On causal and semicausal codes for joint information embedding and source coding

The problem of joint compression and information embedding under various causality restrictions on the encoder and decoder is studied in this paper. The minimax game between causal encoder-decoder pairs and causal attackers is characterized by a single-letter formula due to the fact that there is a saddle-point where both parties apply memoryless strategies. Main results are based on semicausal codes where causality is required only with respect to the covertext source. Semicausal embedding is related to communication with causal side information at the transmitter. The results are also extended to the case of attacks, and single-letter formulas are provided for the characterization of the minimax game between the communicators and the attacker.