Precoding-Based Network Alignment For Three Unicast Sessions

We consider the problem of network coding across three unicast sessions over a directed acyclic graph, where each sender and the receiver is connected to the network via a single edge of unit capacity. We consider a network model in which the middle of the network only performs random linear network coding, and restrict our approaches to precoding-based linear schemes, where the senders use precoding matrices to encode source symbols. We adapt a precoding-based interference alignment technique, originally developed for the wireless interference channel, to construct a precoding-based linear scheme, which we refer to as as a {\em precoding-based network alignment scheme (PBNA)}. A primary difference between this setting and the wireless interference channel is that the network topology can introduce dependencies between elements of the transfer matrix, which we refer to as coupling relations, and can potentially affect the achievable rate of PBNA. We identify all possible such coupling relations, and interpret these coupling relations in terms of network topology and present polynomial-time algorithms to check the presence of these coupling relations. Finally, we show that, depending on the coupling relations present in the network, the optimal symmetric rate achieved by precoding-based linear scheme can take only three possible values, all of which can be achieved by PBNA.Comment: arXiv admin note: text overlap with arXiv:1202.340

Alignment based Network Coding for Two-Unicast-Z Networks

In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has apriori side information of the first message. We make three contributions in this paper: 1. We describe a new linear network coding algorithm for two-unicast-Z networks over directed acyclic graphs. Our approach includes the idea of interference alignment as one of its key ingredients. For graphs of a bounded degree, our algorithm has linear complexity in terms of the number of vertices, and polynomial complexity in terms of the number of edges. 2. We prove that our algorithm achieves the rate-pair (1, 1) whenever it is feasible in the network. Our proof serves as an alternative, albeit restricted to two-unicast-Z networks over directed acyclic graphs, to an earlier result of Wang et al. which studied necessary and sufficient conditions for feasibility of the rate pair (1, 1) in two-unicast networks. 3. We provide a new proof of the classical max-flow min-cut theorem for directed acyclic graphs.Comment: The paper is an extended version of our earlier paper at ITW 201

On the Capacity of the Finite Field Counterparts of Wireless Interference Networks

This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over $\mathbb{F}_{p^n}$ are analogous to n x n vector (MIMO) channels in the wireless setting, but with an important distinction -- there is additional structure due to finite field arithmetic which enforces commutativity of matrix multiplication and limits the channel diversity to n, making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity optimal solutions for their finite field counterparts. This is shown through the study of the 2-user X channel and the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over $\mathbb{F}_{p^n}$ also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between p and SNR, and n and diversity.Comment: Full version of paper accepted for presentation at ISIT 201

Robust cell-free mmWave/sub-THz access using minimal coordination and coarse synchronization

This study investigates simpler alternatives to coherent joint transmission for supporting robust connectivity against signal blockage in mmWave/sub-THz access networks. By taking an information-theoretic viewpoint, we demonstrate analytically that with a careful design, full macrodiversity gains and significant SNR gains can be achieved through canonical receivers and minimal coordination and synchronization requirements at the infrastructure side. Our proposed scheme extends non-coherent joint transmission by employing a special form of diversity to counteract artificially induced deep fades that would otherwise make this technique often compare unfavorably against standard transmitter selection schemes. Additionally, the inclusion of an Alamouti-like space-time coding layer is shown to recover a significant fraction of the optimal performance. Our conclusions are based on an insightful multi-point intermittent block fading channel model that enables rigorous ergodic and outage rate analysis, while also considering timing offsets due to imperfect delay compensation. Although simplified, our approach captures the essential features of modern mmWave/sub-THz communications, thereby providing practical design guidelines for realistic systems

Multiuser Random Beamforming in Millimetre-Waves Channels

This thesis aims to show that in mmWaves channels, schemes based on randomly-directional beamforming allow to harness both the spatial multiplexing and multi-user diversity characterizing the broadcast channel by using only limited feedback and a simple transmitter architecture. The number of necessary users with respect to the number of transmitting antennas for optimal performances is investigated as well as the fairness issue, for which the use of NOMA is shown to be advantageous w.r.t. OMA