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Spectrum recycling: salvaging analog spectral waste

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

JasminFlorian
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Spectrum recycling: salvaging analog spectral waste

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  1. Spectrum recycling: salvaging analog spectral waste Kannan RamchandranEECS Dept. University of California at Berkeley kannanr@eecs.berkeley.edu http://www.eecs.berkeley.edu/~kannanr

  2. 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

  3. 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

  4. 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

  5. ^ 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. ^ 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

  18. 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

  19. 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

  20. 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

  21. ^ ^ 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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

  37. 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

  38. 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

  39. 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

  40. 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

  41. 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

  42. 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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