We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing the indices of the selected matrices, even when a certain number of workers collude with each other.
A majority of coded matrix-matrix computation literature has broadly focused in two directions: matrix partitioning for computing a single computation task and batch processing of multiple distinct computation tasks. While these works provide codes with good straggler resilience and fast decoding for their problem spaces, these codes would not be able to take advantage of the natural redundancy of re-using matrices across batch jobs.
Although blockchain, the supporting technology of various cryptocurrencies, has offered a potentially effective framework for numerous decentralized trust management systems, its performance is still sub-optimal in real-world networks. With limited bandwidth, the communication complexity for nodes to process a block scales with the growing network size and hence becomes the limiting factor of blockchain’s performance. In this paper, we suggest a re-design of existing blockchain systems, which addresses the issue of the communication burden.
We consider over-the-air convex optimization on a $d$ dimensional space where coded gradients are sent over an additive Gaussian noise channel with variance $\sigma ^{2}$ . The codewords satisfy an average power constraint $P$ , resulting in the signal-to-noise ratio (SNR) of $P/\sigma ^{2}$ . We derive bounds for the convergence rates for over-the-air optimization. Our first result is a lower bound for the convergence rate showing that any code must slowdown the convergence rate by a factor of roughly $\sqrt {d/\log (1+ \mathtt {SNR})}$ .
Information theory, starting with Shannon’s groundbreaking work, has fundamentally shaped the way communication systems are designed and operated. Information theoretic principles form the underpinnings of modern communication networks. This issue explores how new advances in information theory can impact future communication systems.
In this paper, we characterize resolution limits for imaging in electromagnetic spectrum where multipath is commonly encountered, e.g., spectrum often used for wireless communication. We analyze a passive system configuration with an aperture of fixed spatial extent sampling fields backscattered from an imaging scene consisting of both line-of-sight (LOS) and non-line-of-sight (NLOS) paths. We characterize the resolution limits using the degrees of freedom (DoF) metric.