Code-rate-optimized differentially modulated near-capacity cooperation

It is widely recognized that half-duplex-relay-aided differential decode-and-forward (DDF) cooperative transmission schemes are capable of achieving a cooperative diversity gain, while circumventing the potentially excessive-complexity and yet inaccurate channel estimation, especially in mobile environments. However, when a cooperative wireless communication system is designed to approach the maximum achievable spectral efficiency by taking the cooperation-induced multiplexing loss into account, it is not obvious whether or not the relay-aided system becomes superior to its direct-transmission based counterpart, especially, when advanced channel coding techniques are employed. Furthermore, the optimization of the transmit-interval durations required by the source and relay is an open issue, which has not been well understood in the context of half-duplex relaying schemes. Hence, we first find the optimum transmission duration, which is proportional to the adaptive channel-code rate of the source and relay in the context of Code-Rate-Optimized (CRO) TDMA-based DDF-aided half-duplex systems for the sake of maximizing the achievable network throughput. Then, we investigate the benefits of introducing cooperative mechanisms into wireless networks, which may be approached in the context of the proposed CRO cooperative system both from a pure capacity perspective and from the practical perspective of approaching the Discrete-input Continuous-output Memoryless Channel (DCMC) capacity with the aid of the proposed Irregular Distributed Differential (IrDD) coding aided scheme. In order to achieve a near-capacity performance at a low-complexity, an adaptive-window-duration based Multiple-Symbol Differential Sphere Detection (MSDSD) scheme is employed in the iterative detection aided receiver. Specifically, upon using the proposed near-capacity system design, the IrDD coding scheme devised becomes capable of performing within about 1.8 dB from the corresponding single-relay-aided DDF cooperative system’s DCMC capacity

Dispensing with channel estimation: differentially modulated cooperative wireless communications

As a benefit of bypassing the potentially excessive complexity and yet inaccurate channel estimation, differentially encoded modulation in conjunction with low-complexity noncoherent detection constitutes a viable candidate for user-cooperative systems, where estimating all the links by the relays is unrealistic. In order to stimulate further research on differentially modulated cooperative systems, a number of fundamental challenges encountered in their practical implementations are addressed, including the time-variant-channel-induced performance erosion, flexible cooperative protocol designs, resource allocation as well as its high-spectral-efficiency transceiver design. Our investigations demonstrate the quantitative benefits of cooperative wireless networks both from a pure capacity perspective as well as from a practical system design perspective

A Nonparametric Ensemble Binary Classifier and its Statistical Properties

In this work, we propose an ensemble of classification trees (CT) and artificial neural networks (ANN). Several statistical properties including universal consistency and upper bound of an important parameter of the proposed classifier are shown. Numerical evidence is also provided using various real life data sets to assess the performance of the model. Our proposed nonparametric ensemble classifier doesn't suffer from the `curse of dimensionality' and can be used in a wide variety of feature selection cum classification problems. Performance of the proposed model is quite better when compared to many other state-of-the-art models used for similar situations

Rank Minimization over Finite Fields: Fundamental Limits and Coding-Theoretic Interpretations

This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random sensing matrices. Necessary and sufficient conditions on the number of measurements required are provided. It is shown that these conditions are sharp and the minimum-rank decoder is asymptotically optimal. The reliability function of this decoder is also derived by appealing to de Caen's lower bound on the probability of a union. The sufficient condition also holds when the sensing matrices are sparse - a scenario that may be amenable to efficient decoding. More precisely, it is shown that if the n\times n-sensing matrices contain, on average, \Omega(nlog n) entries, the number of measurements required is the same as that when the sensing matrices are dense and contain entries drawn uniformly at random from the field. Analogies are drawn between the above results and rank-metric codes in the coding theory literature. In fact, we are also strongly motivated by understanding when minimum rank distance decoding of random rank-metric codes succeeds. To this end, we derive distance properties of equiprobable and sparse rank-metric codes. These distance properties provide a precise geometric interpretation of the fact that the sparse ensemble requires as few measurements as the dense one. Finally, we provide a non-exhaustive procedure to search for the unknown low-rank matrix.Comment: Accepted to the IEEE Transactions on Information Theory; Presented at IEEE International Symposium on Information Theory (ISIT) 201

Quantum SDP-Solvers: Better upper and lower bounds

Brand\~ao and Svore very recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension $n$ of the problem and the number $m$ of constraints, but worse in terms of various other parameters. In this paper we improve their algorithms in several ways, getting better dependence on those other parameters. To this end we develop new techniques for quantum algorithms, for instance a general way to efficiently implement smooth functions of sparse Hamiltonians, and a generalized minimum-finding procedure. We also show limits on this approach to quantum SDP-solvers, for instance for combinatorial optimizations problems that have a lot of symmetry. Finally, we prove some general lower bounds showing that in the worst case, the complexity of every quantum LP-solver (and hence also SDP-solver) has to scale linearly with $mn$ when $m\approx n$, which is the same as classical.Comment: v4: 69 pages, small corrections and clarifications. This version will appear in Quantu