Tiffany Jing Li

Optimal Locally Repairable Linear Codes

Linear erasure codes with local repairability are desirable for distributed data storage systems. An [n, k, d] linear code having all-symbol (r, δ)-locality, denoted as (r, δ)_a, is considered optimal if it has the actual highest minimum distance of any code of the given parameters n, k, r and δ. A minimum distance bound is given in [10]. The existing results on the existence and the construction of optimal (r, δ)_a linear codes are limited to only two small regions within this special case, namely, i) m = 0 and ii) m ≥ (v+δ-1) > (δ-1) and δ = 2, where m = n mod (r+δ-1) and v = k mod r. This paper investigates the properties and existence conditions for optimal (r, δ)_a linear codes with general r and δ. First, a structure theorem is derived for general optimal (r, δ)_a codes which helps illuminate some of their structure properties. Next, the entire problem space with arbitrary n, k, r and δ is divided into eight different cases (regions) with regard to the specific relations of these parameters. For two cases, it is rigorously proved that no (r, δ)_a linear code can achieve the minimum distance bound in [10]. For four other cases the optimal (r, δ)_a codes are shown to exist over a field of size q ≥ (_k-1ⁿ), deterministic constructions are proposed. Our new constructive algorithms not only cover more cases, but for the same cases where previous algorithms exist, the new constructions require a smaller field, which translates to potentially lower computational complexity. Our findings substantially enriches the knowledge on optimal (r, δ)_a linear codes, leaving only two cases in which the construction of optimal codes are not yet known.

Minimizing Transmission Cost for Third-Party Information Exchange with Network Coding

In wireless networks, getting the global knowledge of channel state information (CSI, e.g., channel gain or link loss probability) is always beneficial for the nodes to optimize the network design. However, the node usually only has the local CSI between itself and other nodes, and lacks the CSI between any pair of other nodes. To enable all the nodes to get the global CSI, in this paper, we propose a network-coded third-party information exchange scheme, with an emphasis on minimizing the total transmission cost for ( ) exchanging the CSI among the nodes. We show that for a network of N nodes, if and only if any k nodes (1 ≤ k <; N) send at least (2 : k) packets, a feasible solution exists for third-party information exchange. Formulating the problem of feasible and optimal solutions as an integer linear programming (ILP) problem, we compute the optimal number of packets that must be transmitted by every node. Guided by the necessary and sufficient condition, we construct two practical transmission schemes: fair load (FL) scheme and proportional load (PL) scheme. A deterministic encoding strategy based on XORs coding over GF(2) is further designed to guarantee that with FL or PL scheme, each node finally can decode the complete packets. It is shown that in two specific networks, these two schemes are optimal, achieving the minimum transmission cost. In more general networks, simulation results show that PL is still close to optimal with a high probability. Finally, a distributed transmission protocol is developed, which allows FL and PL schemes to be operated in a distributed and hence scalable manner.

Error Correction for Cooperative Data Exchange

This paper considers the problem of error correction for a cooperative data exchange (CDE) system, where some clients are compromised or failed and send false messages. Assuming each client possesses a subset of the total messages, we analyze the error correction capability when every client is allowed to broadcast only one linearly-coded message. Our error correction capability bound determines the maximum number of clients that can be compromised or failed without jeopardizing the final decoding solution at each client. We show that deterministic, feasible linear codes exist that can achieve the derived bound. We also evaluate random linear codes, where the coding coefficients are drawn randomly, and then develop the probability for a client to withstand a certain number of compromised or failed peers and successfully deduce the complete message for any network size and any initial message distributions.

Optimal linear precoding and postcoding for MIMO multi-sensor noisy observation problem

This paper proposes an efficient method for optimal joint precoding-postcoding design in a multi-input multi-output (MIMO) multi-sensor noisy observation context - a problem that is of great interest to the multi-relay MIMO transmission system. A set of wireless sensors, each provisioned with a different number of antennas and a different power constraint, precode and send their noisy observations of the same data to a common fusion center, which postcodes the data to make a best estimate of the original data. Taking the mean square error as a performance metric, we show that the optimal joint precoding-postcoding design problem is non-convex. Leveraging the alternative minimization framework, we are able to decompose it to two convex subproblems, one of which promises closed-form solutions. However, unlike previous studies that assume a total power constraint, the condition of individual power constraint and individual noise uncertainty at each sensor has tremendously complicated the second convex subproblem. Rather than numerically solve it via conventional convex optimization tools, we attack it analytically by transforming, approximating, and decomposing it to a set of new problems. We show that the new problems can be efficiently tackled via the Karush-Kuhn-Tucker conditions in an iterative manner. Simultions show that it leads to a convergence much faster and more robust than the conventional convex optimization tools.

Energy-Efficient Coverage Hole Self-Repair in Mobile Sensor Networks

With the advancement of MEMS techniques, mobile sensors with low cost and high capability are being deployed widely to carry out all kinds of complicated, risky tasks in large scale networks, especially in the areas are inaccessible to the human. Mobile sensors, which have the function of self-detection and self-repair, are desirable to solve the problem of failure of sensors, which causes costly maintenance expenditure and fatal loss. In this paper, we propose a novel heuristic self-repair algorithm to fix coverage holes in sensor networks using mobile nodes. The algorithm works successfully and efficiently to cover holes using reasonable numbers of mobile sensors. Numerical simulation results show our algorithm is near optimal for small coverage holes in terms of the metrics in number of mobile sensors, time and space complexity compared to optimal scheme. Our scheme is especially suitable for repairing multiple irregular areas of coverage holes simultaneously.

Multi-terminal joint transceiver design for MIMO systems with contaminated source and individual power constraint

This paper considers optimal transceiver design for a multi-terminal multi-inputmulti-output (MIMO) system, where L sensors wirelessly communicate individually-contaminated observations of the same source to the fusion center. The constraint that each sensor has individual power cap significantly complicates the non-convex optimization problem, and the optimal (linear) precoding and postcoding are not previously known. Using the signal-to-noise-ratio (SNR) as the performance metric, and employing the alternative minimization approach, we decompose the original problem into multiple subproblems that will run iteratively. The key results include the development of a closed-form solution to the optimal postcoder given the precoders, and the development of a closed-form solution for the ε-optimal precoders given the postcoder. The former is achieved via eigenvalue decomposition, and the latter is achieved by bounding the optimal solutions from above and from below, designing a series of fast-converging bisection search, and developing the closed-form analytical solution for each search. The convergence and the complexity of the proposed algorithm is analyzed and simulations are provided to confirm the efficiency of our proposal.

Cooperative Spectrum Sensing for Cognitive Radios: Bounds and Algorithms

This paper considers wireless spectrum sensing in harsh environments dominated by shadowing and fading. By modeling the network of the secondary users as Markov random fields and pulling a group of secondary users to cooperate through distributed probabilistic inference, effective sensing and fusion can be achieved. The proposed framework subsumes belief propagation, as well as conventional weighted hard/soft combining (such as maximal ratio combining and equal gain combing). It can also account for the distance-dependent correlation among individual sensing results by setting appropriate compatibility function. Theoretic upper and lower bounds are derived, demonstrating the significant gains made possible by effective cooperation. Extensive simulations confirm the analytical results.

On achievable rate region for decode-and-forward multi-way relay network

This paper investigates the general achievable rate region (ARR) for a wireless multi-way relay (MWR) network with full message exchange and decode-and-forward (DF) cooperative strategy. The MWR network consists of K users, each equipped with M antennas, and a single relay equipped with N antennas; and there is no user-user direct connectivity. Since different schedules would result in different ARRs, the general ARR must subsume all possible schedules; and this result is not previously known. We first present a cut set outer bound, and then derive and analyze the general ARR for DF by considering all meaningful schedules. We show that the general ARR is a convex hull expanded from a set of ARRs corresponding to special schedules. We further show that the ARR of a specific schedule can be expanded by its extreme points via the Krein-Milman theorem. In this, we have shown that the general ARR (of a MWR network using DF) is obtained by identifying and expanding these extreme points. We demonstrate the numerical results via exemplary cases.

A Distributed Topology Management Protocol for Wireless Sensor Networks

A new clustering approach, termed Distributed Energy Efficient clustering Protocol (DEEP), is proposed for wireless sensor networks. Using a non-iterative cluster formation operation, the protocol spends an extremely low overhead energy compared to the existing protocols and terminates faster than the energy-expensive iterative processes. The distributed head election algorithm guarantees that the periodically-elected leaders have the highest residual energy among their members in each data reporting cycle, effectively balancing the energy consumption among sensors. The DEEP also accounts for sensor limitations as well as practical concerns such as wireless collision that has not been considered by the existing clustering protocols. It intelligently exploits the overhearing ability of sensors to alleviate the loss of clustering control packets due to collisions. The proposed protocol is very effective in forming well-distributed clusters that ensure the required load balancing, the connectivity of clusters, and the minimum data communication energy during the data collection stage. In addition, the DEEP does not make any advanced assumptions about the required number of clusters, the network density, the energy consumption pattern of sensors or their clock synchronization and capabilities. For a thorough evaluation, we have compared the performance of DEEP with an existing clustering protocol. The simulation results show the effectiveness of DEEP in reducing the energy expenditure besides assuring other desirable features. We have also examined its performance in prolonging the network lifetime in the context of a practical routing protocol.

On full message exchange in MIMO DF multi-way relay networks

This paper considers a half-duplex multi-way relay (MWR) network where K users exchange messages among themselves with the assist of a relay. The relay is equipped with N antennas and all the users are each equipped with M antennas. The rate region of the network is first characterized by the cut-set bound, and then the degree-of-freedom (DoF) is computed. It is shown that the maximum DoF of the MWR network is K min{M,N} /2(K-1), and a DoF of equation can be achieved by the decode-and-forward (DF) relaying strategy. Using the technology of zero-forcing signal alignment and successive interference cancellation, a DF scheme is further proposed to provide a practical and efficient mechanism for the K-user MWR (K ≥ 2). Compared to the existing schemes, the new scheme has the advantage either in interference cancellation or in delay. Simulations confirm the effectiveness of the new scheme.