Efficient Coding for Computation Over Gaussian Multiple-Access Channel with Noiseless/Noisy Feedback

Reliably reconstructing a function of independent Gaussian sources over a white Gaussian multiple-access channel (GMAC) is reconsidered by exploring channel feedback. First, an efficient linear feedback scheme is proposed to compute arbitrary linear functions of sources over GMAC in the presence of noiseless feedback, which is based on a variation of the well-known Schalkwijk-Kailath type scheme. Next, we extend our proposed scheme to the noisy feedback case (the feedback channel is a white Gaussian channel) by introducing modulo lattice function and dither signal into the original scheme. Finally, the results of this paper are further explained by numerical examples, and it is shown that our proposed schemes outperform the existing ones in some cases.