Blind Interference Alignment for MapReduce: Exploiting Side-Information With Reconfigurable Antennas

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> 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 the Shuffle phase 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. We approach this problem by decomposing it into distinctive stages that help identify key ingredients of the overall solution. The novel elements that emerge from the first stage, called broadcast with groupcast messages, include an outer maximum distance separable (MDS) code structure at the transmitter, and an algorithm for iteratively determining groupcast-optimal reconfigurable antenna switching patterns at the receiver to achieve intra-message (among the symbols of the same message) alignment. The next stage, called unicast with side-information, reveals optimal inter-message (among symbols of different messages) alignment patterns to exploit side-information, and by a relabeling of messages, connects to the desired MapReduce setting.