Question: maximum information density in the print-scan process?

Does anybody know how much information can be stored and reliably retrieved from a piece of paper, using a standard printer (inkjet or laser, 300dpi) and a scanner (1200 dpi)? Since a piece of paper can be affected by bit rot (literally) and can be damaged in various ways, some error correction (e.g. Reed Solomon) and detection (e.g. CRC) is necessary. Also, I do not want to rely on high-quality paper so I have to accept some ink diffusion and "background noise" introduced by defects in the paper.

I found some references to 2D barcodes (such as DataMatrix, PDF-417 and others) but these codes are designed to be scanned efficiently by relatively cheap and fast CCD scanners. I am not worried about the scanning time (I am using a flatbed scanner) or the processing time (I can accept some heavy image processing). Also, I would like to encode raw bits and pack as much information as possible on a sheet of paper, regardless of its size. These 2D barcodes have a fixed or maximum symbol size and it is necessary to use several of them if I want to fill a sheet of paper, wasting space in the duplicated calibration areas and guard areas.

PDF-417 has a maximum density of 106 bytes per square centimeter (686 bytes per square inch, for you retrogrades), which is quite low. It is certainly possible to do better, but I would like to know if there are any standards for doing that. I am especially interested in methods that are in the public domain, because most 2D barcodes are patented (e.g. PDF-417 is covered by US patent 5,243,655 and DataMatrix is covered by 4,939,354, 5,053,609 and 5,124,536).

If you know any good references, please post them in a diary entry (I try to check the recent diaries once a day, but I may miss some of them) or send them to me by e-mail: quinet (at) gamers (dot) org. Thanks!

Hmmm... This is a bit long for a diary entry. But I don't think that such a question deserves an article in the front page. If you think that I should I have posted this as an article, then send me an e-mail and I will re-post this question and edit it out of my diary.