A Fixed Precoding Approach to Achieve the Degrees of Freedom in X channel

This paper aims to provide a fixed precoding scheme to achieve the Degrees of Freedom DoF of the generalized ergodic X channel. This is achieved through using the notion of ergodic interference alignment technique. Accordingly, in the proposed method the transmitters do not require to know the full channel state information, while this assumption is the integral part of existing methods. Instead, a finite-rate feed-back channel is adequate to achieve the DoF. In other words, it is demonstrated that quantized versions of channel gains are adequate to achieve theDOF. To get an insight regarding the functionality of the proposed method, first we rely on finite field channel models, and then extend the terminology to more realistic cases, including dispersive fading channels in the presence of quantizer. Accordingly, in a Rayliegh fading environment, it is shown a feedback rate of 2log(p)+Theta(log(log(p))) can provide the DoF, where $p$ is the total transmit power.