The index coding problem is studied from an interference alignment perspective providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between the capacity of multiple unicast index coding (where each message is desired by exactly one receiver), and groupcast index coding (where a message can be desired by multiple receivers), which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with groupcast settings, where this question has previously been answered. Necessary and sufficient conditions for the achievability of rate half per message in the index coding problem are shown to be a natural consequence of interference alignment constraints, and generalizations to feasibility of rate 1/(L + 1) per message when each destination desires at least L messages, are similarly obtained. Finally, capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks. The solutions are based on vector linear coding.

The high repair bandwidth cost of (n,k) maximum distance separable (MDS) erasure codes has motivated a new class of codes that can reduce repair bandwidth over that of conventional MDS codes. In this paper, we address (n,k,d) exact repair MDS codes, which allow for any single failed node to be repaired exactly with access to any arbitrary set ofdsurvivor nodes. We show the existence of exact repair MDS codes that achieve minimum repair bandwidth (matching the cut-set lower bound) for arbitrary admissible (n,k,d), i.e.,k≤d≤n-1. Moreover, we extend our results to show the optimality of our codes for multiple-node failure scenarios in which an arbitrary set ofr≤n-kfailed nodes needs to repaired. Our approach is based on asymptotic interference alignment proposed by Cadambe and Jafar. As a byproduct, we also characterize the capacity of a class of multisource nonmulticast networks.

The index coding problem is a multiple unicast wireline communication network where the network is represented by a directed graph having exactly one link with finite capacity (also known as the bottleneck link). There are K independent sources which share the ingress of this bottleneck link. Correspondingly there are K destinations which are on the receiving end of the bottleneck link, with each destination intending to decode the message of one (unique) corresponding source. Each destination can have apriori side-information of a (different) subset of the original source messages. In this paper, we study the capacity of such a network from the perspective of interference alignment, and derive information theoretically optimal schemes for a class of networks. In our first main result, we identify the set of graphs where each user can achieve half rate in the index coding problem. In a second result, we derive the capacity for a class of symmetric index coding networks.

In this paper, we explore the possibility of achieving interference alignment with delayed CSIT when the transmitters are distributed. Our main contribution is an interference alignment scheme, called retrospective interference alignment, that is specialized to settings with distributed transmitters. With this scheme we show that the interference channel with 3 users with only delayed channel state information at the transmitters can achieve 9/8 DoF, while the the 2 user X channel is able to achieve 8/7 DoF. We also consider another setting where delayed channel output feedback is available to transmitters. In this setting the 3 user interference channel and the 2 user X channel are shown to achieve 6/5 and 4/3 DoF, respectively.

In this paper, we investigate the average capacity and its scaling law of the user scheduling for the multiuser MIMO systems exploiting multiuser and antenna diversities. We show that the limiting distribution of maximum SNR is of the Gumbel-type and average capacity scaling law follows log log K form. We also consider the effect of scheduling delay on the performance of scheduling scheme. Then, we propose two limited feedback scheduling and obtain their average capacity and show that they match the simulation results very well. In the first approach, the base station (BS) always collects feedback from the user with the best channel condition. We derive the normalized feedback load as well as the threshold value that minimizes it. The second approach employs quantization for each user, so that few bits of SNR are sent to the BS. We show that even with 1-bit quantization, the proposed quantized feedback scheduling can exploit multiuser diversity at the expense of trivial decrease of average capacity.