The Capacity Region of the L -User Gaussian Inverse Compute-and-Forward Problem

• Published in: IEEE transactions on information theory Vol. 62; no. 12; pp. 6953 - 6968
• Main Authors: Yanying Chen, Yiwei Song, Devroye, Natasha
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Channel capacity; Channel models; Communication; Computational modeling; compute-and-forward; correlated sources; Decoding; Information theory; joint source-channel coding; Linear equations; Mathematical model; multiple access channel; multiuser channels; Normal distribution; Receivers; Relays; Transmitters
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2016.2620466

We consider an L-user multiple access channel where transmitter m has access to the linear equation u m = ⊕ l=1 L f ml w l of independent messages w l ∈ F p k l with f ml ∈ F p , and the destination wishes to recover all L messages. This problem may be 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. In particular, we exploit the particular form of dependencies between the equations at the different relays to improve the reliable communication rates beyond those achievable by simply forwarding all equations to the destination independently. The presented achievable rate region for the discrete memoryless channel model is shown to be capacity for the additive white Gaussian noise channel.