Characterization of degrees of freedom versus receivers backhaul load in K-user interference channel

We consider a K-user Interference Channel where each transmitter is interested in conveying a message to its corresponding receiver. In addition, we assume a fully connected noiseless backhaul network through which receivers can collaborate and help each other recover their desired messages. In this paper, we fully characterize the trade-off between the rate in wireless link (per user) in terms of degrees of freedom (DoF) versus backhaul load (per user) for large values of K. In particular, we characterize the optimal trade-off for all values of K, where K is an even number. For odd values of K, we characterize the trade-off within a gap of 2(k - 1)/k(k + 1), which goes to zero as K increases. For achievability we use time-sharing between two corner points: (i) using interference alignment for the case where backhaul load is zero, and (ii) collecting a quantized version of all the received signals at one of the receivers to jointly decode the messages, for the case where DoF of one per user is desired. For the converse, we develop a new outer-bound based on the results from two-user multiple antenna interference channel with limited backhaul cooperation. Recently, it was shown that for the case of three-user interference channel, the optimal trade-off is achieved by some sort of alignment in the backhaul messaging, known as Cooperation Alignment. Our result shows that unlike the gain of interference alignment, the gain of cooperation alignment does not scale with the number of users K.