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In this paper, we consider a K-user interference channel where interference among the users is neither too strong nor too weak, a scenario that is relatively underexplored in the literature. We propose a novel deep learning-based approach to design the encoder and decoder functions that aim to maximize the sumrate of the interference channel for discrete constellations. We first consider the MaxSINR algorithm, a state-of-the-art linear scheme for Gaussian inputs, as the baseline and then propose a modified version of the algorithm for discrete inputs. We then propose a neural network-based approach that learns a constellation mapping with the objective of maximizing the sumrate. We provide numerical results to show that the constellations learned by the neural network-based approach provide enhanced alignments, not just in beamforming directions but also in terms of the effective constellation at the receiver, thereby leading to improved sum-rate performance.

The $N$-sum box protocol specifies a class of $\mathbb{F}_d$ linear functions $f(W_1,\cdots,W_K)=V_1W_1+V_2W_2+\cdots+V_KW_K\in\mathbb{F}_d^{m\times 1}$ that can be computed at information theoretically optimal communication cost (minimum number of qudits $\Delta_1,\cdots,\Delta_K$ sent by the transmitters Alice$_1$, Alice$_2$,$\cdots$, Alice$_K$, respectively, to the receiver, Bob, per computation instance) over a noise-free quantum multiple access channel (QMAC), when the input data streams $W_k\in\mathbb{F}_d^{m_k\times 1}, k\in[K]$, originate at the distributed transmitters, who share quantum entanglement in advance but are not otherwise allowed to communicate with each other. In prior work this set of optimally computable functions is identified in terms of a strong self-orthogonality (SSO) condition on the transfer function of the $N$-sum box. In this work we consider an `inverted' scenario, where instead of a feasible $N$-sum box transfer function, we are given an arbitrary $\mathbb{F}_d$ linear function, i.e., arbitrary matrices $V_k\in\mathbb{F}_d^{m\times m_k}$ are specified, and the goal is to characterize the set of all feasible communication cost tuples $(\Delta_1,\cdots,\Delta_K)$, not just based on $N$-sum box protocols, but across all possible quantum coding schemes. As our main result, we fully solve this problem for $K=3$ transmitters ($K\geq 4$ settings remain open). Coding schemes based on the $N$-sum box protocol (along with elementary ideas such as treating qudits as classical dits, time-sharing and batch-processing) are shown to be information theoretically optimal in all cases. As an example, in the symmetric case where rk$(V_1)$=rk$(V_2)$=rk$(V_3) \triangleq r_1$, rk$([V_1, V_2])$=rk$([V_2, V_3])$=rk$([V_3, V_1])\triangleq r_2$, and rk$([V_1, V_2, V_3])\triangleq r_3$ (rk = rank), the minimum total-download cost is $\max \{1.5r_1 + 0.75(r_3 - r_2), r_3\}$.

In order to explore how blind interference alignment (BIA) schemes may take advantage of side-information in computation tasks, we study the degrees of freedom (DoF) of a $K$ user wireless network setting that arises in full-duplex wireless MapReduce applications. In this setting the receivers are assumed to have reconfigurable antennas and channel knowledge, while the transmitters have neither, i.e., the transmitters lack channel knowledge and are only equipped with conventional antennas. The central ingredient of the problem formulation is the message structure arising out of MapReduce, whereby each transmitter has a subset of messages that need to be delivered to various receivers, and each receiver has a subset of messages available to it in advance as side-information. The challenge resides in both achievability and converse arguments. Unlike conventional BIA where alignments occur only within the symbols of the same message (intra-message) the new achievable scheme also requires inter-message alignments, as well as an outer MDS (maximum distance separable) code structure. The scheme emerges from two essential ideas: 1) understanding the DoF of a $K$ user vector broadcast channel with groupcast messages, and 2) a mapping of messages from the broadcast setting to the MapReduce setting that makes use of inter-message alignment. On the converse side, whereas prior BIA converse bounds relied only on a compound channel argument, in the new setting our converse bounds also require a statistical equivalence assumption.