Finite-blocklength linear superposition coding for the Gaussian MAC with quantized feedback

We propose a linear transceiver scheme for the asymmetric two-user Gaussian multiple access channel with quantized feedback in the practically important regime of finite blocklength. Our scheme is an extension of results obtained for the asymptotic (infinite blocklength) regime. The quantized feedback link is modeled via the information bottleneck method. Our block-feedback superposition coding scheme splits the transmit power between an Ozarow-like linear feedback code and a conventional code that ignores the feedback. We study the achievable sum rate for fixed error probabilities as a function of the blocklength. We use asymptotically optimal power allocation and further optimize the superposition via finding the optimal trade-off in the blocklengths that maximizes the achievable sum rate of the constituent schemes of the superposition.