Ari Trachtenberg

Set reconciliation with nearly optimal communication complexity

We consider the problem of efficiently reconciling two similar sets held by different hosts while minimizing the communication complexity. This type of problem arises naturally from gossip protocols used for the distribution of information, but has other applications as well. We describe an approach to such reconciliation based on the encoding of sets as polynomials. The resulting protocols exhibit tractable computational complexity and nearly optimal communication complexity. Moreover, these protocols can be adapted to work over a broadcast channel, allowing many clients to reconcile with one host based on a single broadcast.

Rateless Deluge: Over-the-Air Programming of Wireless Sensor Networks Using Random Linear Codes

Over-the-air programming (OAP) is a fundamental service in sensor networks that relies upon reliable broadcast for efficient dissemination. As such, existing OAP protocols become decidedly inefficient (with respect to energy, communication or delay) in unreliable broadcast environments, such as those with relatively high node density or noise. In this paper, we consider OAP approaches based on rateless codes, which significantly improve OAP in such environments by drastically reducing the need for packet rebroadcasting. We thus design and implement two rateless OAP protocols, rateless Deluge and ACKless Deluge, both of which replace the data transfer mechanism of the established OAP Deluge protocol with rateless analogs. Experiments with Tmote Sky motes on single-hop networks with packet loss rates of 7% show these protocols to save significantly in communication over regular Deluge (roughly 15-30% savings in the data plane, and 50-80% in the control plane), and multi-hop experiments reveal similar trends. Simulations further shows that our new protocols scale better than standard Deluge (in terms of communication and energy) to high network density. TinyOS code for our implementation can be found at http://nislab.bu.edu.

Robust location detection in emergency sensor networks

We propose a new framework for providing robust location detection in emergency response systems, based on the theory of identifying codes. The key idea of this approach is to allow sensor coverage areas to overlap in such a way that each resolvable position is covered by a unique set of sensors. In this setting, determining a sensor-placement with a minimum number of sensors is equivalent to constructing an optimal identifying code, an NP-complete problem in general. We thus propose and analyze a new polynomial-time algorithm for generating irreducible codes for arbitrary topologies. We also generalize the concept of identifying codes to incorporate robustness properties that are critically needed in emergency networks and provide a polynomial-time algorithm to compute irreducible robust identifying codes. Through analysis and simulation, we show that our approach typically requires significantly fewer sensors than existing proximity-based schemes. Alternatively, for a fixed number of sensors, our scheme can provide robustness in the face of sensor failures or physical damage to the system.

Which codes have cycle-free Tanner graphs?

If a linear block code C of length n has a Tanner graph without cycles, then maximum-likelihood soft-decision decoding of C can be achieved in time O(n/sup 2/). However, we show that cycle-free Tanner graphs cannot support good codes. Specifically, let C be an (n,k,d) linear code of rate R=k/n that can be represented by a Tanner graph without cycles. We prove that if R/spl ges/0.5 then d/spl les/2, while if R<0.5 then C is obtained from a code of rate /spl ges/0.5 and distance /spl les/2 by simply repeating certain symbols. In the latter case, we prove that d/spl les/[n/k+1]+[n+1/k+1]<2/R. Furthermore, we show by means of an explicit construction that this bound is tight for all values of n and k. We also prove that binary codes which have cycle-free Tanner graphs belong to the class of graph-theoretic codes, known as cut-set codes of a graph. Finally, we discuss the asymptotics for Tanner graphs with cycles, and present a number of open problems for future research.

On the scalability of data synchronization protocols for PDAs and mobile devices

Personal digital assistants and other mobile computing devices rely on synchronization protocols in order to maintain data consistency. These protocols operate in environments where network resources such as bandwidth, memory and processing power are limited. We examine a number of popular and representative synchronization protocols, such as Palms HotSync, Pumatechs Intellisync and the industry-wide SyncML initiative. We investigate the scalability performance of these protocols as a function of data and network sizes and compare them to a novel synchronization approach, CPISync, which addresses some of their scalability concerns. The conclusions of this survey are intended to provide guidance for handling scalability issues in synchronizing data on large, heterogeneous, tetherless networks.

Robust location detection with sensor networks

We propose a novel framework for location detection with sensor networks, based on the theory of identifying codes. The key idea of this approach is to allow sensor coverage areas to overlap so that each resolvable position is covered by a unique set of sensors. In this setting, determining a sensor-placement with a minimum number of sensors is equivalent to constructing an optimal identifying code, an NP-complete problem in general. We, thus, propose and analyze new polynomial-time algorithms for generating irreducible (but not necessarily optimal) codes for arbitrary topologies. Our algorithms incorporate robustness properties that are critically needed in harsh environments. We further introduce distributed versions of these algorithms, allowing sensors to self-organize and determine a (robust) identifying code without any central coordination. Through analysis and simulation, we show that our algorithms produce nearly optimal solutions for a wide range of parameters. In addition, we demonstrate a tradeoff between system robustness and the number of active sensors (which is related to the expected lifetime of the system). Finally, we present experimental results, obtained on a small testbed, that demonstrate the feasibility of our approach.

Rateless Coding with Feedback

The erasure resilience of rateless codes, such as Luby-Transform (LT) codes, makes them particularly suitable to a wide variety of loss-prone wireless and sensor network applications, ranging from digital video broadcast to software updates. Yet, traditional rateless codes usually make no use of a feedback communication channel, a feature available in many wireless settings. As such, we generalize LT codes to situations where receiver(s) provide feedback to the broadcaster. Our approach, referred to as Shifted LT (SLT) code, modifies the robust soliton distribution of LT codes at the broadcaster, based on the number of input symbols already decoded at the receivers. While implementing this modification entails little change to the LT encoder and decoder, we show both analytically and through real experiments, that it achieves significant savings in communication complexity, memory usage, and overall energy consumption. Furthermore, we show that significant savings can be even achieved with a low number of feedback messages (on the order of the square root of the total number of input symbols) transmitted at a uniform rate. The practical benefits of Shifted LT codes are demonstrated through the implementation of a real over-the-air programming application for sensor networks, based on the Deluge protocol.

Identifying Codes and Covering Problems

The identifying code problem for a given graph involves finding a minimum set of vertices whose neighborhoods uniquely overlap at any given graph vertex. Initially introduced in 1998, this problem has demonstrated its fundamental nature through a wide variety of applications, such as fault diagnosis, location detection, and environmental monitoring, in addition to deep connections to information theory, superimposed and covering codes, and tilings. This work establishes efficient reductions between the identifying code problem and the well-known set-covering problem, resulting in a tight hardness of approximation result and novel, provably tight polynomial-time approximations. The main results are also extended to r -robust identifying codes and analogous set (2r+1)-multicover problems. Finally, empirical support is provided for the effectiveness of the proposed approximations, including good constructions for well-known topologies such as infinite two-dimensional grids.

Fast data access over asymmetric channels using fair and secure bandwidth sharing

We propose a peer-to-peer architecture designed to overcome asymmetries in upload/download speeds that are typical in end-user dialup, broadband and cellular wireless Internet connections. Our approach allows users at remote locations to access information stored on their home computers at rates often exceeding their home connection’s upload capacity. The key to this approach is to share file data when communications are idle using random linear coding, so that, when needed, an end-user can download a file from several sources at a higher data rate than his home computer’s upload capacity. We prove that our proposed system is asymptotically fair, in that (even malicious) users are proportionally assigned idle bandwidth depending on how much bandwidth they contribute, and that there is a natural incentive to join and cooperate fairly in the system. In addition, our approach provides cryptographic security and geographic data robustness to the participating peers.

An Implementation of Indoor Location Detection Systems Based on Identifying Codes

We present the design, implementation and evaluation of a location detection system built over a Radio Frequency network based on the IEEE 802.11 standard. Our system employs beacons to broadcast identifying packets from strategic positions within a building infrastructure in such a way that each resolvable position is covered by a unique collection of beacons; a user of such a system can thus determine his location by means of the beacon packets received. The locations from which beacons broadcast is determined from a formalization of the problem based on identifying codes over arbitrary graphs. We present experimental evidence that our location detecting system is practical and useful, and that it can achieve good accuracy even with a very small number of beacons.