Two-User Erasure Interference Channels with Local Delayed CSIT

We study the capacity region of two-user erasure interference channels with local delayed channel state information at the transmitters. In our model, transmitters have local mismatched outdated knowledge of the channel gains. We propose a transmission strategy that only relies on the delayed knowledge of the {\it outgoing} links at each transmitter and achieves the outer-bound for the scenario in which transmitters learn the entire channel state with delay. Our result reveals the subset of the channel state information that affects the capacity region the most. We also identify cases in which local delayed knowledge of the channel state does not provide any gain over the zero knowledge assumption. To do so, we revisit a long-known intuition about interference channels that as long as the marginal distributions at the receivers are conserved, the capacity remains the same. We take this intuition and impose a certain spatial correlation among channel gains such that the marginal distributions remain unchanged. Then we provide an outer-bound on the capacity region of the channel with correlation that matches the capacity region when transmitters do not have access to channel state information.Comment: Accepted for publication in IEEE Transactions on Information Theor

When Does Spatial Correlation Add Value to Delayed Channel State Information?

Fast fading wireless networks with delayed knowledge of the channel state information have received significant attention in recent years. An exception is networks where channels are spatially correlated. This paper characterizes the capacity region of two-user erasure interference channels with delayed knowledge of the channel state information and spatially correlated channels. There are instances where spatial correlation eliminates any potential gain from delayed channel state information and instances where it enables the same performance that is possible with instantaneous knowledge of channel state. The key is an extremal entropy inequality for spatially correlated channels that separates the two types of instances. It is also shown that to achieve the capacity region, each transmitter only needs to rely on the delayed knowledge of the channels to which it is connected.Comment: To appear in ISIT 2016. arXiv admin note: text overlap with arXiv:1503.0344

Completely Stale Transmitter Channel State Information is Still Very Useful

Transmitter channel state information (CSIT) is crucial for the multiplexing gains offered by advanced interference management techniques such as multiuser MIMO and interference alignment. Such CSIT is usually obtained by feedback from the receivers, but the feedback is subject to delays. The usual approach is to use the fed back information to predict the current channel state and then apply a scheme designed assuming perfect CSIT. When the feedback delay is large compared to the channel coherence time, such a prediction approach completely fails to achieve any multiplexing gain. In this paper, we show that even in this case, the completely stale CSI is still very useful. More concretely, we show that in a MIMO broadcast channel with $K$ transmit antennas and $K$ receivers each with 1 receive antenna, $\frac{K}{1+1/2+ ...+ \frac{1}{K}} (> 1)$ degrees of freedom is achievable even when the fed back channel state is completely independent of the current channel state. Moreover, we establish that if all receivers have independent and identically distributed channels, then this is the optimal number of degrees of freedom achievable. In the optimal scheme, the transmitter uses the fed back CSI to learn the side information that the receivers receive from previous transmissions rather than to predict the current channel state. Our result can be viewed as the first example of feedback providing a degree-of-freedom gain in memoryless channels.Comment: Initially reported as Technical Report No. UCB/EECS-2010-122 at the University of California--Berkeley, Sept. 6, 2010. Presented at the Forty-Eighth Annual Allerton Conference, Sept. 2010. Accepted for IEEE Transactions on Information Theor

Erasure Broadcast Channels with Intermittent Feedback

Achievable data rates in wireless systems rely heavily on the available channel state information (CSI) throughout the network. However, feedback links, which provide this information, are scarce, unreliable, and subject to security threats. In this work, we study the impact of having intermittent feedback links on the capacity region of the canonical two-user erasure broadcast channels. In our model, at any time instant, each receiver broadcasts its CSI, and at any other node, this information either becomes available with unit delay or gets erased. For this setting, we develop a new set of outer bounds to capture the intermittent nature of the feedback links. These outer bounds depend on the probability that the CSI from both receivers are erased at the transmitter. In particular, if at any time, the CSI from at least one of the two receivers is available at the other two nodes, then the outer-bounds match the capacity with global delayed CSI. We also provide capacity-achieving transmission strategies under certain scenarios, and we establish a connection between this problem and Blind Index Coding with feedback.Comment: Submitte

Throughput Region of Spatially Correlated Interference Packet Networks

In multi-user wireless packet networks interference, typically modeled as packet collision, is the throughput bottleneck. Users become aware of the interference pattern via feedback and use this information for contention resolution and for packet retransmission. Conventional random access protocols interrupt communication to resolve contention which reduces network throughput and increases latency and power consumption. In this work we take a different approach and we develop opportunistic random access protocols rather than pursuing conventional methods. We allow wireless nodes to communicate without interruption and to observe the interference pattern. We then use this interference pattern knowledge and channel statistics to counter the negative impact of interference. We prove the optimality of our protocols using an extremal rank-ratio inequality. An important part of our contributions is the integration of spatial correlation in our assumptions and results. We identify spatial correlation regimes in which inherently outdated feedback becomes as good as idealized instantaneous feedback, and correlation regimes in which feedback does not provide any throughput gain. To better illustrate the results, and as an intermediate step, we characterize the capacity region of finite-field spatially correlated interference channels with delayed channel state information at the transmitters.Comment: Accepted for publication in IEEE Transactions on Information Theor

Fundamental Limits of Cache-Aided Wireless BC: Interplay of Coded-Caching and CSIT Feedback

Building on the recent coded-caching breakthrough by Maddah-Ali and Niesen, the work here considers the $K$-user cache-aided wireless multi-antenna (MISO) symmetric broadcast channel (BC) with random fading and imperfect feedback, and analyzes the throughput performance as a function of feedback statistics and cache size. In this setting, our work identifies the optimal cache-aided degrees-of-freedom (DoF) within a factor of 4, by identifying near-optimal schemes that exploit the new synergy between coded caching and delayed CSIT, as well as by exploiting the unexplored interplay between caching and feedback-quality. The derived limits interestingly reveal that --- the combination of imperfect quality current CSIT, delayed CSIT, and coded caching, guarantees that --- the DoF gains have an initial offset defined by the quality of current CSIT, and then that the additional gains attributed to coded caching are exponential, in the sense that any linear decrease in the required DoF performance, allows for an exponential reduction in the required cache size.Comment: 14 pages, 2 figures, submission Trans IT, V

Informational Bottlenecks in Two-Unicast Wireless Networks with Delayed CSIT

We study the impact of delayed channel state information at the transmitters (CSIT) in two-unicast wireless networks with a layered topology and arbitrary connectivity. We introduce a technique to obtain outer bounds to the degrees-of-freedom (DoF) region through the new graph-theoretic notion of bottleneck nodes. Such nodes act as informational bottlenecks only under the assumption of delayed CSIT, and imply asymmetric DoF bounds of the form $mD_1 + D_2 \leq m$. Combining this outer-bound technique with new achievability schemes, we characterize the sum DoF of a class of two-unicast wireless networks, which shows that, unlike in the case of instantaneous CSIT, the DoF of two-unicast networks with delayed CSIT can take an infinite set of values.Comment: In proceedings of the 53rd Annual Allerton Conference on Communication, Control, and Computin

The Synergistic Gains of Coded Caching and Delayed Feedback

In this paper, we consider the $K$-user cache-aided wireless MISO broadcast channel (BC) with random fading and delayed CSIT, and identify the optimal cache-aided degrees-of-freedom (DoF) performance within a factor of 4. The achieved performance is due to a scheme that combines basic coded-caching with MAT-type schemes, and which efficiently exploits the prospective-hindsight similarities between these two methods. This delivers a powerful synergy between coded caching and delayed feedback, in the sense that the total synergistic DoF-gain can be much larger than the sum of the individual gains from delayed CSIT and from coded caching. The derived performance interestingly reveals --- for the first time --- substantial DoF gains from coded caching, even when the (normalized) cache size $\gamma$ (fraction of the library stored at each receiving device) is very small. Specifically, a microscopic $\gamma \approx e^{-G}$ can come within a factor of $G$ from the interference-free optimal. For example, storing at each device only a \emph{thousandth} of what is deemed as `popular' content ($\gamma\approx 10^{-3}$), we approach the interference-free optimal within a factor of $ln(10^3) \approx 7$ (per user DoF of $1/7$), for any number of users. This result carries an additional practical ramification as it reveals how to use coded caching to essentially buffer CSI, thus partially ameliorating the burden of having to acquire real-time CSIT.Comment: 7 pages. Smaller part from a bigger journal submission arXiv:1511.0396

Feedback-Aided Coded Caching for the MISO BC with Small Caches

This work explores coded caching in the symmetric $K$-user cache-aided MISO BC with imperfect CSIT-type feedback, for the specific case where the cache size is much smaller than the library size. Building on the recently explored synergy between caching and delayed-CSIT, and building on the tradeoff between caching and CSIT quality, the work proposes new schemes that boost the impact of small caches, focusing on the case where the cumulative cache size is smaller than the library size. For this small-cache setting, based on the proposed near-optimal schemes, the work identifies the optimal cache-aided degrees-of-freedom (DoF) performance within a factor of 4.Comment: 8 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1511.0396

Capacity Results for Intermittent X-Channels with Delayed Channel State Feedback

We characterize the capacity region of noiseless X-Channels with intermittent connectivity and delayed channel state information at the transmitters. We consider the general case in which each transmitter has a common message for both receivers, and a private message for each one of them. We develop a new set of outer-bounds that quantify the interference alignment capability of each transmitter with delayed channel state feedback and when each receiver must receive a baseline entropy corresponding to the common message. We also develop a transmission strategy that achieves the outer-bounds under homogeneous channel assumption by opportunistically treating the X-Channel as a combination of a number of well-known problems such as the interference channel and the multicast channel. The capacity-achieving strategies of these sub-problems must be interleaved and carried on simultaneously in certain regimes in order to achieve the X-Channel outer-bounds. We also extend the outer-bounds to include non-homogeneous channel parameters.Comment: Submitted to IEEE Transactions on Information Theory, 201