Noisy DPC and Application to a Cognitive Channel

TL;DR

This paper analyzes the capacity of a Gaussian channel with two independent noises and introduces a causal noisy dirty paper coding strategy for a cognitive interference channel, demonstrating its effectiveness in approaching capacity bounds.

Contribution

It provides new capacity formulas for channels with noisy state information and proposes a novel noisy DPC method for cognitive interference channels.

Findings

Capacity increases with noisy state knowledge but remains below perfect knowledge.

Derived explicit capacity formulas for different noisy state scenarios.

Proposed noisy DPC achieves near upper-bound rates in cognitive channels.

Abstract

In this paper, we first consider a channel that is contaminated by two independent Gaussian noises $S ~ N(0,Q)$ and $Z_0 ~ N(0,N_0)$. The capacity of this channel is computed when independent noisy versions of $S$ are known to the transmitter and/or receiver. It is shown that the channel capacity is greater then the capacity when $S$ is completely unknown, but is less then the capacity when $S$ is perfectly known at the transmitter or receiver. For example, if there is one noisy version of $S$ known at the transmitter only, the capacity is $0.5log(1+P/(Q(N_1/(Q+N_1))+N_0))$, where $P$ is the input power constraint and $N_1$ is the power of the noise corrupting $S$. We then consider a Gaussian cognitive interference channel (IC) and propose a causal noisy dirty paper coding (DPC) strategy. We compute the achievable region using this noisy DPC strategy and quantify the regions when it achieves the upper bound on the rate.