We study the degrees of freedom (DoFs) of the multiple-input multiple-output X-channel (MIMO XC) with delayed channel state information at the transmitters (delayed CSITs), assuming linear coding strategies at the transmitters. We present two results: 1) the linear sum DoF for MIMO XC with general antenna configurations and 2) the linear DoF region for MIMO XC with symmetric antennas. The converse for each result is based on developing a novel rank-ratio inequality that characterizes the maximum ratio between the dimensions of received linear subspaces at the two multiple-antenna receivers. The achievability of the linear sum DoF is based on a three-phase strategy, in which during the first two phases only the transmitter with fewer antennas exploits delayed CSIT in order to minimize the dimension of its signal at the unintended receiver. During the third phase, both transmitters use delayed CSIT to send linear combinations of past transmissions, such that each receiver receives a superposition of desired message data and known interference, thus simultaneously serving both receivers. We also derive other linear DoF outer bounds for the MIMO XC that, in addition to the outer bounds from the sum DoF converse and the proposed transmission strategy, allow us to characterize the linear DoF region for symmetric antenna configurations.

We introduce the blind index coding (BIC) problem, in which a single sender communicates distinct messages to multiple users over a shared channel. Each user has partial knowledge of each message as side information. However, unlike classical index coding, in BIC, the sender is uncertain of what side information is available to each user. In particular, the sender only knows the amount of bits in each user's side information but not its content. This problem can arise naturally in caching and wireless networks. In order to blindly exploit side information in the BIC problem, we develop a hybrid coding scheme that XORs uncoded bits of a subset of messages with random combinations of bits from other messages. This scheme allows us to strike the right balance between maximizing the transmission rate to each user and minimizing the interference leakage to others. We also develop a general outer bound, which relies on a strong data processing inequality to effectively capture the senders uncertainty about the users' side information. Additionally, we consider the case where communication takes place over a shared wireless medium, modeled by an erasure broadcast channel, and show that surprisingly, combining repetition coding with hybrid coding improves the achievable rate region and outperforms alternative strategies of coping with channel erasure and while blindly exploiting side information.

In this paper, we study the communication problem from rovers on Mars' surface to Mars-orbiting satellites. We first justify that, to a good extent, the rover-to-orbiter communication problem can be modeled as communication over a 2 × 2 X-channel with the network topology varying over time. For such a fading X-channel where transmitters are only aware of the time-varying topology but not the time-varying channel state (i.e., no CSIT), we propose coding strategies that code across topologies, and develop upper bounds on the sum degrees-of-freedom (DoF) that is shown to be tight under certain pattern of the topology variation. Furthermore, we demonstrate that the proposed scheme approximately achieves the ergodic sum-capacity of the network. Using the proposed coding scheme, we numerically evaluate the ergodic rate gain over a time-division-multiple-access (TDMA) scheme for Rayleigh and Rice fading channels. We also numerically demonstrate that with practical orbital parameters, a 9.6% DoF gain, as well as more than 11.6% throughput gain can be achieved for a rover-to-orbiter communication network.

We introduce an index coding problem over wireless channels where a transmitter broadcasts to multiple receivers through an erasure channel, and receivers have access to some side-information unknown to the transmitter. Such scenarios can arise naturally, for example, in caching networks where users locally store popular files as side-information or in relay networks where users opportunistically overhear transmissions from multiple relays. For this problem, we present a coding scheme based on repetition coding combined with random linear coding, that allows us to send a message to one receiver while blindly exploiting side-information to control interference at the other. Within this class of coding schemes, we identify a tension between number of repetitions and random linear coding, characterize the achievable rate region, and compare the performance of our scheme against that of conventional methods.

We introduce the “blind index coding” (BIC) problem, which generalizes the classic index coding problem by considering a sender that has some uncertainty about the side information that is available at each receiver. This problem naturally arises in wireless networks in which users obtain their side information through wireless channels with errors that may be unknown to the sender. For the proposed BIC problem, we develop a new general outer bound by first proving it for the 3-user case and then generalizing its construction to K users. The proof of the outer bound relies on developing a key lemma that uses a strong data processing inequality to account for the sender's uncertainty. We also propose a hybrid coding scheme that XORs random combinations of bits from a subset of messages with uncoded bits of other messages in order to blindly exploit side information, and illustrate its gain.

In this paper, we study the problem of communication from rovers on Mars' surface to Mars-orbiting satellites (orbiters). We first justify that, to a good extent, the problem can be modelled as communication over a 2×2 Gaussian Xchannel with varying topologies. We then study the capacity of such a channel under the assumption that no channel state information is provided to the transmitters (i.e., no CSIT) other than the network topology. By proposing a strategy that takes advantage of coding across topologies and developing novel upper bounds, we characterize the sum degree-of-freedom (DoF) and the ergodic sum capacity to within a constant gap for the 2×2 X-channel with varying topologies. In addition, we demonstrate the performance gain of the proposed scheme over the baseline time-division-multiple-access (TDMA) scheme currently in use.

We establish the sum degrees of freedom of the multiple-input multiple-output X-channel with delayed Channel State Information at the transmitters (CSIT), assuming linear coding strategies at the transmitters. The converse is based on developing a novel rank-ratio inequality that upper bounds the ratio between the dimensions of received linear subspaces at the two receivers. The achievability is based on a three-phase strategy that optimally exploits delayed CSIT in each phase.

We consider the problem of broadcast over wireless erasure networks. To understand the challenges and opportunities of these setups, we study a two-hop erasure broadcast channel consisting of a single source, two relays, and two destinations desiring independent messages. In our network, no transmitter has channel state knowledge of erasures on outgoing links (i.e., no CSIT): The source has no knowledge of any channel state, each relay only has knowledge of the channel states of its incoming link, and destinations are provided with full channel knowledge. We propose a scheme, referred to as Align-and-Forward, that exploits the (unknown) common subspace of received signals at the relays, which results from the source-to-relay broadcast, in order to minimize the dimension of the interference subspace at each destination. We show that Align-and-Forward outperforms available alternative schemes in terms of sum-rate. We also present new outer-bounds and demonstrate the optimality of Align-and-Forward in certain regimes.

Dirty paper codes are a powerful tool for combating known interference. However, there is a significant difference between knowing the transmitted interference sequence and knowing the received interference sequence, especially when the channel modifying the interference is uncertain. We present an upper bound on the capacity of a compound vector dirty paper channel where although an additive Gaussian sequence is known to the transmitter, the channel matrix between the interferer and receiver is uncertain but known to lie within a bounded set. Our bound is tighter than previous bounds in the low-SIR regime for the scalar version of the compound dirty paper channel and employs a construction that focuses on the relationship between the dimension of the message-bearing signal and the dimension of the additive state sequence. Additionally, a bound on the high-SNR behavior of the system is established.

We study the limits of reliable communication in two-user interference channels where each of the two transmitters knows a different subset of the four channel gains characterizing the network state. In order to systematically analyze this problem, we introduce two concepts. First, we define a local view model for network state information at each transmitter, wherein each transmitter knows only a subset of the four channel gains. This subset may be mismatched from that of the other transmitter, limiting the ability of the two transmitters to coordinate transmission decisions. Second, we define a notion of maximal rate regions achievable by transmission policies that dominate time-division multiplexing (TDM). Specifically, these “TDM-dominating capacity regions” characterize rates achievable when transmission schemes must, for every possible realization of network state, achieve rates at least as good as what can be achieved through TDM. We consider a set of seven symmetric local views based on an assumption that each transmitter uses the same mechanism to gather its local view. For five out of the seven local views, we show that TDM is sufficient to achieve the full TDM-dominating capacity region for the linear deterministic interference channel. For these five local views, our result implies that no single policy can achieve a rate point outside the TDM region without inducing sub-TDM performance in another network state. The common traits shared by the two remaining local views (those with better performance than TDM) are: first, each transmitter knows its outgoing interference channel gain, and second, there exists at least one channel gain known to both transmitters. For these two local views, transmitters can use their knowledge to achieve opportunistic rate gains beyond TDM. Using the relationship between the linear deterministic channel and the Gaussian channel, we extend our conclusions to bounded gap characterizations of the TDM-dominating capacity region for the Gaussian interference channel with local views.

In this work, we report the first study of an important realization of directional communication, beamforming, on mobile devices. We first demonstrate that beamforming is already feasible on mobile devices in terms of form factor, device mobility and power efficiency. Surprisingly, we show that by making an increasingly profitable tradeoff between transmit and circuit power, beamforming with state-of-the-art integrated CMOS implementations can be more power-efficient than its single antenna counterpart. We then investigate the optimal way of using beamforming in terms of device power efficiency, by allowing a dynamic number of active antennas. We propose a simple yet effective solution, BeamAdapt, which allows each mobile client in a network to individually identify the optimal number of active antennas with guaranteed convergence and close-to-optimal performance. We finally report a WARP-based prototype of BeamAdapt and experimentally demonstrate its effectiveness in realistic environments, and then complement the prototype-based experiments with Qualnet-based simulation of a large-scale network. Our results show that BeamAdapt with four antennas can reduce the power consumption of mobile clients by more than half compared to a single antenna, while maintaining a required network throughput.

We present five axioms for fairness measures in resource allocation. A family of fairness measures satisfying the axioms is constructed. Special cases of this family include ¿-fairness, Jain's index, and entropy. Properties of fairness measures satisfying the axioms are proven, including Schur-concavity. Among the engineering implications is a generalized Jain's index that tunes the resolution of fairness measure, a new understanding of ¿-fair utility functions, and an interpretation of "larger ¿ is more fair". We also construct an alternative set of axioms to capture system efficiency and feasibility constraints.

In this paper, we examine how the precision of network topology knowledge impacts the achievable degree of max-min fairness. We focus on time-division multiple access (TDMA) networks, and employ a model based on physical-layer events that sufficiently describes the topology effects with respect to TDMA. Using Jain's fairness index, our key contribution is a characterization of the fairness loss resulting from allocation of resources (in our case time-divisions) based on imprecise knowledge of topology. We find loss is more pronounced when a single link has low signal-to-noise ratio (SNR); i.e. links which have poor throughput also make the allocation more unfair. Conversely, our analysis suggests that if the relative error in estimating link qualities is identical for all links in the network, no one link dominates the fairness loss.