Supratim Deb

Algebraic gossip: a network coding approach to optimal multiple rumor mongering

The problem of simultaneously disseminating k messages in a large network of n nodes, in a decentralized and distributed manner, where nodes only have knowledge about their own contents, is studied. In every discrete time-step, each node selects a communication partner randomly, uniformly among all nodes and only one message can be transmitted. The goal is to disseminate rapidly, with high probability, all messages to all nodes. It is shown that a random linear coding (RLC) based protocol disseminates all messages to all nodes in time ck+/spl Oscr/(/spl radic/kln(k)ln(n)), where c<3.46 using pull-based dissemination and c<5.96 using push-based dissemination. Simulations suggest that c<2 might be a tighter bound. Thus, if k/spl Gt/(ln(n))/sup 3/, the time for simultaneous dissemination RLC is asymptotically at most ck, versus the /spl Omega/(klog/sub 2/(n)) time of sequential dissemination. Furthermore, when k/spl Gt/(ln(n))/sup 3/, the dissemination time is order optimal. When k/spl Lt/(ln(n))/sup 2/, RLC reduces dissemination time by a factor of /spl Omega/(/spl radic/k/lnk) over sequential dissemination. The overhead of the RLC protocol is negligible for messages of reasonable size. A store-and-forward mechanism without coding is also considered. It is shown that this approach performs no better than a sequential approach when k=/spl prop/n. Owing to the distributed nature of the system, the proof requires analysis of an appropriate time-varying Bernoulli process.

Algorithms for Enhanced Inter-Cell Interference Coordination (eICIC) in LTE HetNets

The success of LTE heterogeneous networks (HetNets) with macrocells and picocells critically depends on efficient spectrum sharing between high-power macros and low-power picos. Two important challenges in this context are: 1) determining the amount of radio resources that macrocells should offer to picocells, and 2) determining the association rules that decide which user equipments (UEs) should associate with picos. In this paper, we develop a novel algorithm to solve these two coupled problems in a joint manner. Our algorithm has provable guarantee, and furthermore, it accounts for network topology, traffic load, and macro-pico interference map. Our solution is standard compliant and can be implemented using the notion of Almost Blank Subframes (ABS) and Cell Selection Bias (CSB) proposed by LTE standards. We also show extensive evaluations using RF plan from a real network and discuss self-optimized networking (SON)-based enhanced inter-cell interference coordination (eICIC) implementation.

Real-Time Video Multicast in WiMAX Networks

IEEE 802.16e WiMAX is a promising new technology for broadband access networks. Amongst the class of applications that can be supported is real time video services (such as IPTV, broadcast of live events etc.). These applications are bandwidth hungry and have stringent delay constraints. Thus, scalable support for such applications is a challenging problem. To address this challenge, we consider a combination of approaches using multicast, layer encoded video and adaptive modulation of transmissions. Using these, we develop algorithms to ensure efficient, fair and timely delivery of video in WiMAX networks. The corresponding resource allocation problem is challenging because scheduling decisions (within a WiMAX base station) are performed in real-time across two dimensions, time and frequency. Moreover, combining layered video with appropriate modulation calls for novel MAC algorithms. We model the multicast resource allocation problem in WiMAX and demonstrate this problem to be NP-hard. We present a fast greedy algorithm that is (i) provably within a constant approximation of the optimal solution (based on a metric that reflects video quality as perceived by the user), and (ii) performs within 87-95% of the optimal as demonstrated by realistic simulations. We also demonstrate that our algorithm offers a 25% improvement over a naive algorithm. Moreover, in terms of the average rate received by each user, our algorithm out-performs the naive algorithm by more than 50%.

Global stability of congestion controllers for the Internet

We consider a single link accessed by a single source which responds to congestion signals from the network. The design of controllers for such sources in the presence of feedback delay has received much attention recently. Here, we present conditions for the global, asymptotic stability and semiglobal exponential stability of congestion controllers. These conditions are natural extensions of conditions obtained through linearized analysis of such systems. Our result on exponential stability provides the missing link in the proof of how one obtains a single deterministic congestion control equation from a system with many congestion-controlled sources and random disturbances. Using numerical examples, we compare the conditions on the congestion-control parameters obtained using local and global stability analysis.

Dynamic spectrum access in DTV whitespaces: design rules, architecture and algorithms

In November 2008, the FCC ruled that the digital TV whitespaces be used for unlicensed access. This is an exciting development because DTV whitespaces are in the low frequency range (50-698 MHz) compared to typical cellular and ISM bands, thus resulting in much better propagation characteristics and much higher spectral efficiencies. The FCC has also mandated certain guidelines for short range unlicensed access, so as to avoid any interference to DTV receivers. We consider the problem of WiFi like access (popularly referred to as WiFi 2.0) for enterprizes. We assume that the access points and client devices are equipped with cognitive radios, i.e., they can adaptively choose the center frequency, bandwidth and ower of operation. The access points can be equipped with one or more radios. Our goal is to design a complete system, which (i) does not violate the FCC mandate, (ii) dynamically assigns center frequency and bandwidth to each access point based on their demands and (iii) squeezes the maximum efficiency from the available spectrum. This problem is far more general than prior work that investigated dynamic spectrum allocation in cellular and ISM bands, due to the non-homogenous nature of the whitespaces, i.e., different whitespace widths in different parts of the spectrum and the large range of frequency bands with different propagation characteristics. This calls for a more holistic approach to system design that also accounts for frequency dependent propagation characteristics and radio frontend characteristics. In this paper, we first propose design rules for holistic system design. We then describe an architecture derived from our design rules. Finally we propose demand based dynamic spectrum allocation algorithms with provable worst case guarantees. We provide extensive simulation results showing that (i) the performance of our algorithm is within 94% of the optimal in typical settings and (ii) and the DTV whitespaces can provide significantly higher data rates compared to the 2.4GHz ISM band. Our approach is general enough for designing any system with access to a wide range of spectrum.

WiMAX relay networks: opportunistic scheduling to exploit multiuser diversity and frequency selectivity

We study the problem of scheduling in OFDMA-based relay networks with emphasis on IEEE 802.16j based WiMAX relay networks. In such networks, in addition to a base station, multiple relay stations are used for enhancing the throughput, and/or improving the range of the base station. We solve the problem of MAC scheduling in such networks so as to serve the mobiles in a fair manner while exploiting the multiuser diversity, as well as the frequency selectivity of the wireless channel. The scheduling resources consist of tiles in a two-dimensional scheduling frame with time slots along one axis, and frequency bands or sub-channels along the other axis. The resource allocation problem has to be solved once every scheduling frame which is about 5 - 10 ms long. While the original scheduling problem is computationally complex, we provide an easy-to-compute upper bound on the optimum. We also propose three fast heuristic algorithms that perform close to the optimum (within 99.5%), and outperform other algorithms such as OFDM2A proposed in the past. Through extensive simulation results, we demonstrate the benefits of relaying in throughput enhancement (an improvement in the median throughput of about 25%), and feasibility of range extension (for e.g., 7 relays can be used to extend the cell-radius by 60% but mean throughput reduces by 36%). Our algorithms are easy to implement, and have an average running time of less than 0.05 ms making them appropriate for WiMAX relay networks.

Global stability of congestion controllers for the internet

We consider a single link accessed by a single source which responds to congestion signals from the network. The design of controllers for such sources in the presence of feedback delay has received much attention recently. In this paper we present conditions for the global, asymptotic stability and semi-global exponential stability of congestion controllers which are natural extensions of earlier linearized analysis of such systems. Our result on exponential stability provides the missing link in the proof of how one obtains a single deterministic congestion control equation from a system with many congestion-controlled sources and random disturbances. Using numerical examples, we compare the conditions on the congestion-control parameters obtained using local and global stability analysis.

Efficient gossip-based aggregate computation

Recently, there has been a growing interest in gossip-based protocols that employ randomized communication to ensure robust information dissemination. In this paper, we present a novel gossip-based scheme using which all the nodes in an n-node overlay network can compute the common aggregates of MIN, MAX, SUM, AVERAGE, and RANK of their values using O(n log log n) messages within O(log n log log n) rounds of communication. To the best of our knowledge, ours is the first result that shows how to compute these aggregates with high probability using only O(n log log n) messages. In contrast, the best known gossip-based algorithm for computing these aggregates requires O(nlog n) messages and O(log n) rounds. Thus, our algorithm allows system designers to trade off a small increase in round complexity with a significant reduction in message complexity. This can lead to dramatically lower network congestion and longer node lifetimes in wireless and sensor networks, where channel bandwidth and battery life are severely constrained.

Efficient Detection of Distributed Constraint Violations

In many distributed environments, the primary function of monitoring software is to detect anomalies, i.e., instances when system behavior deviates substantially from the norm. In this paper, we propose communication-efficient schemes for the anomaly detection problem, which we model as one of detecting the violation of global constraints defined over distributed system variables. Our approach eliminates the need to continuously track the global system state by decomposing global constraints into local constraints that can be checked efficiently at each site. Only in the occasional event that a local constraint is violated, do we resort to more expensive global constraint checking. We show that the problem of selecting the local constraints, based on frequency distribution of individual system variables, so as to minimize the communication cost is NP-hard. We propose approximation algorithms for computing provably near-optimal (in terms of the number of messages) local constraints. Experimental results with real-life network traffic data sets demonstrate that our technique can reduce message communication overhead by as much as 70% compared to existing data distribution-agnostic approaches.

On random network coding based information dissemination

We study the gains to be had by using random linear coding (RLC) for simultaneously disseminating k distinct messages in a network of n nodes in a decentralized and distributed manner for arbitrary k and n. The goal is to rapidly disseminate all the messages among all the nodes. Any node can communicate with any of the other nodes but only one at a time, nodes only have knowledge about their own contents, and the bandwidth for every transmission between two nodes is limited (does not scale with k or n). An efficient and well-studied protocol for message dissemination in such a framework is randomized gossip based message dissemination. The problem has been studied extensively without using any coding for message dissemination. We show using analysis and simulation that, in the regime k ges (ln(n))3, RLC based dissemination reduces the dissemination time (the time-steps to disseminate all the messages among all the nodes) by a factor of otimes(ln(n)) as compared to disseminating the messages sequentially (i.e., one after the other) as implicit in most non-coding based technique. In the regime k les (ln(n))2, the dissemination time with RLC goes down by a factor of Omega(radick / ln k). More precisely, our results indicate that a RLC based protocol disseminates all the messages among all the nodes in time ck + O(radick ln(k)(ln(n)) for a suitable constant c > 0. Analytical results show that, c < 3.46 using pull based dissemination, and c < 5.96 using push based dissemination, but reported simulations suggest c < 2 might be a tighter bound