Center for Pervasive Communications and Computing

Blind Interference Alignment (BIA) schemes create and exploit channel coherence patterns without the knowledge of channel realizations at transmitters, while beamforming schemes rely primarily on channel knowledge available to the transmit- ters without regard to channel coherence patterns. In order to explore the compatibility of these disparate ideas and the possibility of synergistic gains, this work studies the Degrees of Freedom (DoF) of the 2-user (𝑀1 × 𝑁1)(𝑀2 × 𝑁2) Multiple- Input Multiple-Output (MIMO) Interference Channel (IC) where Transmitter 1 is equipped with reconfigurable antennas and has no channel knowledge, while Transmitter 2 has partial channel knowledge but no reconfigurable antennas. Taking a fundamental dimensional analysis perspective, the main question is to identify which antenna configurations allow synergistic DoF gains. The main results of this work are two-fold. The first result identifies antenna configurations where both reconfigurable antennas and partial channel knowledge are individually beneficial, as those where 𝑀1 < 𝑁1 < min(𝑀2,𝑁2). The second result shows that synergistic gains exist in each of these settings, over the best known solutions that rely on either reconfigurable antennas or partial channel knowledge alone. Coding schemes that jointly exploit partial channel knowledge and reconfigurable antennas emerge as a byproduct of the analysis.

Sum-set inequalities based on Aligned-Images bounds have been recently introduced as essential elements of converse proofs for asymptotic/approximate wireless network capacity characterizations under robust assumptions, i.e., as- sumptions that limit channel knowledge at the transmitters to finite precision. While these sum-set inequalities have produced robust Generalized Degrees of Freedom (GDoF) results for various wireless networks, their scope and limitations in general are not well understood. To explore these limitations, in this work we study the robust secure GDoF of a symmetric 3-user many- to-one interference channel. We identify regimes where existing sum-set inequalities are sufficient, settling the GDoF for those settings. For the remaining regime we conjecture the form of new sum-set inequalities that may be needed, whose validity remains an open problem for future work.

The goal of coded distributed batch matrix multiplication  is to efficiently multiply  L instances of \lambda x \kappa matrices, A=(A_1, ..., A_L)$,  with L instances of \kappa x \mu matrices  B=(B_1,..., B_L), by distributing the computation across S servers, such that the response from any R servers (R is called the recovery threshold) is sufficient to compute the L matrix products, AB=(A_1B_1, A_2B_2, ..., A_LB_L).  Existing solutions either compute each $A_lB_l$ one at a time by partitioning individual matrices and coding across these partitions, or rely only on batch processing, i.e.,  coding across the batch of matrices without any matrix partitioning. The state-of-art for matrix-partitioning and batch processing approaches is represented by Entangled Polynomial Codes (EP codes), and Lagrange Coded Computing (LCC), respectively.  In order to combine the benefits of the two approaches, we propose Generalized Cross-Subspace Alignment Codes (GCSA codes) that unify, generalize and improve upon the state of art. GCSA codes bridge the two extremes by efficiently combining both matrix-partitioning and batch processing, and offer flexibility in how much of each approach is used. Both EP codes and LCC codes can be recovered as special cases of GCSA codes. Remarkably, even without matrix partitioning, GCSA codes demonstrate an advantage over LCC codes in download-constrained settings. This is due to cross-subspace alignment, characterized by a Cauchy-Vandermonde code structure that aligns interference along Vandermonde terms, while the desired matrix products remain resolvable along Cauchy terms.

A parameter regime is identified where the simple scheme of treating interference as Gaussian noise (TIN), with power control and jamming, is optimal for the secure generalized degrees of freedom (GDoF) region of Gaussian broadcast networks under the robust assumption of finite-precision channel state information at the transmitter (CSIT). The network consists of one transmitter equipped with K antennas, and K single-antenna receivers. The results are generalized to groupcast (equivalently, compound broadcast) settings where each message is desired by a disjoint group of receivers. Noting that messages are independently encoded in the GDoF-optimal scheme, the result for the broadcast channel is extended to its counterpart Gaussian interference channel under finite precision CSIT. Evidently, both secrecy constraints and finite precision CSIT limit the benefits of more sophisticated schemes, leading to optimality of simpler schemes for larger parameter regimes. Aligned Image bounds are the key to the proof of optimality for these larger parameter regimes under finite precision CSIT.