OpenRaiser/Intern-Atlas huggingface dataset:
Jointly Optimal Channel Pairing and Power Allocation for Multichannel Multihop Relaying
Venue: arXiv cs.IT 2015
Year: 2015

We study the problem of channel pairing and power allocation in a multichannel multihop relay network to enhance the end-to-end data rate. Both amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are considered. Given fixed power allocation to the channels, we show that channel pairing over multiple hops can be decomposed into independent pairing problems at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal, where each relay pairs its incoming and outgoing channels by their SNR order. For the joint optimization of channel pairing and power allocation under both total and individual power constraints, we show that the problem can be decoupled into two subproblems solved separately. This separation principle is established by observing the equivalence between sorting SNRs and sorting channel gains in the jointly optimal solution. It significantly reduces the computational complexity in finding the jointly optimal solution. It follows that the channel pairing problem in joint optimization can be again decomposed into independent pairing problems at each relay based on sorted channel gains. The solution for optimizing power allocation for DF relaying is also provided, as well as an asymptotically optimal solution for AF relaying. Numerical results are provided to demonstrate substantial performance gain of the jointly optimal solution over some suboptimal alternatives. It is also observed that more gain is obtained from optimal channel pairing than optimal power allocation through judiciously exploiting the variation among multiple channels. Impact of the variation of channel gain, the number of channels, and the number of hops on the performance gain is also studied through numerical examples.
Computing Shortest Paths among Curved Obstacles in the Plane
Venue: arXiv cs.CG 2015
Year: 2015

A fundamental problem in computational geometry is to compute an obstacle-avoiding Euclidean shortest path between two points in the plane. The case of this problem on polygonal obstacles is well studied. In this paper, we consider the problem version on curved obstacles, commonly modeled as splinegons. A splinegon can be viewed as replacing each edge of a polygon by a convex curved edge (polygons are special splinegons). Each curved edge is assumed to be of O(1) complexity. Given in the plane two points s and t and a set of $h$ pairwise disjoint splinegons with a total of $n$ vertices, we compute a shortest s-to-t path avoiding the splinegons, in $O(n+h\log^{1+ε}h+k)$ time, where k is a parameter sensitive to the structures of the input splinegons and is upper-bounded by $O(h^2)$. In particular, when all splinegons are convex, $k$ is proportional to the number of common tangents in the free space (called "free common tangents") among the splinegons. We develop techniques for solving the problem on the general (non-convex) splinegon domain, which also improve several previous results. In particular, our techniques produce an optimal output-sensitive algorithm for a basic visibility problem of computing all free common tangents among $h$ pairwise disjoint convex splinegons with a total of $n$ vertices. Our algorithm runs in $O(n+h\log h+k)$ time and $O(n)$ space, where $k$ is the number of all free common tangents. Even for the special case where all splinegons are convex polygons, the previously best algorithm for this visibility problem takes $O(n+h^2\log n)$ time.
Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors
Venue: arXiv cs.IT 2015
Year: 2015

The Compressive Sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each measurement to a finite number of bits; moreover, there is an inverse relationship between the achievable sampling rate and the bit depth. In this paper, we investigate an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement. In particular, we explore the extreme case of 1-bit CS measurements, which capture just their sign. Our results come in two flavors. First, we consider ideal reconstruction from noiseless 1-bit measurements and provide a lower bound on the best achievable reconstruction error. We also demonstrate that i.i.d. random Gaussian matrices describe measurement mappings achieving, with overwhelming probability, nearly optimal error decay. Next, we consider reconstruction robustness to measurement errors and noise and introduce the Binary $ε$-Stable Embedding (B$ε$SE) property, which characterizes the robustness measurement process to sign changes. We show the same class of matrices that provide almost optimal noiseless performance also enable such a robust mapping. On the practical side, we introduce the Binary Iterative Hard Thresholding (BIHT) algorithm for signal reconstruction from 1-bit measurements that offers state-of-the-art performance.
The Gaussian Multiple Access Diamond Channel
Venue: arXiv cs.IT 2015
Year: 2015

In this paper, we study the capacity of the diamond channel. We focus on the special case where the channel between the source node and the two relay nodes are two separate links with finite capacities and the link from the two relay nodes to the destination node is a Gaussian multiple access channel. We call this model the Gaussian multiple access diamond channel. We first propose an upper bound on the capacity. This upper bound is a single-letterization of an $n$-letter upper bound proposed by Traskov and Kramer, and is tighter than the cut-set bound. As for the lower bound, we propose an achievability scheme based on sending correlated codes through the multiple access channel with superposition structure. We then specialize this achievable rate to the Gaussian multiple access diamond channel. Noting the similarity between the upper and lower bounds, we provide sufficient and necessary conditions that a Gaussian multiple access diamond channel has to satisfy such that the proposed upper and lower bounds meet. Thus, for a Gaussian multiple access diamond channel that satisfies these conditions, we have found its capacity.
Hyperincursive Cogitata and Incursive Cogitantes: Scholarly Discourse as a Strongly Anticipatory System
Venue: arXiv cs.DL 2015
Year: 2015

Strongly anticipatory systems-that is, systems which use models of themselves for their further development-and which additionally may be able to run hyperincursive routines-that is, develop only with reference to their future states-cannot exist in res extensa, but can only be envisaged in res cogitans. One needs incursive routines in cogitantes to instantiate these systems. Unlike historical systems (with recursion), these hyper-incursive routines generate redundancies by opening horizons of other possible states. Thus, intentional systems can enrich our perceptions of the cases that have happened to occur. The perspective of hindsight codified at the above-individual level enables us furthermore to intervene technologically. The theory and computation of anticipatory systems have made these loops between supra-individual hyper-incursion, individual incursion (in instantiation), and historical recursion accessible for modeling and empirical investigation.
The solution space geometry of random linear equations
Venue: arXiv cs.DS 2015
Year: 2015

We consider random systems of linear equations over GF(2) in which every equation binds k variables. We obtain a precise description of the clustering of solutions in such systems. In particular, we prove that with probability that tends to 1 as the number of variables, n, grows: for every pair of solutions σ, τ, either there exists a sequence of solutions σ,...,τ, in which successive elements differ by O(log n) variables, or every sequence of solutions σ,...,τ, contains a step requiring the simultaneous change of Ω(n) variables. Furthermore, we determine precisely which pairs of solutions are in each category. Our results are tight and highly quantitative in nature. Moreover, our proof highlights the role of unique extendability as the driving force behind the success of Low Density Parity Check codes and our techniques also apply to the problem of so-called pseudo-codewords in such codes.
Downlink Scheduling over Markovian Fading Channels
Venue: arXiv cs.NI 2015
Year: 2015

We consider the scheduling problem in downlink wireless networks with heterogeneous, Markov-modulated, ON/OFF channels. It is well-known that the performance of scheduling over fading channels relies heavily on the accuracy of the available Channel State Information (CSI), which is costly to acquire. Thus, we consider the CSI acquisition via a practical ARQ-based feedback mechanism whereby channel states are revealed at the end of only scheduled users' transmissions. In the assumed presence of temporally-correlated channel evolutions, the desired scheduler must optimally balance the exploitation-exploration trade-off, whereby it schedules transmissions both to exploit those channels with up-to-date CSI and to explore the current state of those with outdated CSI. In earlier works, Whittle's Index Policy had been suggested as a low-complexity and high-performance solution to this problem. However, analyzing its performance in the typical scenario of statistically heterogeneous channel state processes has remained elusive and challenging, mainly because of the highly-coupled and complex dynamics it possesses. In this work, we overcome these difficulties to rigorously establish the asymptotic optimality properties of Whittle's Index Policy in the limiting regime of many users. More specifically: (1) we prove the local optimality of Whittle's Index Policy, provided that the initial state of the system is within a certain neighborhood of a carefully selected state; (2) we then establish the global optimality of Whittle's Index Policy under a recurrence assumption that is verified numerically for our problem. These results establish that Whittle's Index Policy possesses analytically provable optimality characteristics for scheduling over heterogeneous and temporally-correlated channels.
Universal Computation Is 'Almost Surely' Chaotic
Venue: arXiv cs.CC 2015
Year: 2015

Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard notions of a chaotic system is not readily applicable for them. Changing the state space of Turing Machines from integer to rational space, the condition for chaotic dynamics can be suitably established, as presented in the current paper. Further it is deduced that, given random input, computation performed by a Universal Turing Machine would be 'almost surely' chaotic.
Lossy Compression via Sparse Linear Regression: Performance under Minimum-distance Encoding
Venue: arXiv cs.IT 2015
Year: 2015

We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a design matrix. Called a Sparse Superposition or Sparse Regression codebook, this structure is motivated by an analogous construction proposed recently by Barron and Joseph for communication over an AWGN channel. For i.i.d Gaussian sources and minimum-distance encoding, we show that such a code can attain the Shannon rate-distortion function with the optimal error exponent, for all distortions below a specified value. It is also shown that sparse regression codes are robust in the following sense: a codebook designed to compress an i.i.d Gaussian source of variance $σ^2$ with (squared-error) distortion $D$ can compress any ergodic source of variance less than $σ^2$ to within distortion $D$. Thus the sparse regression ensemble retains many of the good covering properties of the i.i.d random Gaussian ensemble, while having having a compact representation in terms of a matrix whose size is a low-order polynomial in the block-length.
Secure Multi-Party Computation in Large Networks
Venue: arXiv cs.DS 2015
Year: 2015

We describe scalable protocols for solving the secure multi-party computation (MPC) problem among a large number of parties. We consider both the synchronous and the asynchronous communication models. In the synchronous setting, our protocol is secure against a static malicious adversary corrupting less than a $1/3$ fraction of the parties. In the asynchronous setting, we allow the adversary to corrupt less than a $1/8$ fraction of parties. For any deterministic function that can be computed by an arithmetic circuit with $m$ gates, both of our protocols require each party to send a number of field elements and perform an amount of computation that is $\tilde{O}(m/n + \sqrt n)$. We also show that our protocols provide perfect and universally-composable security. To achieve our asynchronous MPC result, we define the \emph{threshold counting problem} and present a distributed protocol to solve it in the asynchronous setting. This protocol is load balanced, with computation, communication and latency complexity of $O(\log{n})$, and can also be used for designing other load-balanced applications in the asynchronous communication model.
Iterative rounding approximation algorithms for degree-bounded node-connectivity network design
Venue: arXiv cs.DS 2015
Year: 2015

We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this problem. For directed graphs and $k$-out-connectivity requirements from a root, our algorithm computes a solution that is a 2-approximation on the cost, and the degree of each node $v$ in the solution is at most $2b(v) + O(k)$ where $b(v)$ is the degree upper bound on $v$. For undirected graphs and element-connectivity requirements with maximum connectivity requirement $k$, our algorithm computes a solution that is a $4$-approximation on the cost, and the degree of each node $v$ in the solution is at most $4b(v)+O(k)$. These ratios improve the previous $O(\log k)$-approximation on the cost and $O(2^k b(v))$ approximation on the degrees. Our algorithms can be used to improve approximation ratios for other node-connectivity problems such as undirected $k$-out-connectivity, directed and undirected $k$-connectivity, and undirected rooted $k$-connectivity and subset $k$-connectivity.
Optimism for Boosting Concurrency
Venue: arXiv cs.DC 2015
Year: 2015

Modern concurrent programming benefits from a large variety of synchronization techniques. These include conventional pessimistic locking, as well as optimistic techniques based on conditional synchronization primitives or transactional memory. Yet, it is unclear which of these approaches better leverage the concurrency inherent to multi-cores. In this paper, we compare the level of concurrency one can obtain by converting a sequential program into a concurrent one using optimistic or pessimistic techniques. To establish fair comparison of such implementations, we introduce a new correctness criterion for concurrent programs, defined independently of the synchronization techniques they use. We treat a program's concurrency as its ability to accept a concurrent schedule, a metric inspired by the theories of both databases and transactional memory. We show that pessimistic locking can provide strictly higher concurrency than transactions for some applications whereas transactions can provide strictly higher concurrency than pessimistic locks for others. Finally, we show that combining the benefits of the two synchronization techniques can provide strictly more concurrency than any of them individually. We propose a list-based set algorithm that is optimal in the sense that it accepts all correct concurrent schedules. As we show via experimentation, the optimality in terms of concurrency is reflected by scalability gains.
Mesh Learning for Classifying Cognitive Processes
Venue: arXiv cs.NE 2015
Year: 2015

A relatively recent advance in cognitive neuroscience has been multi-voxel pattern analysis (MVPA), which enables researchers to decode brain states and/or the type of information represented in the brain during a cognitive operation. MVPA methods utilize machine learning algorithms to distinguish among types of information or cognitive states represented in the brain, based on distributed patterns of neural activity. In the current investigation, we propose a new approach for representation of neural data for pattern analysis, namely a Mesh Learning Model. In this approach, at each time instant, a star mesh is formed around each voxel, such that the voxel corresponding to the center node is surrounded by its p-nearest neighbors. The arc weights of each mesh are estimated from the voxel intensity values by least squares method. The estimated arc weights of all the meshes, called Mesh Arc Descriptors (MADs), are then used to train a classifier, such as Neural Networks, k-Nearest Neighbor, Naïve Bayes and Support Vector Machines. The proposed Mesh Model was tested on neuroimaging data acquired via functional magnetic resonance imaging (fMRI) during a recognition memory experiment using categorized word lists, employing a previously established experimental paradigm (Öztekin & Badre, 2011). Results suggest that the proposed Mesh Learning approach can provide an effective algorithm for pattern analysis of brain activity during cognitive processing.
Topological arguments for Kolmogorov complexity
Venue: arXiv cs.DM 2015
Year: 2015

We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties.
Achievable rate region for three user discrete broadcast channel based on coset codes
Venue: arXiv cs.IT 2015
Year: 2015

We present an achievable rate region for the general three user discrete memoryless broadcast channel, based on nested coset codes. We characterize 3-to-1 discrete broadcast channels, a class of broadcast channels for which the best known coding technique\footnote{We henceforth refer to this as Marton's coding for three user discrete broadcast channel.}, which is obtained by a natural generalization of that proposed by Marton for the general two user discrete broadcast channel, is strictly sub-optimal. In particular, we identify a novel 3-to-1 discrete broadcast channel for which Marton's coding is \textit{analytically} proved to be strictly suboptimal. We present achievable rate regions for the general 3-to-1 discrete broadcast channels, based on nested coset codes, that strictly enlarge Marton's rate region for the aforementioned channel. We generalize this to present achievable rate region for the general three user discrete broadcast channel. Combining together Marton's coding and that proposed herein, we propose the best known coding technique, for a general three user discrete broadcast channel.
Random linear multihop relaying in a general field of interferers using spatial Aloha
Venue: arXiv cs.NI 2015
Year: 2015

In our basic model, we study a stationary Poisson pattern of nodes on a line embedded in an independent planar Poisson field of interfering nodes. Assuming slotted Aloha and the signal-to-interference-and-noise ratio capture condition, with the usual power-law path loss model and Rayleigh fading, we explicitly evaluate several local and end-to-end performance characteristics related to the nearest-neighbor packet relaying on this line, and study their dependence on the model parameters (the density of relaying and interfering nodes, Aloha tuning and the external noise power). Our model can be applied in two cases: the first use is for vehicular ad-hoc networks, where vehicles are randomly located on a straight road. The second use is to study a typical route traced in a (general) planar ad-hoc network by some routing mechanism. The approach we have chosen allows us to quantify the non-efficiency of long-distance routing in pure ad-hoc networks and evaluate a possible remedy for it in the form of additional fixed relaying nodes, called road-side units in a vehicular network. It also allows us to consider a more general field of interfering nodes and study the impact of the clustering of its nodes the routing performance. As a special case of a field with more clustering than the Poison field, we consider a Poisson-line field of interfering nodes, in which all the nodes are randomly located on random straight lines. The comparison to our basic model reveals a paradox: clustering of interfering nodes decreases the outage probability of a single (typical) transmission on the route, but increases the mean end-to-end delay.
Characterizing co-NL by a group action
Venue: arXiv cs.LO 2015
Year: 2015

In a recent paper, Girard proposes to use his recent construction of a geometry of interaction in the hyperfinite factor in an innovative way to characterize complexity classes. We begin by giving a detailed explanation of both the choices and the motivations of Girard's definitions. We then provide a complete proof that the complexity class co-NL can be characterized using this new approach. We introduce as a technical tool the non-deterministic pointer machine, a concrete model to computes algorithms.
Testing Small Set Expansion in General Graphs
Venue: arXiv cs.DS 2015
Year: 2015

We consider the problem of testing small set expansion for general graphs. A graph $G$ is a $(k,ϕ)$-expander if every subset of volume at most $k$ has conductance at least $ϕ$. Small set expansion has recently received significant attention due to its close connection to the unique games conjecture, the local graph partitioning algorithms and locally testable codes. We give testers with two-sided error and one-sided error in the adjacency list model that allows degree and neighbor queries to the oracle of the input graph. The testers take as input an $n$-vertex graph $G$, a volume bound $k$, an expansion bound $ϕ$ and a distance parameter $\varepsilon>0$. For the two-sided error tester, with probability at least $2/3$, it accepts the graph if it is a $(k,ϕ)$-expander and rejects the graph if it is $\varepsilon$-far from any $(k^*,ϕ^*)$-expander, where $k^*=Θ(k\varepsilon)$ and $ϕ^*=Θ(\frac{ϕ^4}{\min\{\log(4m/k),\log n\}\cdot(\ln k)})$. The query complexity and running time of the tester are $\widetilde{O}(\sqrt{m}ϕ^{-4}\varepsilon^{-2})$, where $m$ is the number of edges of the graph. For the one-sided error tester, it accepts every $(k,ϕ)$-expander, and with probability at least $2/3$, rejects every graph that is $\varepsilon$-far from $(k^*,ϕ^*)$-expander, where $k^*=O(k^{1-ξ})$ and $ϕ^*=O(ξϕ^2)$ for any $0<ξ<1$. The query complexity and running time of this tester are $\widetilde{O}(\sqrt{\frac{n}{\varepsilon^3}}+\frac{k}{\varepsilon ϕ^4})$. We also give a two-sided error tester with smaller gap between $ϕ^*$ and $ϕ$ in the rotation map model that allows (neighbor, index) queries and degree queries.