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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

Spectrum recycling: salvaging analog spectral waste

Kannan RamchandranEECS Dept.

University of California at Berkeley

kannanr@eecs.berkeley.edu

http://www.eecs.berkeley.edu/~kannanr

motivation
Motivation:
  • Legacy analog systems can be spectrally v. wasteful
    • AM/FM radio
    • Broadcast and cable (analog) TV
  • NTSC TV is 6 MHz. per channel
    • Digital NTSC-quality ~ 1-2 Mb/s (MPEG)
    • Analog system spectral efficiency < 0.33 bits/sec/Hz.
      • Digital spectral efficiency of DTV ~ 4 b/s/Hz. (use 16 QAM)
  • What’s the problem then?

let’s nuke analog…

let’s get digital!

University of California, Berkeley

motivation contd
Motivation (contd.):
  • Not so fast…
  • Radio and television are legacy systems: millions of analog TV’s and AM/FM radios…
  • Digital simulcast is current FCC solution
    • Duplicate identical content with extra digital spectrum
  • Switchover to all-digital mandated by 2006
    • Not likely to happen.
    • Analog systems are here to stay, at least for a while.
  • Question:Are we stuck then with this spectral inefficiency till we turn the digital corner?
  • Answer:Not necessarily.

University of California, Berkeley

motivation contd1
Motivation (contd.):
  • Can “steal” analog spectrum to do digital transmission
  • Fully backward-compatible with legacy analog system:
    • No need to touch existing analog receivers
    • Digital upgrade system will have superior quality
    • Can control the switchover from analog to digital
  • Idea is to “embed” the digital data in the analog signal
    • Similar in concept to data-hiding/watermarking
    • Data embedding framework known in theory as channel coding with side-information (CCSI)

University of California, Berkeley

slide5

^

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

motivation contd2
Motivation (contd.):
  • Question:How much do we lose in terms of the digital quality due to backward compatibility with analog system?
  • Answer:Nothing, in some cases, (in theory of course!)…
  • host is i.i.d. Gaussian signal and channel is AWGN
    • Analog transmission is actually optimal (analog perf.= digital perf.)
    • Digital embedding “corrupts” analog system – takes away quality
    • Digital upgrade system at receiver – fully restores lost quality due to embedding
    • All-digital system instrumented from scratch cannot do better!
  • Question:Then why bother with digital systems if analog transmission is optimal?

University of California, Berkeley

motivation contd3
Motivation (contd.):
  • Answer: Get real: real-world signals are not i.i.d. Gaussian!
  • Considerable amount of memory (correlation)
    • Audio, image, video, speech, text….
  • Analog systems ignore the correlation:
    • no easy way to do analog compression!
  • Digital systems are much more efficient:
    • Can pack ~10 NTSC digital channels in the place of 1 analog NTSC channel (and cable companies do!)
  • So, digital data embedding can allow for:
    • Simultaneous analog/digital broadcast
    • No need for digital simulcast on separate spectrum…can use the same analog spectrum!
  • Analog spectral waste can be recycled seamlessly!

University of California, Berkeley

roadmap for rest of talk
Roadmap for rest of talk
  • Overview of data embedding: channel coding with side information (CCSI)
    • Dual of distributed source coding (DISCUS)
  • Practical examples of data-hiding systems
    • Data-embedding in images
    • Data-embedding in audio: toy demo to show power
  • Other applications and future directions

University of California, Berkeley

data hiding watermarking
Data Hiding (Watermarking)
  • Embedding information in a signal: covert data/ authentication signature
  • Needs to be minimally perturb host signal (power constraint on the “watermark” added on the signal)
    • Existing system should be minimally disturbed
  • Need to be robust to natural and man-made sources of interference
  • The intended receiver should be able to recover the data/ watermark without the aid of the host signal

University of California, Berkeley

data hiding embedding problem

Data hiding: channel coding with side info. at the receiver

Channel

(watermark)

(watermark msg.)

Decoder

Encoder

N (attacker)

S (host signal)

Data Hiding/Embedding Problem
  • The encoder has access to information S related to the statistical nature of the channel
  • X is the transmitted signal over the channel

University of California, Berkeley

slide11

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

slide12

CCSI: illustrative example

Binary data-embedding/watermarking

  • Consider a 3-bit host signal S (e.g. binary fax)
  • Desired to embed data in the host
  • Max. allowed distortion between S and embedded host X:
  • Clean channel (no attack) model: received signal Y=X.

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

slide13

Coset-3

0 0 0

1 1 1

0 0 1

1 1 0

0 1 0

1 0 1

1 0 0

0 1 1

Coset-1

Coset-4

Coset-2

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.

  • Codebook: partition U into 4 cosets
  • Each of 4 messages indexes a coset in U.
  • Encoder “perturbs” S to
  • closest entry X in desired coset of U:
  • Decoder receives Y=X and
  • declares coset index of Y as message sent.

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

slide14

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

encoding decoding

X

X

X

Codeword

Sphere

X

ENCODING/DECODING

- Coset 1

X

- Coset 2

- Coset 3

- Side Info

- Received Signal

Received Signal Sphere

(within scale factor)

Side-Info Sphere (within scale factor)

Assume signal and channel are Gaussian, iid

University of California, Berkeley

slide16

There is a fundamental “duality” between

  • CCSI and the problem of distributed coding
  • (SCSI: source coding with side information)
  • Encoder and decoder can be interchanged functionally
  • Allows cross-leveraging of progress between the data
  • embedding problem and the problem of distributed coding
  • (DISCUS) used in sensor networks!

University of California, Berkeley

slide17

^

Y

X

Encoder

Decoder

X

Y

X

Distributed Source coding:(source coding with side information):

  • The encoder needs to compress the source X.
  • The decoder has access to correlated side
  • information Y.
  • Encoder knows only H(X|Y).

Information theory:X can be compressed (in some cases) at a rate

equal to that when the encoder too has access to Y (Slepian-Wolf ’72)

University of California, Berkeley

duality with channel coding with side info

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.
  • Encoder knows some information regarding channel S (not available at decoder)
  • X transmitted over channel: studied by Gel’fand/Pinsker, Heegard/El Gamal, Costa
  • Can be applied to “blind” watermarking/data-hiding: host signal available at encoder only. Capacity independent of strength of host signal!

University of California, Berkeley

slide19

Y

Source coding with side information:

Illustrative Example ( binary case):

Let X and Y be length-3 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 and Y are correlated.
  • Y is available at
  • encoder and decoder.

X

X

Decoder

Encoder

SYSTEM-1

0 0 0

0 0 1

0 1 0

1 0 0

Need 2 bits to index this.

X+Y=

University of California, Berkeley

slide20

1 0 0

0 1 1

0 0 0

1 1 1

0 1 0

1 0 1

0 0 1

1 1 0

Coset-1

Coset-3

Coset-4

Coset-2

^

X

X

  • X and Y are correlated.
  • Y is available to only
  • the decoder.

Decoder

Encoder

Y

SYSTEM-2

What is the best one can do?

The answer is still 2 bits.

How?

  • The Encoder sends the index
  • of the coset containing X.
  • The Decoder with this
  • information and the
  • knowledge of Y, reconstructs
  • X without error.

University of California, Berkeley

slide21

^

^

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)

Data-hiding

Encoder

(10)

M:

data to be

embedded

Data-hiding

Decoder

M

embedded

host

recovered

data

S

(host)

(011)

Data embedding (CCSI)

University of California, Berkeley

data embedding code constructions

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

Data-embedding Code Constructions
  • Want codebook with property that it can be partitioned into “sub-codebooks” (Chou, Pradhan, Ramchandran ’00)
  • In general, lattices and trellises good (geometrically uniform)
  • Digital data can then be drawn from a set of “labels” that have a one-to-one correspondence with the “sub-codebooks”.

Coset-1

Coset-3

(00)

(10)

Coset-2

Coset-4

(11)

(01)

University of California, Berkeley

slide23

Data

Data Hiding Encoder

Rate n/m

Rate k/n

Host

Code Constructions

  • Consider

G0 / 2Zn/ G1embedded coset codes

  • Framework allows us to partition state-of-the-art channel codes (e.g., turbo codes, TCM) into state-of-the-art source codes (e.g., TCQ)
  • Our formulation performs near capacity!

University of California, Berkeley

slide24

Code Constructions (Trellis)

  • TCM/TCQ encoder

Data, d, determines the rate-k/m code to use

E[d2] <= X

Viterbi Algorithm

Rate – k/m code

Side Information, S

a

To Channel

+

1-a

University of California, Berkeley

slide25

Code Constructions (Trellis)

  • TCM/TCQ decoder

Viterbi Algorithm

Rate – n/m code

Codebook

g

d’

From Channel (X+S+Z)

Calculate

Syndrome

University of California, Berkeley

slide26

Code Constructions (Turbo)

  • Can extend trellis framework to include turbo codes (channel code is similar to TTCM of Robertson et. al)!

Data

Rate n/m

Rate k/n

Data Hiding

Encoder

Rate n/m

p

-1

p

Side Information

University of California, Berkeley

slide27

Code Constructions (Turbo)

  • TTCM/TCQ encoder

Side Information, S

1-a

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

slide28

Code Constructions (Turbo)

  • TTCM/TCQ decoder

From Channel, Y=X+S+Z

P(y|gu)

MAP

+

1

-

d’

Calculate

Syndrome

p

p

P(y|gu)

MAP

1

-

Hard

Decision

+

p

-1

p

-1

University of California, Berkeley

slide29

Simulation Results

  • We use a rate-2/3 convolutional code in concatenation with a rate-3/4 convolutional code for both the TCM/TCQ construction and the TTCM/TCQ construction. (Convolutional codes are constraint-length 4 Ungerboeck codes.)
  • Assume side-information (S) is i.i.d. Gaussian and Z is also i.i.d. Gaussian: S can be arbitrarily large and can be arbitrary
  • Embedding rate is 1 bit/sample

University of California, Berkeley

slide30

Results

  • At 1 bit/sample, Capacity = 4.77 dB:(C=1/2 log (1 + P/N) regardless of interference strength of side-information S.
  • Shannon limit if you ignore that S is available at encoder:
  • C= ½ log(1 + P/(S+N))  If S/N ~ 12 dB, Eb/No  17 dB (gap is 12.23 dB)

More recent

results

(< 2 dB)

(< 3.5 dB)

2.72 dB

4.5-5.5 dB

University of California, Berkeley

slide31

Image Watermarking

  • Case: Signal (S) is the “Lena” image and the attack is JPEG compression.
  • Embedding Rate: 1/64 Bits/Sample
  • Probability of decoding error < 10-5

University of California, Berkeley

image watermarking simulation results
Image watermarking: simulation results
  • Example of robustness of watermark to lossy compression

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 < 10-7) up to 4 Kbits of

watermarking data in a 512x512 image.

University of California, Berkeley

slide33

Data

Audio

Encoded Audio

Wavelet

Decomposition

Coset

Code

Perceptual

Model

STFT

Audio Data Hiding

  • Data-hiding capacity can be perceptually optimized
  • Attractive for legacy systems like FM radio/NTSC TV
  • Practically possible to hide over 150 kbps in CD quality
  • audio (noiseless channel) or ~ 45 kbps (14.5 dB SNR channel) with no perceptual degradation
  • (Chou & Ramchandran ICASSP ’01)

University of California, Berkeley

slide34

Audio Data Hiding

  • Model audio coefficients with vector Gaussian (or generalized Gaussian) distribution.
  • Capacity: C = S Ci
  • Ci = ½ log(1+Di1/Di2) where Di1 is distortion variance and
  • Di2 is the channel noise variance

University of California, Berkeley

slide35

Audio Data Hiding

  • The amount of quantization noise allowed is determined by the perceptual mask.
  • Data specifies path in tree
  • Nodes correspond to source code
  • Side info needed for depth of tree
  • In general, we can use a code C0/C1/ … /Cn
  • Coset codes (Forney) provide nice constructions.

Z

0

1

2Z+1

2Z

1

0

0

1

4Z

4Z+2

4Z+1

4Z+3

.

.

.

*

*

*

*

*

*

*

*

*

*

*

*

*

*

University of California, Berkeley

slide36

Audio Data Hiding

  • Can use a composite trellis code and divide it into multi-stage trellises (Chou et. al. ICIP’ 00) to provide a good channel code and good source codes!
  • With a good channel code, one can hide data while being robust to channel noise

University of California, Berkeley

slide37

Applications

  • Audio data hiding over analog communication channels

Data

Analog

Audio

DATA

HIDING

D/A

A/D

Data

Analog

Receiver

Analog Audio

Channel

Digital

Receiver

A/D

University of California, Berkeley

slide38

Design and Simulation results:

  • Audio data sampled at 44.1 kHz (CD Quality)
  • 6 Stage scalar quantizer (with and without FEC)
  • Without FEC can hide around 150 kbps (of course this is with disregard to the channel)
  • With BCH codes can hide 42.7 kbps (and transmit reliably over channels with 14.5 dB SNR).

University of California, Berkeley

slide39

Design and Simulation results (cont.):

  • With better codes (i.e., Trellis codes, etc) should be able to perform even better!
  • Original Audio File (44.1kHz,14.99 sec.)
  • Audio File (44.1kHz, 14.99 sec.)with 154.7 kbps (2.32 Mbits total) of data hidden in!

University of California, Berkeley

big picture new constructive way to do multiuser communication

Channel

p(y|x,s)

Enc 1

Dec 1

Enc N

Dec N

New user

New user

Big picture: new constructive way to do multiuser communication
  • Can add more user(s) by “piggybacking” signal on compound signal of other users: minimal obtrusion on other users: fully backward compatible with existing receivers!
  • Constructive way to do broadcast (optimal theoretical way!)

University of California, Berkeley

other communication system applications
Other communication system applications
  • Multi-antenna broadcast (BS to mobiles)
    • Embedding users’ information inside one another’s signals is information-theoretically optimal.
    • Downlink capacity can be increased.
  • ISI cancellation (improved precoding)
    • Treat ISI noise as “side information”
  • DSL cross-channel interference
    • CO hub to residential units is a broadcast channel
    • Can treat cross-channel interference as side-information that is deterministically known (can be completely removed in theory!)

University of California, Berkeley

slide42

Data-hiding idea is very powerful and can be

  • applied to the original problem of spectrum
  • recycling of wasteful analog bandwidth
  • Challenges are many-fold: theoretical, algorithmic,
  • implementational and system-level.
  • Target specific applications of interest
  • BWRC is perfect place to make a lot of this happen!

Conclusions and future directions

University of California, Berkeley

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