The Ergodic Capacity of Phase-Fading Interference Networks

We identify the role of equal strength interference links as bottlenecks on the ergodic sum capacity of a $K$ user phase-fading interference network, i.e., an interference network where the fading process is restricted primarily to independent and uniform phase variations while the channel magnitudes are held fixed across time. It is shown that even though there are $K(K-1)$ cross-links, only about $K/2$ disjoint and equal strength interference links suffice to determine the capacity of the network regardless of the strengths of the rest of the cross channels. This scenario is called a \emph{minimal bottleneck state}. It is shown that ergodic interference alignment is capacity optimal for a network in a minimal bottleneck state. The results are applied to large networks. It is shown that large networks are close to bottleneck states with a high probability, so that ergodic interference alignment is close to optimal for large networks. Limitations of the notion of bottleneck states are also highlighted for channels where both the phase and the magnitudes vary with time. It is shown through an example that for these channels, joint coding across different bottleneck states makes it possible to circumvent the capacity bottlenecks.Comment: 19 page

Elements of Cellular Blind Interference Alignment --- Aligned Frequency Reuse, Wireless Index Coding and Interference Diversity

We explore degrees of freedom (DoF) characterizations of partially connected wireless networks, especially cellular networks, with no channel state information at the transmitters. Specifically, we introduce three fundamental elements --- aligned frequency reuse, wireless index coding and interference diversity --- through a series of examples, focusing first on infinite regular arrays, then on finite clusters with arbitrary connectivity and message sets, and finally on heterogeneous settings with asymmetric multiple antenna configurations. Aligned frequency reuse refers to the optimality of orthogonal resource allocations in many cases, but according to unconventional reuse patterns that are guided by interference alignment principles. Wireless index coding highlights both the intimate connection between the index coding problem and cellular blind interference alignment, as well as the added complexity inherent to wireless settings. Interference diversity refers to the observation that in a wireless network each receiver experiences a different set of interferers, and depending on the actions of its own set of interferers, the interference-free signal space at each receiver fluctuates differently from other receivers, creating opportunities for robust applications of blind interference alignment principles

Constraining a possible variation of G with Type Ia supernovae

Astrophysical cosmology constrains the variation of Newton's Constant in a manner complementary to laboratory experiments, such as the celebrated lunar laser ranging campaign. Supernova cosmology is an example of the former and has attained campaign status, following planning by a Dark Energy Task Force in 2005. In this paper we employ the full SNIa dataset to the end of 2013 to set a limit on G variation. In our approach we adopt the standard candle delineation of the redshift distance relation. We set an upper limit on its rate of change |G dot / G| of 0.1 parts per billion per year over 9 Gyrs. By contrast lunar laser ranging tests variation of G over the last few decades. Conversely, one may adopt the laboratory result as a prior and constrain the effect of variable G in dark energy equation of state experiments to delta w < 0.02. We also examine the parameterization G ~ 1 + z. Its short expansion age conflicts with the measured values of the expansion rate and the density in a flat Universe. In conclusion, supernova cosmology complements other experiments in limiting G variation. An important caveat is that it rests on the assumption that the same mass of 56Ni is burned to create the standard candle regardless of redshift. These two quantities, f and G, where f is the Chandrasekhar mass fraction burned, are degenerate. Constraining f variation alone requires more understanding of the SNIa mechanism.Comment: to appear in PAS

The Capacity of Private Information Retrieval

In the private information retrieval (PIR) problem a user wishes to retrieve, as efficiently as possible, one out of $K$ messages from $N$ non-communicating databases (each holds all $K$ messages) while revealing nothing about the identity of the desired message index to any individual database. The information theoretic capacity of PIR is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. For $K$ messages and $N$ databases, we show that the PIR capacity is $(1+1/N+1/N^2+\cdots+1/N^{K-1})^{-1}$. A remarkable feature of the capacity achieving scheme is that if we eliminate any subset of messages (by setting the message symbols to zero), the resulting scheme also achieves the PIR capacity for the remaining subset of messages

Optimal Use of Current and Outdated Channel State Information - Degrees of Freedom of the MISO BC with Mixed CSIT

We consider a multiple-input-single-output (MISO) broadcast channel with mixed channel state information at the transmitter (CSIT) that consists of imperfect current CSIT and perfect outdated CSIT. Recent work by Kobayashi et al. presented a scheme which exploits both imperfect current CSIT and perfect outdated CSIT and achieves higher degrees of freedom (DoF) than possible with only imperfect current CSIT or only outdated CSIT individually. In this work, we further improve the achievable DoF in this setting by incorporating additional private messages, and provide a tight information theoretic DoF outer bound, thereby identifying the DoF optimal use of mixed CSIT. The new result is stronger even in the original setting of only delayed CSIT, because it allows us to remove the restricting assumption of statistically equivalent fading for all users