On the Capacity of Compound State-Dependent Channels with States Known at the Transmitter

TL;DR

This paper derives a new capacity lower bound for compound state-dependent channels with transmitter-only known states, fully characterizing the capacity in degraded cases and applying results to Gaussian channels relevant in wireless communications.

Contribution

It introduces a novel lower bound on capacity for these channels and provides a complete characterization for degraded cases, including specific Gaussian channel results.

Findings

New capacity lower bound derived

Capacity characterized for degraded channels

Bounds shown to be tight in specific Gaussian cases

Abstract

This paper investigates the capacity of compound state-dependent channels with non-causal state information available at only the transmitter. A new lower bound on the capacity of this class of channels is derived. This bound is shown to be tight for the special case of compound channels with stochastic degraded components, yielding the full characterization of the capacity. Specific results are derived for the compound Gaussian Dirty-Paper (GDP) channel. This model consists of an additive white Gaussian noise (AWGN) channel corrupted by an additive Gaussian interfering signal, known at the transmitter only, where the input and the state signals are affected by fading coefficients whose realizations are unknown at the transmitter. Our bounds are shown to be tight for specific cases. Applications of these results arise in a variety of wireless scenarios as multicast channels, cognitive radio and problems with interference cancellation.