The capacity region of three user Gaussian inverse-compute-and-forward channels

• Published in: Proceedings / IEEE International Symposium on Information Theory pp. 1476 - 1480
• Main Authors: Yanying Chen, Yiwei Song, Devroye, Natasha
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.07.2013
• Subjects: Channel models; Decoding; Equations; Mathematical model; Relays; Vectors
• ISSN: 2157-8095
• DOI: 10.1109/ISIT.2013.6620472

We consider a three user multiple access channel where transmitter m has access to the linear equation u m = Σ 3 l = 1 f ml w l of independent messages w 1 ϵ F p k1 , w2 ϵ F p k2 , w3 ϵ F p k3 (and f ml ϵ F p ), and the destination wishes to recover all three messages. This problem is motivated as the last hop in a network where relay nodes employ the Compute-and-Forward strategy and decode linear equations of messages; we seek to do the reverse and extract messages from sums over a multiple access channel. An achievable rate region for the two user problem was previously derived; here we extend and strengthen this work to show capacity for the two and three user Gaussian channel models subject to invertability conditions on the matrix of coefficients describing the given linear equations of messages. The optimal transmission scheme is not to independently send the three equations u m over the MAC but rather to exploit their special correlation structure.