Capacity Bounds for Dirty Paper with Exponential Dirt

TL;DR

This paper derives capacity bounds for an exponential noise channel with known interference, providing exact capacity at high SNRs by using Gelfand-Pinsker coding techniques.

Contribution

It introduces the first capacity bounds for the exponential interference channel with non-causal state information at the transmitter, including an exact capacity characterization at high SNRs.

Findings

Outer and inner bounds on channel capacity derived.

Inner and outer bounds coincide at high SNRs, establishing capacity.

Provides a theoretical framework for exponential channels with interference.

Abstract

The additive exponential noise channel with additive exponential interference (AENC-AEI) known non-causally at the transmitter is studied. This channel can be considered as an exponential version of the discrete memoryless channel with state known non-causally at the encoder considered by Gelfand and Pinsker. We make use of Gelfand-Pinsker classic capacity Theorem to derive inner and outer bounds on the capacity of this channel under a non-negative input constraint as well as a constraint on the mean value of the input. First we obtain an outer bound for AENC-AEI. Then by using the input distribution achieving the outer bound, we derive an inner bound which this inner bound coincides with the obtained outer bound at high signal to noise ratios (SNRs) and therefore, gives the capacity of the AENC-AEI at high SNRs.