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Capacity and Coding for 2D ChannelsKhare, Aparna 2010 December 1900 (has links)
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.
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Protograph-Based Generalized LDPC Codes: Enumerators, Design, and ApplicationsAbu-Surra, Shadi Ali January 2009 (has links)
Among the recent advances in the area of low-density parity-check (LDPC) codes, protograph-based LDPC codes have the advantages of a simple design procedure and highly structured encoders and decoders. These advantages can also be exploited in the design of protograph-based generalized LDPC (G-LDPC) codes. In this dissertation we provide analytical tools which aid the design of protograph-based LDPC and G-LDPC codes. Specifically, we propose a method for computing the codeword-weight enumerators for finite-length protograph-based G-LDPC code ensembles, and then we consider the asymptotic case when the block-length goes to infinity. These results help the designer identify good ensembles of protograph-based G-LDPC codes in the minimum distance sense (i.e., ensembles which have minimum distances grow linearly with code length). Furthermore, good code ensembles can be characterized by good stopping set, trapping set, or pseudocodeword properties, which assist in the design of G-LDPC codes with low floors. We leverage our method for computing codeword-weight enumerators to compute stopping-set, and pseudocodeword enumerators for the finite-length and the asymptotic ensembles of protograph-based G-LDPC codes. Moreover, we introduce a method for computing trapping set enumerators for finite-length (and asymptotic) protograph-based LDPC code ensembles. Trapping set enumerators for G-LDPC codes represents a more complex problem which we do not consider here. Inspired by our method for computing trapping set enumerators for protograph-based LDPC code ensembles, we developed an algorithm for estimating the trapping set enumerators for a specific LDPC code given its parity-check matrix. We used this algorithm to enumerate trapping sets for several LDPC codes from communication standards. Finally, we study coded-modulation schemes with LDPC codes and pulse position modulation (LDPC-PPM) over the free-space optical channel. We present three different decoding schemes and compare their performances. In addition, we developed a new density evolution tool for use in the design of LDPC codes with good performances over this channel.
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