Linear superposition coding for the Gaussian MAC with quantized feedback

We propose a linear transceiver scheme for the symmetric two-user multiple access channel with additive white 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 of each user between an Ozarow-like code (designed for perfect rate-limited feedback) and a conventional code that ignores the feedback. 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.