Spectrum recycling: salvaging analog spectral waste. Kannan Ramchandran EECS Dept. University of California at Berkeley. [email protected] http://www.eecs.berkeley.edu/~kannanr. Motivation:. Legacy analog systems can be spectrally v. wasteful AM/FM radio
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Kannan RamchandranEECS Dept.
University of California at Berkeley
http://www.eecs.berkeley.edu/~kannanr
let’s nuke analog…
let’s get digital!
University of California, Berkeley
University of California, Berkeley
University of California, Berkeley
X
Motivation: Spectrum reuse
AM/FM/TV
broadcast
Legacy receiver
X
Transmitter
Data
Embedder
Digital
Upgrader
Data
Digital
Music/TV
Extra
data
University of California, Berkeley
University of California, Berkeley
University of California, Berkeley
University of California, Berkeley
University of California, Berkeley
Data hiding: channel coding with side info. at the receiver
Channel
(watermark)
(watermark msg.)
Decoder
Encoder
N (attacker)
S (host signal)
Data Hiding/Embedding ProblemUniversity of California, Berkeley
Channel
^
M
Y
X
M
+
+
Decoder
Encoder
S
N
Capacity: 1/2 log (1 +X/(S+N))
Example:
Channel
^
M
Y
X
M
+
+
Decoder
Encoder
S
N
“Writing on dirty paper”: Costa (1982)
Capacity: 1/2 log (1 +X/N) independent of strength of S!
University of California, Berkeley
Binary dataembedding/watermarking
Case: 1:Both encoder and decoder have access to host signal S:
00
01
10
11
000
001
010
100
4 messages can be embedded: select
one of 4 “legal” embedding patterns
Encoder outputs X=S+e (mod 2)
Decoder receives Y=X and recovers e by: e=S+X (mod 2)
University of California, Berkeley
0 0 0
1 1 1
0 0 1
1 1 0
0 1 0
1 0 1
1 0 0
0 1 1
Coset1
Coset4
Coset2
Case 2: When encoder alone knows the host S.
Q:
Can we still embed 2 bits of information in the S while
satisfying distortion constraint between S and X?
A: Yes.
Messages index one of 4 cosets of U:
(10)
(00)
(11)
Example: S=011, m=01;
X=001 (off in <= 1 bit)
01
University of California, Berkeley
General encoder and decoder structure for CCSI:
DECODER
ENCODER
Decode Y in
the composite
channel code
and declare
the coset
containing it
as the message
Find the
coset ‘g’
with
the given
index
Find a
codeword, U
in coset ‘g’,
compatible
with S and send
X, a function
of U and S.
X
g
Y
M
^
M
Channel
S
University of California, Berkeley
X
X
Codeword
Sphere
X
ENCODING/DECODING Coset 1
X
 Coset 2
 Coset 3
 Side Info
 Received Signal
Received Signal Sphere
(within scale factor)
SideInfo Sphere (within scale factor)
Assume signal and channel are Gaussian, iid
University of California, Berkeley
University of California, Berkeley
Y
X
Encoder
Decoder
X
Y
X
Distributed Source coding:(source coding with side information):
Information theory:X can be compressed (in some cases) at a rate
equal to that when the encoder too has access to Y (SlepianWolf ’72)
University of California, Berkeley
DISCUS: source coding with side info. at the Rx
X
Y
Encoder
Decoder
Channel
^
M
X
M
Encoder
Decoder
+
+
S
N
Duality with channel coding with side info.University of California, Berkeley
Source coding with side information:
Illustrative Example ( binary case):
Let X and Y be length3 binary data (equally likely), with the
correlation: Hamming distance between X and Y is at most 1.
Example: When X=[0 1 0],
Y can equally likely be [0 1 0], [0 1 1], [0 0 0], [1 1 0].
^
X
X
Decoder
Encoder
SYSTEM1
0 0 0
0 0 1
0 1 0
1 0 0
Need 2 bits to index this.
X+Y=
University of California, Berkeley
0 1 1
0 0 0
1 1 1
0 1 0
1 0 1
0 0 1
1 1 0
Coset1
Coset3
Coset4
Coset2
^
X
X
Decoder
Encoder
Y
SYSTEM2
What is the best one can do?
The answer is still 2 bits.
How?
University of California, Berkeley
^
X
X
X
X
noisy
host
source
0 0 0
1 1 1
0 1 0
1 0 1
(00)
(01)
(10)
(11)
1 0 0
0 1 1
0 0 1
1 1 0
Duality:SCSI/CCSI encoder/decoder can be swapped!
(010)
(10)
(10)
(010)
M: coset index
DISCUS
Encoder
M
DISCUS
Decoder
reconst.
S
(correlated source)
Distributed compression (SCSI)
(011)
(010)
(010)
(10)
Datahiding
Encoder
(10)
M:
data to be
embedded
Datahiding
Decoder
M
embedded
host
recovered
data
S
(host)
(011)
Data embedding (CCSI)
University of California, Berkeley
X
1 0 0
0 1 1
0 0 1
1 1 0
0 1 0
1 0 1
0 0 0
1 1 1
X
Codeword
Sphere
X
Dataembedding Code ConstructionsCoset1
Coset3
(00)
(10)
Coset2
Coset4
(11)
(01)
University of California, Berkeley
Data Hiding Encoder
Rate n/m
Rate k/n
Host
Code Constructions
G0 / 2Zn/ G1embedded coset codes
University of California, Berkeley
Data, d, determines the ratek/m code to use
E[d2] <= X
Viterbi Algorithm
Rate – k/m code
Side Information, S
a
To Channel
+
1a
University of California, Berkeley
Viterbi Algorithm
Rate – n/m code
Codebook
g
d’
From Channel (X+S+Z)
Calculate
Syndrome
University of California, Berkeley
Data
Rate n/m
Rate k/n
Data Hiding
Encoder
Rate n/m
p
1
p
Side Information
University of California, Berkeley
Side Information, S
1a
a
Viterbi Algorithm
Rate – k/m code
Data, d
Rate n/m
E[d2] <= X
Constellation
Mapper
+
Rate n/m
p
1
p
To Channel
University of California, Berkeley
From Channel, Y=X+S+Z
P(ygu)
MAP
+
1

d’
Calculate
Syndrome
p
p
P(ygu)
MAP
1

Hard
Decision
+
p
1
p
1
University of California, Berkeley
University of California, Berkeley
More recent
results
(< 2 dB)
(< 3.5 dB)
2.72 dB
4.55.5 dB
University of California, Berkeley
University of California, Berkeley
Watermarked image(SDR = 42.22 dB)
Original image
Can withstand attack up to 32.07 dB (JPEG Q=25%) and
yet perfectly embed (with BER < 107) up to 4 Kbits of
watermarking data in a 512x512 image.
University of California, Berkeley
Audio
Encoded Audio
Wavelet
Decomposition
Coset
Code
Perceptual
Model
STFT
Audio Data Hiding
University of California, Berkeley
University of California, Berkeley
Z
0
1
2Z+1
2Z
1
0
0
1
4Z
4Z+2
4Z+1
4Z+3
.
.
.
*
*
*
*
*
*
*
*
*
*
*
*
*
*
University of California, Berkeley
University of California, Berkeley
Data
Analog
Audio
DATA
HIDING
D/A
A/D
Data
Analog
Receiver
Analog Audio
Channel
Digital
Receiver
A/D
University of California, Berkeley
Design and Simulation results:
University of California, Berkeley
Design and Simulation results (cont.):
University of California, Berkeley
p(yx,s)
Enc 1
Dec 1
Enc N
Dec N
New user
New user
Big picture: new constructive way to do multiuser communicationUniversity of California, Berkeley
University of California, Berkeley
Conclusions and future directions
University of California, Berkeley