Linear superposition coding for the Gaussian broadcast channel with quantized feedback

We propose a linear transceiver scheme for the symmetric two-user broadcast channel with additive Gaussian noise and quantized feedback. The quantized feedback link is modeled as an information bottleneck subject to a rate constraint. We introduce a superposition scheme that splits the transmit power between an Ozarow-like linear-feedback code and a conventional code that ignores the feedback. The recently established MAC-BC duality with linear-feedback coding is key as it allows us to extend our previously proposed linear-feedback MAC scheme to the BC. We study the achievable sum rate as a function of the feedback quantization rate and we show that sum rate maximization leads to a difference of convex functions problem that we solve via the convex-concave procedure.