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•Three-layer scheme dominates previous double-layer schemes
•Distortion-diversity tradeoff provides useful comparison in different operating regions
Layered Source-Channel Schemes: A Distortion-Diversity Perspective: S. Jing, L. Zheng and M. Medard
•Diversity can be achieved through source coding techniques, like multiple description codes
•We characterize source-channel schemes with distortion-diversity tradeoff
Distortion-diversity tradeoff better characterizes layered source-channel schemes
MAIN ACHIEVEMENT:
A three-layer source-channel scheme, which includes previous multi-resolution-based and multi-description-based schemes as special cases
HOW IT WORKS: • Multi-description source code with a common
refinement component
• Superposition coding with successive interference cancellation
• Joint source-channel decoding exploits source code correlation
ASSUMPTIONS AND LIMITATIONS:
• Quasi-static block-fading channel
• Receivers have perfect channel state information, but the transmitter only has statistical knowledge of the channel
•Conventional source-channel scheme achieves a single level of reconstruction
•Diversity is usually achieved in the channel coding component
•Extend multi-description-based source-channel scheme while preserving the interface between source and channel coding
•More general channel model
IMPA
CT
NEX
T-P
HA
SE G
OA
LS
ACHIEVEMENT DESCRIPTION
STA
TU
S Q
UO
NEW
IN
SIG
HTS
Multiple Description
with Common
Refinement
Channel 1
s
ˆpartials
Channel 2
1-D ChannelEncoder (SNR)
1bi
2bi
Joint Source-Channel Decoder1-D Channel
Encoder (SNR)
2-D Channel Encoder
ri+
+
refines
ˆfulls
1 2ˆ ˆ or b bi i
1 2ˆ ˆ, b bi i
1-(SNR )
1x 1y
2x 2y
1bx
1rx
2bx1 2
ˆ ˆ ˆ, , and b b ri i i
2rx
partial
refine full,
4 / 31
1/ 3
7 / 95 / 6
Multi-resolution
Multi-description
Three-layer
Source (Image)
PDA 1
PDA 2
Laptop 1
Laptop 2
PDA 1
PDA 2
Laptop 1
Laptop 2
...010011100......010111100...
...101011011...
Sheng Jing, Lizhong Zheng, Muriel Médard
ITMANET
Mar 2009
Motivation
• Multiple user groups
(eg. PDAs vs. Laptops)
• Accuracy: image resolution
• Reliability: successful image loading probability
• Different preferences of accuracy vs. reliability
• How well can we serve multiple user groups simultaneously?
23/4/20 3
Background
• [Diggavi et al ’03]
Layered channel codes (“diversity-embedded codes”)
• [Diggavi et al ’05]
Tradeoff between diversity orders of 2-layer channel code
• [Effros et al ’04] [Laneman et al’05]
Source coding techniques can also improve diversity for certain reconstructions
• We previously looked at the tradeoff between distortion and diversity for SR and MD schemes [Jing et al ’08]
• In this talk, we present a unifying scheme that matches the distortion and diversity (D-D) tradeoff of SR and MD schemes
23/4/20 4
Outline
• Problem formulation
• Review of two schemes– SR with superposition coding– MD with joint decoding
• Unifying scheme: MD with common refinement
• Performance comparison
• Concluding remarks
23/4/20 5
Problem Formulation
• Source: i.i.d. unit-variance complex Gaussian
• Quadratic distortion measure
• Quasi-static parallel fading channel
where and
• Power constraint: SNR per subchannel
• No channel state information at transmitter
• Perfect channel state information at receiver
23/4/20 6
[ ] [ ] [ ], 1, 2i i i iy n h x n w n i
(0,1)ih CN [ ] (0,1)iw n CN
Problem Formulation (cont.)
• At high SNR, for each source reconstruction
– Distortion exponent:
– Diversity order:
23/4/20 7
sˆlog E [ ( , )]
limlogs
SNR
d s sd
SNR
out ˆlog P [ ]lim
logSNR
s
SNR
Problem Formulation (cont.)
• Distortion-Diversity (D-D) tradeoff: achievable distortion exponent & diversity order tuples– Example: three reconstructions (partial, full, and refine),
D-D tradeoff includes all achievable
– Alternative performance metric: average distortion
23/4/20 8
( , , , , , )partial partial full full refine refined d d
Two schemes
• SR with superposition coding
• : two-layer successive refinement source code matched to the distortion levels
• : superposition channel code, with power and
• : successive interference cancelation channel decoder
23/4/20 9
SNR 1SNR
,partial refineD Ds ( , )b ri i
( , , , )partial partial refine refined d
( , )b ri i 1 2( , )x x
1 2( , )y y ˆ ˆ ˆ or ( , )b b ri i i
Two schemes (cont.)
• MD with joint decoding [Laneman et al ’05]
• : symmetric El-Gamal-Cover (EGC) code [El Gamal et al ’82] matched to distortions
• : joint source-channel decoder– Use correlation between source codewords to
identify unlikely pairs of channel codewords
23/4/20 10
1 2( , )i i
( , , , )partial partial full fulld d
s1 2( , )i i
1 2( , )y y1 2 1 2ˆ ˆ ˆ ˆ or or ( , )i i i i
,partial fullD D
Performance Comparison
• SR scheme: D-D tradeoff
along the direction of
• MD scheme: D-D tradeoff
along the direction of
23/4/20 11
( , , , )partial partial refine refined d
, 1.5partial refined d d d
( , , , )partial partial full fulld d
, 1.5partial fulld d d d
Performance Comparison (cont.)
• Compare the D-D regions
at
23/4/20 12
2 / 3d
Common Refinement Scheme
• : symmetric EGC code with common refinement matched to
23/4/20 13
2
2 2,1 ,2
2 2
0 0 0
( , , ) 0 , 0
0 0
r
r b b b b
b b
w w w CN
s ,1 ,2( , , )b b ri i i, ,partial full refineD D D
( , , , , , )partial partial full full refine refined d d
Common Refinement Scheme (cont.)
• Treating refinement layer as noise, form candidate lists of , resp.
• Search for a jointly typical candidate pair – If find only one pair, subtract the corresponding channel
codewords and decode for – Otherwise, search each candidate list for
23/4/20 14
,1 ,2,b bi i
ri
,1 ,2,b bi i
,1 ,2 or b bi i
Connection with SR and MD
• Common refinement scheme includes the MD scheme as a special case (set )
• Common refinement also includes SR scheme?– Simple approach requires huge codebook
– We show, makes the common refinement scheme as good as SR in D-D tradeoff, and avoids exploding
23/4/20 15
( 1)
1 ( 0)SNR
2 2
,1 ,2 2 2
0( , ) ,
0b b
b b
b b
w w CN
1
bR
11 2 22 ( ; ( ; ), )b b b b bR I s ss s I s
Performance Comparison
• D-D tradeoff: ,
• Extreme case 1:
23/4/20 16
( , ) (2 / 3, 1)partial refined d partial full refined d d
full refined d
( , )partial full
( , )partial refine
Performance Comparison (cont.)
• D-D tradeoff: ,
• Extreme case 2:
23/4/20 17
( , ) (2 / 3, 1)partial refined d partial full refined d d
full partiald d
( , )partial full
( , )partial refine
Concluding Remarks
• 3-level unifying scheme– Dominates both SR and MD schemes– Smooth transition between SR and MD schemes– No strictly superior performance
• On-going work– Parallel channel MIMO channel– Unifying source-channel scheme that also preserves the
digital source-channel interface
23/4/20 18