Communication and Information Theory

Capacity of Simultaneous State-Dependent Channels with State Information at the Transmitter

In the recent years, communications over channels controlled by random parameters, namely states, have been greatly developed. Intensive research was undertaken, addressing both theoretical and practical aspects. In this talk we focus on the simultaneous (or compound) state-dependent channel with non-causal state information (SI) at the transmitter. This channel arises in scenarios where there is uncertainty on the channel statistic. The conditional PD of the channel is parameterized by parameters which remain constant during the communication and belong to an arbitrary set. Neither the sender nor the receiver is recognizant of such parameters governing the communication. These channels appear in a variety of scenarios, e.g., the common-message broadcast (or multicast) channel with non-causal SI at the transmitter, the emerging field of cognitive radios, broadcast channels with imperfect CSI, etc.

While the study of such channels is of great interest because of their applications, the problem of determining its capacity is interesting in itself. In fact, the inherent difficulty in proving the converse for this class of channels is also found in other multi-user scenarios, and it seems to be a typical difficulty in channel coding problems. Such difficulty arises in converse proofs when identifying auxiliary (single letter) variables via the conventional approach (starting from Fano's inequality). In this talk we overcome such difficulty by proving a coding theorem and its strong converse that establishes the capacity of these channels. We shall see that the techniques employed, based on image sets, may be of independent interest since thesecould be applicable as a powerful tool to prove converses for other multi-user scenarios. An application to AWGN channels corrupted by an additive Gaussian interfering known at the transmitter, which may be absent on the channel but the transmitter is unaware of this, is also considered.