<p>Embedding information into a printed image is useful in many aspects, in which reliable channel encoding/decoding systems are crucial due to the information loss and error propagation during transmission. So how to improve the transmission accuracy and control the decoding error rate under a predictable level is always crucial to the channel design.</p><p>The current dissertation aims to discuss the design and performance of a two-dimensional coding method for printed materials – Circular Coding. It is a general two-dimensional coding method that allows data recovery with only a cropped portion of the code, and without the knowledge of the carrier image. While some traditional methods add redundancy bits to extend the length of the original massage length, this method embeds the message into image rows in a repeated and shifted manner with redundancy, then uses the majority votes of the redundant bits for recovery.</p><p>We introduce the encoding and decoding system and investigate the performance of the method for noisy and distorted images. For a given required decoding rate, we model the transmission error and compute the minimum requirement for the number of bit repeats.</p><p>Also, we develop a closed form solution to find the the corresponding cropped-window size that will be used for the encoding and decoding system design.</p><p>Finally, we develop a closed-form formula to predict its decoding success rate in a noisy channel under various transmission noise levels, using probabilistic modeling. The theoretical result is validated with simulations. This result enables the optimal parameter selection in the encoder and decoder system design, and decoding rate prediction with different levels of transmission error.</p><p>We also briefly discuss two other projects: development of print quality troubleshooting tools and text line detection in scanned pages.</p>