The goal of a denoising algorithm is to recover a signal from its noise-corrupted observations. Perfect recovery is seldom possible and performance is measured under a given single-letter fidelity criterion. For discrete signals corrupted by a known discrete memoryless channel (DMC), the Discrete Universal DEnoiser (DUDE) was recently shown to perform this task asymptotically optimally, without knowledge of the statistical properties of the source. In the present work, we address the scenario where, in addition to the lack of knowledge of the source statistics, there is also uncertainty in the channel characteristics. We propose a family of discrete denoisers and establish their asymptotic optimality under a minimax performance criterion which we argue is appropriate for this setting. As we show elsewhere, the proposed schemes can also be implemented computationally efficiently.

We extend Shannon's result on the capacity of channels with state information to multiple user channels. More specifically, we characterize the capacity (region) of degraded broadcast channels and physically degraded relay channels where the channel state information is causally available at the transmitters. We also obtain inner and outer bounds on the capacity region for multiple access channels with causal state information at the transmitters

We consider the problem of denoising a binary image corrupted by a noisy medium which flips each component in the original image, independently, to its complementary value with some fixed but unknown probability /spl delta/<1/2. We propose a denoiser which assumes no knowledge of statistical properties of the image, yet asymptotically attains the performance of the scheme that knows the noisy image statistics and operates optimally in a minimax sense. The proposed scheme is implementable, with complexity linear in the image size. Preliminary experimental results are presented which indicate that the scheme has the potential to do well on real data.

Writing on dirty paper, a variation of the standard additive white Gaussian noise (AWGN) channel with the channel output is considered. The Gaussian noise noncausally known at the transmitter does not affect the capacity of the AWGN channel. This is known as WDP property. The WDP property for three Gaussian multiple user channels with known capacity region is established. The achievable rate regions of corresponding discrete channels is proved. Although those regions may be suboptimal in general, they turn out to be optimal for these Gaussian channels. Alternative proofs can be obtained by successive uses of Costa's WDP coding scheme, from which the WDP property can be established for more general noise and state distributions.

The assumption of a known channel was inherent in the structure of the denoising under channel uncertainty (DUDE). There are many scenarios where the DUDE is effective for denoising. A denoising scheme is sought, which will accommodate uncertainty in the statistical characteristics of the noisy medium. Unfortunately, it can be shown that in this setting the task of attaining the performance of the optimum nonuniversal distribution-dependent scheme is impossible, even for a "genie-aided" scheme with complete knowledge of the noisy signal statistics. In this paper, the noise-corrupted signal with the clean components and their values in the finite alphabet are assumed. The corruption mechanism is a discrete memoryless channel (DMC) with an associated invertible channel matrix. It lies in a given uncertainty set.