Signal Space Alignment for an Encryption Message and Successive Network Code Decoding on the MIMO K-Way Relay Channel

This paper investigates a network information flow problem for a multiple-input multiple-output (MIMO) Gaussian wireless network with K-users and a single intermediate relay having M antennas. In this network, each user intends to convey a multicast message to all other users while receiving K-1 independent messages from the other users via an intermediate relay. This network information flow is termed a MIMO Gaussian K-way relay channel. For this channel, we show that K/2 degrees of freedom is achievable if M=K-1. To demonstrate this, we come up with an encoding and decoding strategy inspired from cryptography theory. The proposed encoding and decoding strategy involves a signal space alignment for an encryption message for the multiple access phase (MAC) and zero forcing with successive network code decoding for the broadcast (BC) phase. The idea of the signal space alignment for an encryption message is that all users cooperatively choose the precoding vectors to transmit the message so that the relay can receive a proper encryption message with a special structure, network code chain structure. During the BC phase, zero forcing combined with successive network code decoding enables all users to decipher the encryption message from the relay despite the fact that they all have different self-information which they use as a key.