Embedding information into a printed image is useful in many aspects, in which reliable channel encoding/decoding systems are crucial, since there is information loss and error propagation during transmission. Circular coding is a general twodimensional channel 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 message into image rows in a repeated and shifted manner
with redundancy, then uses the majority votes of the redundancy bits for recovery. In this paper, we developed 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.