Spectrum recycling: salvaging analog spectral waste. Kannan Ramchandran EECS Dept. University of California at Berkeley. kannanr@eecs.berkeley.edu http://www.eecs.berkeley.edu/~kannanr. Motivation:. Legacy analog systems can be spectrally v. wasteful AM/FM radio
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Spectrum recycling: salvaging analog spectral waste
Kannan RamchandranEECS Dept.
University of California at Berkeley
kannanr@eecs.berkeley.edu
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)
University of California, Berkeley
Example:
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
CCSI: illustrative example
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
Coset3
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
X
Codeword
Sphere
X
 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
University of California, Berkeley
Y
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
1 0 0
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
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
Coset1
Coset3
(00)
(10)
Coset2
Coset4
(11)
(01)
University of California, Berkeley
Data
Data Hiding Encoder
Rate n/m
Rate k/n
Host
Code Constructions
G0 / 2Zn/ G1embedded coset codes
University of California, Berkeley
Code Constructions (Trellis)
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
Code Constructions (Trellis)
Viterbi Algorithm
Rate – n/m code
Codebook
g
d’
From Channel (X+S+Z)
Calculate
Syndrome
University of California, Berkeley
Code Constructions (Turbo)
Data
Rate n/m
Rate k/n
Data Hiding
Encoder
Rate n/m
p
1
p
Side Information
University of California, Berkeley
Code Constructions (Turbo)
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
Code Constructions (Turbo)
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
Simulation Results
University of California, Berkeley
Results
More recent
results
(< 2 dB)
(< 3.5 dB)
2.72 dB
4.55.5 dB
University of California, Berkeley
Image Watermarking
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
Data
Audio
Encoded Audio
Wavelet
Decomposition
Coset
Code
Perceptual
Model
STFT
Audio Data Hiding
University of California, Berkeley
Audio Data Hiding
University of California, Berkeley
Audio Data Hiding
Z
0
1
2Z+1
2Z
1
0
0
1
4Z
4Z+2
4Z+1
4Z+3
.
.
.
*
*
*
*
*
*
*
*
*
*
*
*
*
*
University of California, Berkeley
Audio Data Hiding
University of California, Berkeley
Applications
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
Channel
p(yx,s)
Enc 1
Dec 1
Enc N
Dec N
New user
New user
University of California, Berkeley
University of California, Berkeley
Conclusions and future directions
University of California, Berkeley