Degrees-of-Freedom of the MIMO Three-Way Channel with Node-Intermittency

The characterization of fundamental performance bounds of many-to-many communication systems in which participating nodes are active in an intermittent way is one of the major challenges in communication theory. In order to address this issue, we introduce the multiple-input multiple-output (MIMO) three-way channel (3WC) with an intermittent node and study its degrees-of-freedom (DoF) region and sum-DoF. We devise a non-adaptive encoding scheme based on zero-forcing, interference alignment and erasure coding, and show its DoF region (and thus sum-DoF) optimality for non-intermittent 3WCs and its sum-DoF optimality for (node-)intermittent 3WCs. However, we show by example that in general some DoF tuples in the intermittent 3WC can only be achieved by adaptive schemes, such as decode-forward relaying. This shows that non-adaptive encoding is sufficient for the non-intermittent 3WC and for the sum-DoF of intermittent 3WCs, but adaptive encoding is necessary for the DoF region of intermittent 3WCs. Our work contributes to a better understanding of the fundamental limits of multi-way communication systems with intermittency and the impact of adaptation therein

Quantum Achievability Proof via Collision Relative Entropy

In this paper, we provide a simple framework for deriving one-shot achievable bounds for some problems in quantum information theory. Our framework is based on the joint convexity of the exponential of the collision relative entropy, and is a (partial) quantum generalization of the technique of Yassaee et al. (2013) from classical information theory. Based on this framework, we derive one-shot achievable bounds for the problems of communication over classical-quantum channels, quantum hypothesis testing, and classical data compression with quantum side information. We argue that our one-shot achievable bounds are strong enough to give the asymptotic achievable rates of these problems even up to the second order.Comment: 12 page

Uplink CoMP under a Constrained Backhaul and Imperfect Channel Knowledge

Coordinated Multi-Point (CoMP) is known to be a key technology for next generation mobile communications systems, as it allows to overcome the burden of inter-cell interference. Especially in the uplink, it is likely that interference exploitation schemes will be used in the near future, as they can be used with legacy terminals and require no or little changes in standardization. Major drawbacks, however, are the extent of additional backhaul infrastructure needed, and the sensitivity to imperfect channel knowledge. This paper jointly addresses both issues in a new framework incorporating a multitude of proposed theoretical uplink CoMP concepts, which are then put into perspective with practical CoMP algorithms. This comprehensive analysis provides new insight into the potential usage of uplink CoMP in next generation wireless communications systems.Comment: Submitted to IEEE Transactions on Wireless Communications in February 201

Sketching and Neural Networks

High-dimensional sparse data present computational and statistical challenges for supervised learning. We propose compact linear sketches for reducing the dimensionality of the input, followed by a single layer neural network. We show that any sparse polynomial function can be computed, on nearly all sparse binary vectors, by a single layer neural network that takes a compact sketch of the vector as input. Consequently, when a set of sparse binary vectors is approximately separable using a sparse polynomial, there exists a single-layer neural network that takes a short sketch as input and correctly classifies nearly all the points. Previous work has proposed using sketches to reduce dimensionality while preserving the hypothesis class. However, the sketch size has an exponential dependence on the degree in the case of polynomial classifiers. In stark contrast, our approach of using improper learning, using a larger hypothesis class allows the sketch size to have a logarithmic dependence on the degree. Even in the linear case, our approach allows us to improve on the pesky $O({1}/{{\gamma}^2})$ dependence of random projections, on the margin $\gamma$. We empirically show that our approach leads to more compact neural networks than related methods such as feature hashing at equal or better performance

Performance Limits of a Cloud Radio

Cooperation in a cellular network is seen as a key technique in managing other cell interference to observe a gain in achievable rate. In this paper, we present the achievable rate regions for a cloud radio network using a sub-optimal zero forcing equalizer with dirty paper precoding. We show that when complete channel state information is available at the cloud, rates close to those achievable with total interference cancellation can be achieved. With mean capacity gains, of up to 2 fold over the conventional cellular network in both uplink and downlink, this precoding scheme shows great promise for implementation in a cloud radio network. To simplify the analysis, we use a stochastic geometric framework based of Poisson point processes instead of the traditional grid based cellular network model. We also study the impact of limiting the channel state information and geographical clustering to limit the cloud size on the achievable rate. We have observed that using this zero forcing-dirty paper coding technique, the adverse effect of inter-cluster interference can be minimized thereby transforming an interference limited network into a noise limited network as experienced by an average user in the network for low operating signal-to-noise-ratios. However, for higher signal-to-noise-ratios, both the average achievable rate and cell-edge achievable rate saturate as observed in literature. As the implementation of dirty paper coding is practically not feasible, we present a practical design of a cloud radio network using cloud a minimum mean square equalizer for processing the uplink streams and use Tomlinson-Harashima precoder as a sub-optimal substitute for a dirty paper precoder in downlink

Convolutional Codes in Rank Metric with Application to Random Network Coding

Random network coding recently attracts attention as a technique to disseminate information in a network. This paper considers a non-coherent multi-shot network, where the unknown and time-variant network is used several times. In order to create dependencies between the different shots, particular convolutional codes in rank metric are used. These codes are so-called (partial) unit memory ((P)UM) codes, i.e., convolutional codes with memory one. First, distance measures for convolutional codes in rank metric are shown and two constructions of (P)UM codes in rank metric based on the generator matrices of maximum rank distance codes are presented. Second, an efficient error-erasure decoding algorithm for these codes is presented. Its guaranteed decoding radius is derived and its complexity is bounded. Finally, it is shown how to apply these codes for error correction in random linear and affine network coding.Comment: presented in part at Netcod 2012, submitted to IEEE Transactions on Information Theor

What is needed to exploit knowledge of primary transmissions?

Recently, Tarokh and others have raised the possibility that a cognitive radio might know the interference signal being transmitted by a strong primary user in a non-causal way, and use this knowledge to increase its data rates. However, there is a subtle difference between knowing the signal transmitted by the primary and the actual interference at our receiver since there is a wireless channel between these two points. We show that even an unknown phase results in a substantial decrease in the data rates that can be achieved, and thus there is a need to feedback interference channel estimates to the cognitive transmitter. We then consider the case of fading channels. We derive an upper bound on the rate for given outage error probability for faded dirt. We give a scheme that uses appropriate "training" to obtain such estimates and quantify this scheme's required overhead as a function of the relevant coherence time and interference power.Comment: Combination of two papers submitted to ISIT'07 and DySPAN '0

On The Performance of Random Block Codes over Finite-State Fading Channels

As the mobile application landscape expands, wireless networks are tasked with supporting various connection profiles, including real-time communications and delay-sensitive traffic. Among many ensuing engineering challenges is the need to better understand the fundamental limits of forward error correction in non-asymptotic regimes. This article seeks to characterize the performance of block codes over finite-state channels with memory. In particular, classical results from information theory are revisited in the context of channels with rate transitions, and bounds on the probabilities of decoding failure are derived for random codes. This study offers new insights about the potential impact of channel correlation over time on overall performance

Relay Channel with Orthogonal Components and Structured Interference Known at the Source

A relay channel with orthogonal components that is affected by an interference signal that is noncausally available only at the source is studied. The interference signal has structure in that it is produced by another transmitter communicating with its own destination. Moreover, the interferer is not willing to adjust its communication strategy to minimize the interference. Knowledge of the interferer's signal may be acquired by the source, for instance, by exploiting HARQ retransmissions on the interferer's link. The source can then utilize the relay not only for communicating its own message, but also for cooperative interference mitigation at the destination by informing the relay about the interference signal. Proposed transmission strategies are based on partial decode-and-forward (PDF) relaying and leverage the interference structure. Achievable schemes are derived for discrete memoryless models, Gaussian and Ricean fading channels. Furthermore, optimal strategies are identified in some special cases. Finally, numerical results bring insight into the advantages of utilizing the interference structure at the source, relay or destination.Comment: Submitted to the IEEE Transactions on Communications, 28 pages, 11 figure

Learning Immune-Defectives Graph through Group Tests

This paper deals with an abstraction of a unified problem of drug discovery and pathogen identification. Pathogen identification involves identification of disease-causing biomolecules. Drug discovery involves finding chemical compounds, called lead compounds, that bind to pathogenic proteins and eventually inhibit the function of the protein. In this paper, the lead compounds are abstracted as inhibitors, pathogenic proteins as defectives, and the mixture of "ineffective" chemical compounds and non-pathogenic proteins as normal items. A defective could be immune to the presence of an inhibitor in a test. So, a test containing a defective is positive iff it does not contain its "associated" inhibitor. The goal of this paper is to identify the defectives, inhibitors, and their "associations" with high probability, or in other words, learn the Immune Defectives Graph (IDG) efficiently through group tests. We propose a probabilistic non-adaptive pooling design, a probabilistic two-stage adaptive pooling design and decoding algorithms for learning the IDG. For the two-stage adaptive-pooling design, we show that the sample complexity of the number of tests required to guarantee recovery of the inhibitors, defectives, and their associations with high probability, i.e., the upper bound, exceeds the proposed lower bound by a logarithmic multiplicative factor in the number of items. For the non-adaptive pooling design too, we show that the upper bound exceeds the proposed lower bound by at most a logarithmic multiplicative factor in the number of items.Comment: Double column, 17 pages. Updated with tighter lower bounds and other minor edit