On " Dirty-paper Coding "

regardless of what Q is. The title of Costa’s work came by making an analogy to the problem of writing on dirty paper, where the reader cannot nominally distinguish dirt from ink. There are many scenarios where this result may be applied. In the field of information hiding (or watermarking), a message is encoded in u, which is to be embedded in the host waveform i using the signal s. Data compression, image manipulation, or malicious attacks add noise w. Theoretical bounds as well as practical watermarking schemes have been found using Costa’s result [2]. An information-embedding expert uses dirty-paper coding to choose s (as a function of u) such that the watermark u may be decoded as if the original host signal i was present, even if it is not (if there is no noise, u may be recovered perfectly). The figure on the next page illustrates how this might work. Another important application of dirty-paper coding is for a multiuser channel wherein a multiple-antenna transmitter is communicating with multiple users. Using Costa’s result the sum capacity (or highest sum of rates achievable for each user) for this system has been found [3]. To a multiuser-channel expert, dirty-paper coding means techniques that allow a transmitter to send information so that each user sees no interference from other users. In addition to these theoretical results, progress has been made on achieving the capacity promised in (2). Quantizing to a lattice has been identified as an important tool for achieving capacity [4], [5]. We focus on the technique of [4]; similar methods may be applied to both the multiuser channel and to watermarking.