We introduce simple tight upper and lower bounds on capacity for the peak-limited discrete-time additive Gaussian noise channel with a significant reduction in computational burden over existing methods. These bounds provide an envelope of uncertainty sufficiently tight to be employed as effective approximations

Several authors have drawn comparison between embedded signaling or watermarking and communications, especially spread-spectrum communications. We examine the similarities and differences between watermarking and traditional communications. This comparison suggests that watermarking most closely resembles communications with side information at the transmitter and or detector, a configuration originally described by Shannon (1958). This leads to several novel characteristics and insights regarding embedded signaling which are discussed in detail.

We consider uncertainty classes of noise distributions defined by a bound on the divergence with respect to a nominal noise distribution. The noise that maximizes the minimum error probability for binary-input channels is found. The effect of the reduction in uncertainty brought about by knowledge of the signal-to-noise ratio is also studied. The particular class of Gaussian nominal distributions provides an analysis tool for near-Gaussian channels. The asymptotic behavior of the least favorable noise distribution and the resulting error probability are studied in a variety of scenarios, namely: asymptotically small divergence with and without power constraint; asymptotically large divergence with and without power constraint; and asymptotically large signal-to-noise ratio.

Additive-noise channels with binary inputs and zero-threshold detection are considered. We study worst case noise under the criterion of maximum error probability with constraints on both power and divergence with respect to a given symmetric nominal noise distribution. Particular attention is focused on the cases of a) Gaussian nominal distributions and b) asymptotic increase in worst case error probability when the divergence tolerance tends to zero.