Asymmetric information embedding

In the Information Embedding Problem one is given a piece of data which can be altered only conditionally, for example only at certain places. One is then asked to embed an arbitrary message into the data by only applying admissible changes to the data. These changes lead to a distortion which is to be kept low. In this short note, we introduce an ?asymmetric? version of information embedding in which the file is regarded as a string over a finite alphabet, and admissible changes on the alphabet elements are modeled by a directed graph. We introduce embedding techniques based on list-decoding algorithms for algebraic-geometric codes, and analyze their performance.