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 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.