TDMA is Optimal for All-unicast DoF Region of TIM if and only if Topology is Chordal Bipartite

The main result of this work is that an orthogonal access scheme such as TDMA achieves the all-unicast degrees of freedom (DoF) region of the topological interference management (TIM) problem if and only if the network topology graph is chordal bipartite, i.e., every cycle that can contain a chord, does contain a chord. The all-unicast DoF region includes the DoF region for any arbitrary choice of a unicast message set, so e.g., the results of Maleki and Jafar on the optimality of orthogonal access for the sum-DoF of one-dimensional convex networks are recovered as a special case. The result is also established for the corresponding topological representation of the index coding problem

Topological Interference Management: Trade-off Between DoF and SIR for Cellular Systems

International audienceTopological interference management (TIM) allows studying the degrees of freedom (DoF) of partially connected linear interference communication networks, where the channel state information at the transmitters (CSIT) is restricted to the topology of the network, i.e., a knowledge of which interference links are weak and which are strong. In this paper, we consider TIM for an infinite downlink cellular network in the one-dimensional (1D) linear and the two-dimensional (2D) hexagonal models. We consider uniformly distributed users in each cellular cell, effectively creating a continuous distribution of users, aiming to study user classes based on different interference profiles rather than on actual individual users' positions. We also consider the construction of the TIM network topology by analyzing different interference thresholds. Unlike previous works, we use TIM at the user class level to find the system's DoF independent of the actual user position. Finally, after proposing a fractional coloring scheme that can achieve the optimal DoF solution, a trade-off between DoF and SIR is given

On the Impact of Normalized Interference Threshold for Topological Interference Management

International audienceThis paper presents a new formulation to build an interference topology for the multiuser unicast Topological Interference Management (TIM) based wireless network problem. Based on our interference topology formulation, we are able to evaluate the achievable rate's theoretical limit, in the asymptotic signal to noise ratio (SNR) regime, for the underlying wireless network and not just for its topological interference representation. This new formulation allows us to cope with the finite SNR regime and not just with the asymptotic SNR regime with the Degrees of Freedom (DoF) analysis. A new SNR independent interference threshold parameter is proposed and we evaluate the achievable symmetric rates of the wireless network in both the finite SNR regime and the asymptotic SNR regime. Finally, we present outer bound solutions on the new normalized interference threshold parameter for interference topologies with half-DoF-feasibility, considering both an orthogonal resource allocation and Interference Alignment (IA). These bounds specify if a given half-DoF-feasible interference topology can be, in terms of the achievable rate, the best topology or not. Using this result, we limit the search space in the normalized interference threshold parameter range, to find half-DoF-feasible interference topologies having the possibility to be the best topologies in terms of the achievable rate

Topological Interference Management With Transmitter Cooperation

Interference networks with no channel state information at the transmitter except for the knowledge of the connectivity graph have been recently studied under the topological interference management framework. In this paper, we consider a similar problem with topological knowledge but in a distributed broadcast channel setting, i.e., a network where transmitter cooperation is enabled. We show that the topological information can also be exploited in this case to strictly improve the degrees of freedom (DoF) as long as the network is not fully connected, which is a reasonable assumption in practice. Achievability schemes from graph theoretic and interference alignment perspectives are proposed. Together with outer bounds built upon generator sequence, the concept of compound channel settings, and the relation to index coding, we characterize the symmetric DoF for the so-called regular networks with constant number of interfering links, and identify the sufficient and/or necessary conditions for the arbitrary network topologies to achieve a certain amount of symmetric DoF

Topological Interference Management With Decoded Message Passing

The topological interference management (TIM) problem studies partially-connected interference networks with no channel state information except for the network topology (i.e., connectivity graph) at the transmitters. In this paper, we consider a similar problem in the uplink cellular networks, while message passing is enabled at the receivers (e.g., base stations), so that the decoded messages can be routed to other receivers via backhaul links to help further improve network performance. For this TIM problem with decoded message passing (TIM-MP), we model the interference pattern by conflict digraphs, connect orthogonal access to the acyclic set coloring on conflict digraphs, and show that one-to-one interference alignment boils down to orthogonal access because of message passing. With the aid of polyhedral combinatorics, we identify the structural properties of certain classes of network topologies where orthogonal access achieves the optimal degrees-of-freedom (DoF) region in the information-theoretic sense. The relation to the conventional index coding with simultaneous decoding is also investigated by formulating a generalized index coding problem with successive decoding as a result of decoded message passing. The properties of reducibility and criticality are also studied, by which we are able to prove the linear optimality of orthogonal access in terms of symmetric DoF for the networks up to four users with all possible network topologies (218 instances). Practical issues of the tradeoff between the overhead of message passing and the achievable symmetric DoF are also discussed, in the hope of facilitating efficient backhaul utilization