Achievable degrees of freedom of MIMO two-way X relay channel with delayed CSIT

The previous work on interference alignment for multiple-input-multiple-output (MIMO) two-way X relay channel assumes perfect channel state information at the transmitter (CSIT), which is reasonable in slow fading channel. However, in fast fading scenario, this assumption is impractical. In this paper, assuming that each node has delayed CSIT, we study the achievable degrees of freedom (DOF) for MIMO two-way X relay channel in frequency division duplex (FDD) systems. Specifically, in the broadcast (BC) phase, we propose a new multiple-stage transmission (MST) scheme, which utilizes retrospective interference alignment for physical layer network coding (PLNC). We show that MST can achieve significant DOF gain and tremendous power gain over other schemes. When the number of antennas for each user, N, is smaller than the number of the relays, M, the time division multiple access (TDMA) scheme can only achieve an ergodic sum-rate increase by N bps/Hz for every increasing of 3 dB of signal-to-noise power ratio (SNR), while the proposed MST scheme can achieve an ergodic sum-rate increase by M bps/Hz.     

Sleeping on the Job: Energy-Efficient and Robust Broadcast for Radio Networks

We address the problem of minimizing power consumption when broadcasting a message from one node to all the other nodes in a radio network. To enable power savings for such a problem, we introduce a compelling new data streaming problem which we call the Bad Santa problem. Our results on this problem apply for any situation where: (1) a node can listen to a set of n nodes, out of which at least half are non-faulty and know the correct message; and (2) each of these n nodes sends according to some predetermined schedule which assigns each of them its own unique time slot. In this situation, we show that in order to receive the correct message with probability 1, it is necessary and sufficient for the listening node to listen to a \(\Theta(\sqrt{n})\) expected number of time slots. Moreover, if we allow for repetitions of transmissions so that each sending node sends the message O(log?^? n) times (i.e. in O(log?^? n) rounds each consisting of the n time slots), then listening to O(log?^? n) expected number of time slots suffices. We show that this is near optimal.We describe an application of our result to the popular grid model for a radio network. Each node in the network is located on a point in a two dimensional grid, and whenever a node sends a message m, all awake nodes within L _∞ distance r receive m. In this model, up to \(t<\frac{r}{2}(2r+1)\) nodes within any 2r+1 by 2r+1 square in the grid can suffer Byzantine faults. Moreover, we assume that the nodes that suffer Byzantine faults are chosen and controlled by an adversary that knows everything except for the random bits of each non-faulty node. This type of adversary models worst-case behavior due to malicious attacks on the network; mobile nodes moving around in the network; or static nodes losing power or ceasing to function. Let n=r(2r+1). We show how to solve the broadcast problem in this model with each node sending and receiving an expected \(O(n\log^{2}{|m|}+\sqrt{n}|m|)\) bits where |m| is the number of bits in m, and, after broadcasting a fingerprint of m, each node is awake only an expected \(O(\sqrt{n})\) time slots. Moreover, for t≤(1?ε)(r/2)(2r+1), for any constant ε>0, we can achieve an even better energy savings. In particular, if we allow each node to send O(log?^? n) times, we achieve reliable broadcast with each node sending O(nlog?²|m|+(log?^? n)|m|) bits and receiving an expected O(nlog?²|m|+(log?^? n)|m|) bits and, after broadcasting a fingerprint of m, each node is awake for only an expected O(log?^? n) time slots. Our results compare favorably with previous protocols that required each node to send Θ(|m|) bits, receive Θ(n|m|) bits and be awake for Θ(n) time slots.     

Hybrid full-/half-duplex cellular networks: user admission and power control

We consider a single-cell network with a hybrid full-/half-duplex base station. For the practical scenario with N channels, K uplink users, and M downlink users (max{K,M} ≤ N ≤ K + M), we tackle the issue of user admission and power control to simultaneously maximize the user admission number and minimize the total transmit power when guaranteeing the quality-of-service requirement of individual users. We formulate a 0–1 integer programming problem for the joint-user admission and power allocation problem. Because finding the optimal solution of this problem is NP-hard in general, a low-complexity algorithm is proposed by introducing the novel concept of adding dummy users. Simulation results show that the proposed algorithm achieves performance similar to that of branch and bound algorithm and significantly outperforms the random pairing algorithm.     

On the Smallest Size of an Almost Complete Subset of a Conic in PG(2, <Emphasis Type="Italic">q</Emphasis>) and Extendability of Reed–Solomon Codes

Abstract—In the projective plane PG(2, q), a subset S of a conic C is said to be almost complete if it can be extended to a larger arc in PG(2, q) only by the points of C \ S and by the nucleus of C when q is even. We obtain new upper bounds on the smallest size t(q) of an almost complete subset of a conic, in particular,

$$t(q) < \sqrt {q(3lnq + lnlnq + ln3)} + \sqrt {\frac{q}{{3\ln q}}} + 4 \sim \sqrt {3q\ln q} ,t(q) < 1.835\sqrt {q\ln q.} $$

The new bounds are used to extend the set of pairs (N, q) for which it is proved that every normal rational curve in the projective space PG(N, q) is a complete (q+1)-arc, or equivalently, that no [q+1,N+1, q?N+1]_q generalized doubly-extended Reed–Solomon code can be extended to a [q + 2,N + 1, q ? N + 2]_q maximum distance separable code.

     

Novel steganographic method based on generalized <Emphasis Type="Italic">K</Emphasis>-distance <Emphasis Type="Italic">N</Emphasis>-dimensional pixel matching

In this paper, a steganographic scheme adopting the concept of the generalized K _d -distance N-dimensional pixel matching is proposed. The generalized pixel matching embeds a B-ary digit (B is a function of K and N) into a cover vector of length N, where the order-d Minkowski distance-measured embedding distortion is no larger than K. In contrast to other pixel matching-based schemes, a N-dimensional reference table is used. By choosing d, K, and N adaptively, an embedding strategy which is suitable for arbitrary relative capacity can be developed. Additionally, an optimization algorithm, namely successive iteration algorithm (SIA), is proposed to optimize the codeword assignment in the reference table. Benefited from the high dimensional embedding and the optimization algorithm, nearly maximal embedding efficiency is achieved. Compared with other content-free steganographic schemes, the proposed scheme provides better image quality and statistical security. Moreover, the proposed scheme performs comparable to state-of-the-art content-based approaches after combining with image models.     

Observational constraints on a hyperbolic potential in brane-world inflation

We focus on the large field of a hyperbolic potential form, which is characterized by a parameter f, in the framework of the brane-world inflation in Randall-Sundrum-II model. From the observed form of the power spectrum P _R (k), the parameter f should be of order 0.1m _p to 0.001m _p , the brane tension must be in the range λ ~ (1?10)×10⁵⁷ GeV⁴, and the energy scale is around V₀ ^1/4 ~ 10¹⁵ GeV. We find that the inflationary parameters (n _s , r, and dn _s /d(ln k) depend only on the number of e-folds N. The compatibility of these parameters with the last Planck measurements is realized with large values of N.     

On the Advice Complexity of the k-server Problem Under Sparse Metrics

We consider the k-Server problem under the advice model of computation when the underlying metric space is sparse. On one side, we introduce Θ(1)-competitive algorithms for a wide range of sparse graphs. These algorithms require advice of (almost) linear size. We show that for graphs of size N and treewidth α, there is an online algorithm that receives O (n(log α + log log N))^* bits of advice and optimally serves any sequence of length n. We also prove that if a graph admits a system of μ collective tree (q, r)-spanners, then there is a (q + r)-competitive algorithm which requires O (n(log μ + log log N)) bits of advice. Among other results, this gives a 3-competitive algorithm for planar graphs, when provided with O (n log log N) bits of advice. On the other side, we prove that advice of size Ω(n) is required to obtain a 1-competitive algorithm for sequences of length n even for the 2-server problem on a path metric of size N ≥ 3. Through another lower bound argument, we show that at least \(\frac {n}{2}(\log \alpha - 1.22)\) bits of advice is required to obtain an optimal solution for metric spaces of treewidth α, where 4 ≤ α < 2k.     

An efficient protocol for secure multicast key distribution in the presence of adaptive adversaries

In this paper, an efficient construction of multicast key distribution schemes based on semantically secure symmetric-key encryption schemes and cryptographically strong pseudo-random number generators is presented and analyzed. The proposed scheme is provably secure against adaptive adversaries leveraging the security amplification technique defined over the logical key hierarchy structures. Our protocol tolerates any coalition of revoked users; in particular, we do not assume any limit on the size or structure of the coalition. The proposed scheme is efficient as a performance of Join or Leave procedure requires 2 log(N) multicast activities defined over a sibling ancestor node set, 2 log(N) internal state updates of the underlying pseudo-random number generator and 2 log(N) symmetric-key encryption activities for N users in a session.     

The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron. I

We consider a game between a group of n pursuers and one evader moving with the same maximum velocity along the 1-skeleton graph of a regular polyhedron. The goal of the paper is finding, for each regular polyhedron M, a number N(M) with the following properties: if n ≥ N(M), the group of pursuers wins, while if n < N(M), the evader wins. Part I of the paper is devoted to the case of polyhedra in ?³; Part II will be devoted to the case of ? ^d , d ≥ 5; and Part III, to the case of ?⁴.     

Two-armed bandit problem for parallel data processing systems

We consider application of the two-armed bandit problem to processing a large number N of data where two alternative processing methods can be used. We propose a strategy which at the first stages, whose number is at most r ? 1, compares the methods, and at the final stage applies only the best one obtained from the comparison. We find asymptotically optimal parameters of the strategy and observe that the minimax risk is of the order of N ^α , where α = 2 ^r?1/(2 ^r ? 1). Under parallel processing, the total operation time is determined by the number r of stages but not by the number N of data.     

Near-optimal communication-time tradeoff in fault-tolerant computation of aggregate functions

This paper considers the problem of computing general commutative and associative aggregate functions (such as Sum) over distributed inputs held by nodes in a distributed system, while tolerating failures. Specifically, there are N nodes in the system, and the topology among them is modeled as a general undirected graph. Whenever a node sends a message, the message is received by all of its neighbors in the graph. Each node has an input, and the goal is for a special root node (e.g., the base station in wireless sensor networks or the gateway node in wireless ad hoc networks) to learn a certain commutative and associate aggregate of all these inputs. All nodes in the system except the root node may experience crash failures, with the total number of edges incidental to failed nodes being upper bounded by f. The timing model is synchronous where protocols proceed in rounds. Within such a context, we focus on the following question:

Under any given constraint on time complexity, what is the lowest communication complexity, in terms of the number of bits sent (i.e., locally broadcast) by each node, needed for computing general commutative and associate aggregate functions?

This work, for the first time, reduces the gap between the upper bound and the lower bound for the above question from polynomial to polylog. To achieve this reduction, we present significant improvements over both the existing upper bounds and the existing lower bounds on the problem.

     

On the real complexity of a complex DFT

We present a method to construct a theoretically fast algorithm for computing the discrete Fourier transform (DFT) of order N = 2 ⁿ . We show that the DFT of a complex vector of length N is performed with complexity of 3.76875N log₂ N real operations of addition, subtraction, and scalar multiplication.     

Patent Protection in a Model of Economic Growth in Multiple Regions

We study the effects of patent protection on economic growth in the ith region when this ith region is part of an aggregate economy of i?=?1,…,N regions. The regulatory authority in the ith region attempts to curtail the monopoly power of patent holding input producers by requiring them to charge a price that is parametrically related to the unconstrained monopoly price. Our analysis generates three results. First, we show the manner in which the equilibrium growth rate of the ith region is related to the above mentioned parameter. Second, we demonstrate the impact that changes in the stringency of patent protection have on the ith region’s equilibrium growth rate. Finally, we explain why eliminating the monopoly distortion does not maximize social welfare in the ith region.     

Polar Codes with Higher-Order Memory

We introduce a construction of a set of code sequences {C_n^(m) : n ≥ 1, m ≥ 1} with memory order m and code length N(n). {C_n^(m)} is a generalization of polar codes presented by Ar?kan in [1], where the encoder mapping with length N(n) is obtained recursively from the encoder mappings with lengths N(n ? 1) and N(n ? m), and {C_n^(m)} coincides with the original polar codes when m = 1. We show that {C_n^(m)} achieves the symmetric capacity I(W) of an arbitrary binary-input, discrete-output memoryless channel W for any fixed m. We also obtain an upper bound on the probability of block-decoding error P_e of {C_n^(m)} and show that \({P_e} = O({2^{ - {N^\beta }}})\) is achievable for β < 1/[1+m(? ? 1)], where ? ∈ (1, 2] is the largest real root of the polynomial F(m, ρ) = ρ^m ? ρ^{m ? 1} ? 1. The encoding and decoding complexities of {C_n^(m)} decrease with increasing m, which proves the existence of new polar coding schemes that have lower complexity than Ar?kan’s construction.     

On numerical methods for functions depending on a very large number of variables

The question under discussion is why optimal algorithms on classes of functions sometimes become useless in practice. As an example let us consider the class of functions which satisfy a general Lipschitz condition. The methods of integral evaluation over a unit cube of d dimensions, where d is significantly large, are discussed. It is assumed that the integrand is square integrable. A crude Monte Carlo estimation can be used. In this case the probable error of estimation is proportional to 1/√N, where N is the number of values of the integrand. If we use the quasi-Monte Carlo method instead of the Monte Carlo method, then the error does not depend on the dimension d, and according to numerous examples, it depends on the average dimension d? of the integrand. For small d?, the order of error is close to 1/N.     

The weight-constrained maximum-density subtree problem and related problems in trees

Given a tree T=(V,E) of n nodes such that each node v is associated with a value-weight pair (val _v ,w _v ), where value val _v is a real number and weight w _v is a non-negative integer, the density of T is defined as \(\frac{\sum_{v\in V}{\mathit{val}}_{v}}{\sum_{v\in V}w_{v}}\). A subtree of T is a connected subgraph (V′,E′) of T, where V′?V and E′?E. Given two integers w _min? and w _max?, the weight-constrained maximum-density subtree problem on T is to find a maximum-density subtree T′=(V′,E′) satisfying w _min?≤∑_v∈V′ w _v ≤w _max?. In this paper, we first present an O(w _max? n)-time algorithm to find a weight-constrained maximum-density path in a tree T, and then present an O(w _max? ² n)-time algorithm to find a weight-constrained maximum-density subtree in T. Finally, given a node subset S?V, we also present an O(w _max? ² n)-time algorithm to find a weight-constrained maximum-density subtree in T which covers all the nodes in S.     

Guaranteed approach with the farthest of the runaways

Games of the family {Λ _N } _N?2 are formulated and studied with the application of generalized Isaacs’s approach. The game Λ _N is a simplest model of the counteraction of one persecutor P and coalition N of E ^N runaways for the case when the payoff is the distance up to the coalition of E ^N equal to the Euclidean distance between P and the farthest from the runaways; P is in command of the termination moment. Moreover, an approach within the limits of which in games with a smooth terminal payoff are generated strategies prescribing players’ motions in the directions of local gradients of the payoff is described. The approach is used for constructing pursuit strategies in games in which smooth approximations of the maximum of Euclidean distances up to the runaways are in place of payoffs. Pursuit strategies prescribing the motion in the direction of the farthest of the runaways are studied. A numerical simulation of the development of the games Λ₂ and Λ₃ is conducted in using different strategies by the players.     

Generalized cryptanalysis of RSA with small public exponent针对公钥e小于等于N的0.5次幂的RSA算法的广义密码分析

In this paper, we demonstrate that there exist weak keys in the RSA public-key cryptosystem with the public exponent e = N^α ≤ N^0.5. In 1999, Boneh and Durfee showed that when α ≈ 1 and the private exponent d = N^β < N^0.292, the system is insecure. Moreover, their attack is still effective for 0.5 < α < 1.875. We propose a generalized cryptanalytic method to attack the RSA cryptosystem with α ≤ 0.5. For \(c = \left\lfloor {\frac{{1 - \alpha }}{\alpha }} \right\rfloor \) and e^γc ≡ d (mod e^c), when γ, β satisfy \(\gamma < 1 + \frac{1}{c} - \frac{1}{{2\alpha c}}and\beta < \alpha c + \frac{7}{6} - \alpha \gamma c - \frac{1}{3}\sqrt {6\alpha + 6\alpha c + 1 - 6\alpha \gamma c} \), we can perform cryptanalytic attacks based on the LLL algorithm. The basic idea is an application of Coppersmith’s techniques and we further adapt the technique of unravelled linearization, which leads to an optimized lattice. Our advantage is that we achieve new attacks on RSA with α ≤ 0.5 and consequently, there exist weak keys in RSA for most α.     

Analysis of Multi-Sort Algorithm on Multi-Mesh of Trees (MMT) architecture

Various sorting algorithms using parallel architectures have been proposed in the search for more efficient results. This paper introduces the Multi-Sort Algorithm for Multi-Mesh of Trees (MMT) Architecture for N=n ⁴ elements with more efficient time complexity compared to previous architectures. The shear sort algorithm on Single Instruction Multiple Data (SIMD) mesh model requires \(4\sqrt{N}+O\sqrt{N}\) time for sorting N elements, arranged on a \(\sqrt{N}\times \sqrt{N}\) mesh, whereas Multi-Sort algorithm on the SIMD Multi-Mesh (MM) Architecture takes O(N ^1/4) time for sorting the same N elements, which proves that Multi-Sort is a better sorting approach. We have improved the time complexity of intrablock Sort. The Communication time complexity for 2D Sort in MM is O(n), whereas this time in MMT is O(log?n). The time complexity of compare–exchange step in MMT is same as that in MM, i.e., O(n). It has been found that the time complexity of the Multi-Sort on MMT has been improved as on Multi-Mesh architecture.     

A novel constant degree and constant congestion DHT scheme for peer-to-peer networks

1 Introduction and related work In recent years, peer-to-peer computing has attracted significant attention from both industry field and academic field[1-3]. The core component of many proposed peer-to- peer systems is the distributed hash table (DHT) schemes[4,5] that use a hash table-like interface to publish and look up data objects. Many proposed DHT schemes[6-15] are based on some traditional interconnection to- pology: Chord[6], Tapestry[7,8], Pastry[9] are based on hypercube topolog…