We present a set of five axioms for fairness measures in resource allocation. A family of fairness measures satisfying the axioms is constructed. Well-known notions such as α-fairness, Jain's index, and entropy are shown to be special cases. 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 the fairness measure, a new understanding of α-fair utility functions, and an interpretation of "larger α is more fair". We also construct an alternative set of four axioms to capture efficiency objectives and feasibility constraints.

Despite the ability to produce human-level speech for in-domain text, attention-based end-to-end text-to-speech (TTS) systems suffer from text alignment failures that increase in frequency for outof-domain text. We show that these failures can be addressed using simple location-relative attention mechanisms that do away with content-based query/key comparisons. We compare two families of attention mechanisms: location-relative GMM-based mechanisms and additive energy-based mechanisms. We suggest simple modifications to GMM-based attention that allow it to align quickly and consistently during training, and introduce a new location-relative attention mechanism to the additive energy-based family, called Dynamic Convolution Attention (DCA). We compare the various mechanisms in terms of alignment speed and consistency during training, naturalness, and ability to generalize to long utterances, and conclude that GMM attention and DCA can generalize to very long utterances, while preserving naturalness for shorter, in-domain utterances.

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.

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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 classic 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.arXiv:1504.06018v3 [cs.IT] 1 Sep 2015 3 Theorem 5 states the outer bound while the capacity regions for the two scenarios are formally stated as Propositions 3 and 6, respectively. 4 For any three users, such a condition must hold for at least one permutation of indices.

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Abstract-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 modelled as communication over a 2 × 2 Xchannel 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-offreedom (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 sumcapacity of the network. Using the proposed coding scheme, we numerically evaluate the ergodic rate gain over a time-divisionmultiple-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 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.Index Terms-Compound channel, interference channel (IC), local views, wireless networks.