This document discusses using progressive barcodes for archiving applications. Progressive barcodes encode data in both black-and-white and color channels, allowing two channels of information. They are suitable for archiving where one channel, like a document ID, remains static, while the color channel can dynamically track document changes. The document proposes an inference model where tags on individual archive items can be inferred from tags on containing folders and computers, reducing the number of required tags. Progressive barcodes combined with inference could track documents and versions without opening each container.

1. Archive-enabling Tagging Using
Progressive Barcodes
Steven Simske and Marie Vans
HP Labs; Fort Collins, Colorado
May 22, 2015
1

2. Agenda
• Barcodes
• Progressive Barcodes
• Archiving Applications
• Inference Model
• Conclusions
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content/uploads/2012/01/train-tickets.jpg
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content/uploads/2012/08/Does-
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3. Barcodes
i. 1 Dimensional -
ii. 2 Dimensional -
iii. 3 Dimensional –
iv. 4 Dimensional -
3
Data Capacity
11 numeric digits
Data Matrix: 2335 bytes
Aztec: 1914 bytes
QR-Code: 3706 bytes
2.585 bits/tile for 6
colors: RGBCMY
𝑋𝑌 log2 𝑛 𝑏𝑖𝑡𝑠

4. Non-Standard Barcodes
4
ColorTile
Progressive Barcode
Non-payload indicia
Non-payload indicia
The example shown here comprises:
1. 64 data tiles, max 165 bits total
2. 8 non-payload tiles:
a. Two black for orientation & corner
detection
b. 6 color {RGBCMY} for color
calibration
c. Colors are 180 rotated from their color opponency
pair, providing the greatest contrast in hue space and thus
the most reliable opposite-corner orientation detection
possible

5. Example Progression
5
• Reader-Friendly
Progressive
Barcodes
• Columns indicate
progression along
workflow
• Colors saturated
enough so that 2D
barcode reader still
interprets them as
“white”
• 2D barcode reads the
same throughout the
progression.

6. Progressive Barcodes - Statistical Probability
6
• Statistical probability assigned at each step of the progression
• Associated with any transition between two steps in a workflow
• Based on how many bits are written and how many remain

i
i
RB
IU
P
N
N
!
!
Pi = Step i
NRB = the number of residual (0 bits) at end of the workflow
NIU = number of initial unwritten bits

7. Progressive Barcodes - Statistical Probability
7
• If barcode is unique at step i-1, then total number of barcodes of the current
state is 1.
• If the progressive barcode is binary, then the number of bits in the workflow is
NRB-NIU.
• If there are NC colors, number of bits increases to:
𝑙𝑛 𝑁 𝑐
𝑙𝑛 2 ∗ 𝑁 𝑅𝐵 − 𝑁𝐼𝑈
• The size (height and width in tiles) of progressive barcode used in the
workflow can be determined from these equations along with the number of
bits to write at each state

8. Progressive Barcodes - Data Capacity
8
• Each color tile independent
• Define a tile to be N-ary, where N = number of colors allowed at each tile:
log2 𝑛
log2 2
= log2 𝑛 𝑏𝑖𝑡𝑠 𝑎𝑡 𝑎𝑛𝑦 𝑠𝑡𝑎𝑔𝑒
• n=2, e.g. DataMatrix, QR, Aztec: 1 bit per tile
• Color tile with six colors {RGBCMY}: 2.585 bits/tile
• 8 colors allowed {RGBCMYWK}: 3.0 bits/tile
• Color tile barcode X data tiles wide & Y data tiles high contains exactly:
𝑋𝑌 log2(𝑛) 𝑏𝑖𝑡𝑠
• 120x120 DataMatrix barcode with 8 colors allows for 120*120*3 = 43, 200
bits or 5400 bytes >> 1800 bytes using black & white only

9. Progressive Barcodes for Archiving
Applications – Static Channel
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• Amount of data that to be encoded in first set of data limited by
the total number of black & white tiles available & standards.
• URLs to websites - QR Codes
• Data Matrix - serial numbers, invoicing information or product
numbers.
• Possible to encode other information;
• xml fields for archiving purposes,
• ISBNs, other document-related information
• The main characteristic is that information remains static over
time.

10. Progressive Barcodes for Archiving
Applications – Dynamic Channel
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• Second channel of information can be encoded into the white tile channel
• Track and store documents
• Versioning or tracking document changes
• Assign ownership of documents.
• “Hybridization” allows for multiple services:
• open services and proprietary services
• Encoding of a website URL along with security/authentication services.
• These barcodes are readable by any off-the-shelf, QR Code and the Data
Matrix code readers.
• The Data Matrix code can store a large quantity of data in the black-as-black
and rest-as-white tiles.

11. Progressive Barcodes for Archiving
Applications – Two Channels
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Demonstration of barcode with two channels. The black and rest-as-
white will read with an off-the-shelf reader, the right Data Matrix will
display an abstract and the left QR-Code displays a test message.

12. Hybrid barcodes with Progression in the Color
Channel
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Layer 1
Layer 2
Same barcodes with progression
Barcodes don’t change

13. Inference for Archiving Data
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D:Computer containing files C: Directory with files B: My Document with images A: Individual images
• Inference is the relationship between objects and their containers:
• Individual objects (e.g. images) A
• Packaged into file B: At(Bu,Bu+1,Bu+2, …, Bu+v-1)
• Multiple files contained in folders C: Cq(Br,Br+1,Br+2, …, Br+s-1)
• Multiple folders per computer D:
D←{C} ← {B} ← {A}
Dn(Cm,Cm+1,Cm+2, …, Cm+p-1)

14. Inference for Archiving Data
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• How many tags (barcodes) are required to tag n(A) items when they are
inferred to B, C and D containers
• The following ratios are very important: n(A)/n(B), n(B)/n(C), and n(C)/n(D).
• We create series of cryptographically secure tags, in sequence, and assign
them to the containers they are representing as follows:
(D) (C) (B) A….A (B) …. (B) A….A (B) (C) …. (C) …. (C) (D)
• Example:
• Label the associated C, B and A items:
• “A” items: n(A)*n(B)*n(C) tags -- 4*3*1 = 12
• “B” items: 2*n(B)*n(C) tags -- 2*3*1 = 6
• “C” items: 2*n(C) tags – 2*1 = 2

15. Inference for Archiving Data - Continued
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• The overall number of identifiers required, nIDs required, is:
  

M
Bi
M
ij
M
Aj
requiredIDs jnjnn )(*2)(_
)]()(*)()(*)(*)([*2)(*)(*)(*)(_ DnDnCnDnCnBnDnCnBnAnrequiredIDsn 
(3)
• Thus, if M=4 (for the A, B, C, D example above):
where M = levels of containment: M=alphabetic (levels of containment, where M is for Matryoshka,
since it is a Russian doll model )

16. Inference - Use
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• This model for inference allows a wide variety of possibilities.
• If tags on individual items {A} cannot be read –
• Labeled with barcodes and inside a folder that cannot be
read due to permission issues
• The tags on the folder B, would correspond to the start
and end of the sequence of tags corresponding to the two
on container B and all of the individual tags on the A items
within.

17. Document Storage using Inference for tagging
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18. Another Inference Example – GS1
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GS1:
734236023450
GS1:
734236023450
GS1:
734236023450
GS1:
734236023450
DS DS DS
Inferenced or Identical Inferenced or Identical Inferenced or Identical
Pallet Case Carton
Individual
Unit
Tags from GS1: standards for supply chain workflows. Image based on single GS1 tag that is
readable via inference even at the pallet level.

19. Relative & Absolute inference
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• Want to ensure that multiple items infer to the same container in a
statistically meaningful way
• Relatively - No connection to an on-line database
• Relative inference is established when there is a mechanism for associating
a container with an item and vice versa
• Absolute inference requires approval of two or more binary strings
simultaneously
• With or without the overlying relative inference model
• Easiest absolute inference:
• Association of two binary strings in database
• Another form:
• When two strings related to each other through algorithm or process
• E.g., C=digital signature(I)
• C=scrambling_algorithm(I)

20. Conclusions
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• Progressive barcodes ideal mechanisms for applications & services that:
• Take advantage of two channels of information encoded into a single
mark that does not change size over time
• Suitable for document workflow tracking and archiving solutions where data
for one channel does not change
• serial numbers, document IDs, MARC and other archiving information
• Channel represented as color tiles can change over time:
• tracking, security, and other purposes
• Using inference, possible to contain objects inside other objects and verify
their authenticity without having to open the container
• Other archiving applications – I am interested in ideas!

21. Thank You for Your Kind Attention
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Welcome to the “Marker Revolution”