)/ln(Let

/))()(()(

)()(Let 1

iii

iik

i

The expected degree-one encoding nodes

Influence of c (Success rate and operations)

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k=100 k=10

Influence of c and (Average degree and degree-one nodes)

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Influence of c (Number of unrecovered input symbols)

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Minimize the overhead of LT codes Reduce c

Minimize the decoding delay of LT codes Increase c

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