256GB Geometrically Encoded Paper Storage Device

jrieth50 noted that a method of using geometric shapes combined with color to store up to 256GB of data on a sheet of paper or plastic. The article says "Files such as text, images, sounds and video clips are encoded in 'rainbow format' as colored circles, triangles, squares and so on, and printed as dense graphics on paper at a density of 2.7GB per square inch. The paper can then be read through a specially developed scanner and the contents decoded into their original digital format and viewed or played."

Robustness & Feasibility

The Rainbow technology is feasible because printed text, readable by the human eye is a very wasteful use of the potential capacity of paper to store data.

And I'm sure this "Rainbow Technology" is also very wasteful if you would devise a way to encode data on electrons & lay them on the sheet of paper and then read them. The obvious problem being that just exposing the paper to the natural elements would probably render some of the data useless. Now I know that compact disc drives in computers use a form of error correcting codes (I can't recall if it's cyclic redundancy checks or some other form of parity) and I assume that the scheme of this paper technology uses the same (most likely at the cost of a fraction of space). Judging by the word 'rainbow' I'm guessing it uses colorized shapes to encode the data which is a novel idea but what quality must the paper & ink be? Can the paper in my printer be used to encode this data?

My question would be how much wear & tear can a sample of this medium stand before it is rendered unreadable? I would highly doubt one would be able to fold it--however it would be interesting to see whether creating a diagonal read/write scheme would protect from vertical & horizontal folds with the proper ECC. I think the plastic sheets could potentially be as robust as discs but would you be able to bend them? I doubt it though if they allowed it, it'd probably end up being more expensive than a disc.

Interesting technology but I'd sure like to hear a lot more of the details of how it works & how it performs before I make a solid judgment on its feasibility.

Re:Robustness & Feasibility

QR Codes [wikipedia.org] are not as sophisticated, but can reconstruct the original data when 30% image is missing or distorted. Since these guys are obviously pretty clever, I can't imagine this feature would be overlooked.

Cool...

Now it's possible to fold up 256MB worth of data and fly it across the room.

Re:

This could be the dawn of a new era in wireless networking...

Must be a very good scanner.

I would love to know which scanner has the ability to scan with such high fidelity.

Scam...

according to this Indian blogger [blogspot.com].

Re:Scam...

Okay, time to throw out my calculation. As someone else pointed out [slashdot.org]:

Each dot is going to be either cyan, magenta, yellow, or black. Laser and injket printers produce multicolour output by dithering, not by mixing inks, and the "dpi" rating of the printer refers to the dots used when dithering, not to the equivalent of screen pixels.

So instead of multiplying by 256, you have to multiply by 4. Result: about 140MB.

Another approach to analyzing the claim: For a given dpi resolution, how many variations of a single dot must your system be able to produce and distinguish? I get 256 GB / 302940000 dots, or 907 gradiations. Instead, we have four available.

I'm split between "scam" and "incompetent." But believing he may have actually done what he claimed is no longer an option for me.

Scam?

http://itsoup.blogspot.com/2006/11/scam-of-indian- student-developing.html [blogspot.com]
http://www.digg.com/tech_news/Scam_of_Indian_stude nt_developing_technology_to_store_450_GB_on_paper [digg.com]

Re:maybe not scam?

Can you really print 4,096 dots per linear inch on paper and still be able to read each individual dot? My guess is that beyond 300 dpi or so bleeding becomes a major issue and somewhere beyond that the grain size of paper becomes an issue.

Also, can you really have 256 distinguishable color levels on a piece of paper - especially considering that paper is not a uniform color on the micro-scale (it's made up of short strands of cellulose)?

Even if all these problems can be overcome, there is the limiting factor of diffraction, which will limit any optical system (paper or otherwise) to a data density of about 1/wavelength^2, which is roughly the density of a DVD.

C'mon Slashdot

I expect to see a story like this on Digg, but I thought Slashdot was better than this.

It's a scam [blogspot.com].

I tried this...

I wiped my ass on a blank sheet, scanned it in and was greeted with the Windows Vista login screen.

This looks like a lie

What does this bring that normal scanners can't ?

Let's see A4 - 256Gig. Let's say n different colors.

He'd need to store 256*1024*1024*1024*8 = 2199023255552 bits
on A4 = 210 mm x 297 mm = 62370 mm^2 = 2456 inch

That makes 895 367 775 bits per inch. To encode that you'd need 895 367 775 / log2(n) dots. Increasing the number of colors can buy you some leeway, but not that much.

The surface area of such a dot would be 1/30 000 000 th of a millimeter.

Where will you find paper that has surface flaws significantly smaller than that ? No matter what the encoding, you're still going to need it. So this is a scam, plain and simple.

Re:This is a lie

Okay, let's look at some math. First, calculate the number of bits that must be stored to reliably archive 256GB:

256*1024*1024*1024*8*(10/8) = 2.749 * 10^12 [allowing for 25% extra - error detection/correction]

Now, the area of a sheet of paper in mm^2:

210 mm * 297 mm = 6.237 * 10^4

Let's make an assumption: it would be tough for a scanner to correctly identify more than 256 colors (blues especially are problematic). So, going by a pixel based method, we can store 8 bits per pixel, so the number of pixels needed is:

2.749 * 10^12 / 8 = 3.436 * 10^11

Pixels per mm^2 will therefore be:

3.436 * 10^11 / 6.237 * 10^4 = 5.509 * 10^6

Taking the square root of this figure and inverting will give us the size of one side of a pixel in mm, so:

1 / (5.509 * 10^6)^.5 = 4.260 * 10^-4 mm = .426 micro meters = 426 nm

This is smaller than the wavelengths of some frequencies of visible light, therefore a large portion of the spectrum is gone in terms of colors that can be used. Eliminate these colors and you increase density yet again, requiring you eliminate more colours. By the time you get to monochromatic (black white), which you will, the size is smaller than the wavelength of ANY visible light.

So, for this storage density, either you are scanning in ultraviolet light (and printing using an appropriate ink) to get a small enough wavelength, or you have thrown out light all together and you are using an electron microscope as your scanner. (Note - ever see electron microscope images in color? Can't exist unless colorized).

Fairly clever hoax though - if they had stuck with, say, 16GB then it would not have edged into the impossible.

Re:RTFA

You are an idiot because: You ignored the one and only thing he /did/ say, which was that he was doing something differently.

Bzzt.

Encoding data using dots is the most efficient method possible. He has to print the image somehow, and scan it back in again. No combination of triangles and circles can circumvent the resolution limit, which is what is being calculated here.

By showing that the claim exceeds all practical limits of optical resolution (and probably the absolute physical limits), we show that what we have is just another magical compression scam.

He says that he's "doing something differently"; we've proved that what he claims to be doing is impossible. End of story.

Re:RTFA

You are an idiot because: You ignored the one and only thing he /did/ say, which was that he was doing something differently.

Bzzt.

Encoding data using dots is the most efficient method possible. He has to print the image somehow, and scan it back in again. No combination of triangles and circles can circumvent the resolution limit, which is what is being calculated here.

By showing that the claim exceeds all practical limits of optical resolution (and probably the absolute physical limits), we show that what we have is just another magical compression scam.

He says that he's "doing something differently"; we've proved that what he claims to be doing is impossible. End of story.

Indeed. For those not inclined to simple mathematics, here it is in a nutshell-
Assumptions (none of them unreasonable, all of them quite generous even):
1440dpi
8 bit color
8" x 10.5" printing area

Even assuming perfect readability, this resolution yields only 1.4GB per page. Talk of "shapes" is smoke and mirrors to obfuscate one of the cold hard facts of information theory: you cannot accurately represent all permutations of 8 bits of information if you've budgeted less than 8 bits. Compression schemes allow you to compress repetitive patterns is you know they're going to be there beforehand (e.g. an almost arbitrarily large number of only 1's or only 0's can be represented with run length encoding), but X bits of random data requires X bits of allocated space.

Re:This looks like a lie

Your scheme doesn't work because triangles are not atomic; they are made out of lines, which are described in terms of endpoints, which have a finite resolution. For example, an inkjet printer would make a triangle by printing dots at some fixed resolution. A drafting machine or laser printer might be able to draw the triangle without resorting to dots, but the elements of the triangle can still only be positioned with finite accuracy.

Let's say that we're drawing very tiny triangles as close to our resolution limit as possible (which we must do if we want to fit a lot of them). Such a triangle might be, say, 3 x 3 resolution units, so a hollow, up-triangle might look like this:

010
101
111

But look: there are 2^9 (or 512) possible shapes that can be made in this grid -- so by using only 64 different triangles, we are actually underutilising our medium. It doesn't matter what technology you use, any shape other than a "dot" is itself made out of smaller units like "dots", so restricting our vocabulary to certain shapes (rather than arbitrary sequences of dots) will waste space.

Bullshit, complete bullshit

2.7GB per square inch would would require a linear data density of 152292 dpi. Neither my scanner nor my printer come within a hundredth of this. The main problem with the printer at such resolutions is bleeding of the inks into the paper. To form the different shapes several dots would be necessary, which would further decrease the effective resolution by an order of magnitude. For example, suppose a 3x3 grid was used to form each character, the article states that there are four different shapes used, yet that 3x3 grid could encode 512 different patterns. Realistically, at 600dpi (giving 360000 dots per square inch), with 3 ink colours (yielding 8 different colours) you would get 360000 bytes per square inch, or 33MB per A4 page - somewhat short of the 256GB promised. You'd also need to dedicate around 25% of the capacity for error correction. This is complete and utter bollocks.

Do The Numbers

2.7GB per square inch, eh?

Alright, that's 21.6 gigabits per square inch.

For the sake of argument, let's say that the printer and scanner can reliably print and scan colour at 24-bit fidelity (which is nonsense, but makes the numbers nice and tidy): 900 million pixels per square inch.

That's 30,000 dpi.

That means you'd have to print and scan pixels less than a micron across. In full colour.

I don't think so.

hmmm...

600dpi times 8*11 inches makes 32M dots. To get 26GB you need 6500 bits per dot. This gives either an amazing resolution in color separation (as opposed to, say, 32 bits on a screen - maybe 700 different frequencies, each with 10bit separation), or much higher dot density - something like 50000dpi!

Ultimate compression?

This story is a hoax.

Lets just imagine for one second that its true.

Instead of printing this data onto paper, why not just store it loslessly in a bitmap file? After all, printers only have a certain DPI and a certain amount of colours. If you could take this bitmap file and somehow extract 256GB of data from it, that sure would be some cool magic.

I find the comments amusing.

Hey guys, remember back in the day when we stored data on paper using HOLES?

I wouldn't be so quick to say this is a scam.

I've always defended Slashdot, but..

In this Digg generation, I've still kept reading Slashdot. The community here feels a lot nicer (surprising, I know!) and a lot more clued up. It's just a shame, then, that idiotic stories like this get posted. Usually I wouldn't whine about a bad story, but it was an hour or two before this story hit that I read the whole "why it's a scam" story on Digg.. so I read how stupid something is on Digg, only for it to be posted seriously here at Slashdot.

It's time for some sort of shakeup with editorial at Slashdot. Digg is imperfect and a lot of the users are idiots (I'd certainly say the average Slashdotter is significantly more intelligent and clued-up) but Slashdot is slow and has a poor editorial process. Could we, perhaps, strive to produce something with the perfect mix of the two? Fast news, the ability to vote, etc, but coupled with the superb Slashdot audience? It's all false hope, I'm sure, but I have more hope in people than technology.. so Slashdot is just the place to bring this up IMHO.

Re:Not Dots

All the "proofs" in the comments that show this is a scam so far calculates how many dots can be printed/read from a piece of paper, and then corresponds each dot to a bit of data. Well, guess what. The whole point of this thing is he's NOT USING DOTS. This may very well be bullshit, but the "proofs" against it are meaningless.

No, you simply don't understand very basic information theory. Printers print with dots. Any shapes you make on the paper are made up of dots. A 3x3 grid of dots (9 bits) can be marked in 512 different combinations, only 10 of which make a squares(2), triangles(4), or lines(4) that can be easily differentiated. Using shapes does not increase the resolution, it limits it. You cannot represent 8 arbitrarily chosen bits of information if you've budgeted 7 bits of storage. At 1440dpi, 8 bit color, even assuming perfect readability, you cannot record more than 1.4GB of information, no matter what "shapes" you arrange for the dots to make.

An upper bound

Here's an upper bound as a check on your numbers (not restricting ourselves to a small dictionary of shapes). I'll give away the punchline: My numbers agree with yours, but 256 GB is not possible using printers and paper.

Assumptions: I use your printer linear resolution of 1200 dpi, and assume that adjacent pixels can be resolved at this resolution. I also assume that 256 different colors can be distinguished, as you do, and that the paper we are using has an area of 96.6763 inches^2, also as you do.

Calculation: With a linear resolution of 1200 dpi, one can fit 1440000 dots per square inch (Check!), and so 139213872 dots on a sheet of A4. With 256 colors we can store a number as large as (number_of_colors)^(number_of_dots). So:

256^139213872 = 2^N (where N is the equivalent number of bits)
(2^8)^(139213872) = 2^N (recognizing that 256 = 2^8)
2^(8*139213872) = 2^N
N = 8*139213872 (bits)
(and if we just divide by 8 again to get bytes...) => 139213872 bytes = 139 MB

Discussion: This theoretical upper bound is three orders of magnitude smaller than what is being claimed by the article: It is not possible to store 256 GB on a sheet of A4. My result does however agree with your result in that the inequality (my_result)>(your_result) holds, as it should. Ad it's really not too shabby: Accounting for 8-to-14 conversion for some error correction, we can store slightly under 80 MB in this way.

Different assumptions: If I instead use your 2000 dpi laser printer figure, then I can fit 4000000 dots per square inch, and so 386705200 dots on a sheet of A4 and so almost 386 MB. (Including error correction, one might store 220 MB.) Pretty impressive!

The Absurd: Right now, many modern semiconductor fabs have working 90 nm photolithographic processes. That means that the smallest feature size is 3.54330709×10^(-6) in, and the linear resolution is about 282222 dpi. If all we print is the first metal layer, then a dot can either be "with metal" or "without metal" -- that is, one bit. And on a silicon wafer with an area the same as that of a sheet of A4 paper, we can then fit 7700207603555 dots, or 962 GB. Hard drives are about halfway there!

Re:This is brilliant

How much do you love the story's title? "Data can now be stored on paper!"

We truly live in the golden age of technology.