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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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Spectrum recycling salvaging analog spectral waste

Spectrum recycling: salvaging analog spectral waste

Kannan RamchandranEECS Dept.

University of California at Berkeley

[email protected]

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


^

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


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 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


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


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


  • 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


^

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


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


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


^

^

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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


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


  • 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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