Capacity and Coding for 2D Channels



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Consider a piece of information printed on paper and scanned in the form of an image. The printer, scanner, and the paper naturally form a communication channel, where the printer is equivalent to the sender, scanner is equivalent to the receiver, and the paper is the medium of communication. The channel created in this way is quite complicated and it maps 2D input patterns to 2D output patterns. Inter-symbol interference is introduced in the channel as a result of printing and scanning. During printing, ink from the neighboring pixels can spread out. The scanning process can introduce interference in the data obtained because of the finite size of each pixel and the fact that the scanner doesn't have infinite resolution. Other degradations in the process can be modeled as noise in the system. The scanner may also introduce some spherical aberration due to the lensing effect. Finally, when the image is scanned, it might not be aligned exactly below the scanner, which may lead to rotation and translation of the image. In this work, we present a coding scheme for the channel, and possible solutions for a few of the distortions stated above. Our solution consists of the structure, encoding and decoding scheme for the code, a scheme to undo the rotational distortion, and an equalization method. The motivation behind this is the question: What is the information capacity of paper. The purpose is to find out how much data can be printed out and retrieved successfully. Of course, this question has potential practical impact on the design of 2D bar codes, which is why encodability is a desired feature. There are also a number of other useful applications however. We could successfully decode 41.435 kB of data printed on a paper of size 6.7 X 6.7 inches using a Xerox Phasor 550 printer and a Canon CanoScan LiDE200 scanner. As described in the last chapter, the capacity of the paper using this channel is clearly greater than 0.9230 kB per square inch. The main contribution of the thesis lies in constructing the entire system and testing its performance. Since the focus is on encodable and practically implementable schemes, the proposed encoding method is compared with another well known and easily encodable code, namely the repeat accumulate code.