Coding for the degraded broadcast channel with random parameters, with causal and noncausal side information - Steinberg, Y. (IEEE transactions on information theory, 2005)
In this work, coding for the degraded broadcast channel controlled by random parameters is studied. Two main paradigms are considered: where side information on the random parameters is provided to the transmitter in a noncausal manner (termed here noncausal coding), and where side information is provided in a causal manner (termed causal coding). Inner and outer bounds are derived on the capacity region with noncausal coding. For the special case where the nondegraded user is informed about the channel parameters, it is shown that the inner bound is tight, thus deriving the capacity region for that case. For causal coding, a single-letter characterization of the capacity region is derived. This characterization is expressed via auxiliary random variables (RVs), and can also be interpreted by means of Shannon strategies, as the formula for the capacity of the single-user channel with causal coding derived by Shannon. The capacity region of a class of binary broadcast channels with causal coding is computed, as an example. Applications to watermarking are suggested. In particular, the results on noncausal coding can be used to derive the capacity region of a watermarking system where the channel (attacker) is fixed, and the watermark is subject to several stages of attack, or a watermarking system where the encoder is required to encode watermarks for both private and public users