UEP Rateless Codes and LT Parameters
description
Transcript of UEP Rateless Codes and LT Parameters
Kai-Chao Yang
VCLAB, NTHU
1
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
Ulaş C. Kozat and Sean A. Ramprashad
IEEE INFOCOM 2007
3
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
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)
5
Raptor Codes Pre-codes + rateless codes
Example LDPC + LT code Modified Soliton distribution
Decrease probability of low-degree nodes
6
…
Decoder performance 1 (in raptor codes)
Rapid change Bad for small k
2 (in LT codes) Progressive change
7
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
8
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*
9
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
… …
10
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
11
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
12
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
13
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
14
Core layer: ½ r 1 Enhancement layer: r = 1
15
Type 1 vs. Type 2 K=500
16
Type 1:d1 = min([(K1/K)dkM,K1]d2 = d-d1
Elizabeth A. Bodine and Michael K. Cheng
ICC 2008
17
Robust Soliton Distribution Ideal Soliton distribution
Robust Soliton distribution
Normalization
18
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)
19
k=100 k=10
Influence of c and (Average degree and degree-one nodes)
20
Influence of c (Number of unrecovered input symbols)
21
Minimize the overhead of LT codes Reduce c
Minimize the decoding delay of LT codes Increase c
22