Nicholas B. Chang

Revisiting the TTL-based controlled flooding search: optimality and randomization

In this paper we consider the problem of searching for a node or an object (i.e., piece of data, file, etc.) in a large network. Applications of this problem include searching for a destination node in a mobile ad hoc network, querying for a piece of desired data in a wireless sensor network, and searching for a shared file in an unstructured peer-to-peer network. We limit our attention in this study to the class of controlled flooding search strategies where query/search packets are broadcast and propagated in the network until a preset TTL (time-to-live) value carried in the packet expires. Every unsuccessful search attempt results in an increased TTL value (i.e., larger search area) and the same process is repeated. The primary goal of this study is to derive search strategies (i.e., sequences of TTL values) that will minimize the cost of such searches associated with packet transmissions. The main results of this paper are as follows. When the probability distribution of the location of the object is known a priori, we present a dynamic programming formulation with which optimal search strategies can be derived that minimize the expected search cost. We also derive the necessary and sufficient conditions %on the location distribution for two very commonly used search strategies to be optimal. When the probability distribution of the location of the object is not known a priori and the object is to minimize the worst-case search cost, we show that the best strategies are randomized strategies, i.e., successive TTL values are chosen from certain probability distributions rather than deterministic values. We show that given any deterministic TTL sequence, there exists a randomized version that has a lower worst-case expected search cost. We also derive an asymptotically (as the network size increases) optimal strategy within a class of randomized strategies.

Optimal channel probing and transmission scheduling for opportunistic spectrum access

In this study, we consider optimal opportunistic spectrum access (OSA) policies for a transmitter in a multichannel wireless system, where a channel can be in one of multiple states. In such systems, the transmitter typically does not have complete information on the channel states, but can learn by probing individual channels at the expense of certain resources, e.g., energy and time. The main goal is to derive optimal strategies for determining which channels to probe, in what sequence, and which channel to use for transmission. We consider two problems within this context and show that they are equivalent to different data maximization and throughput maximization problems. For both problems, we derive key structural properties of the corresponding optimal strategy. In particular, we show that it has a threshold structure and can be described by an index policy.We further show that the optimal strategy for the first problem can only take one of three structural forms. Using these results, we first present a dynamic program that computes the optimal strategy within a finite number of steps, even when the state space is uncountably infinite. We then present and examine a more efficient, but suboptimal, two-step look-ahead strategy for each problem. These strategies are shown to be optimal for a number of cases of practical interest. We examine their performance via numerical studies.

Controlled flooding search in a large network

In this paper, we consider the problem of searching for a node or an object (i.e., piece of data, file, etc.) in a large network. Applications of this problem include searching for a destination node in a mobile ad hoc network, querying for a piece of desired data in a wireless sensor network, and searching for a shared file in an unstructured peer-to-peer network. We consider the class of controlled flooding search strategies where query/search packets are broadcast and propagated in the network until a preset time-to-live (TTL) value carried in the packet expires. Every unsuccessful search attempt, signified by a timeout at the origin of the search, results in an increased TTL value (i.e., larger search area) and the same process is repeated until the object is found. The primary goal of this study is to find search strategies (i.e., sequences of TTL values) that will minimize the cost of such searches associated with packet transmissions. Assuming that the probability distribution of the object location is not known a priori, we derive search strategies that minimize the search cost in the worst-case, via a performance measure in the form of the competitive ratio between the average search cost of a strategy and that of an omniscient observer. This ratio is shown in prior work to be asymptotically (as the network size grows to infinity) lower bounded by 4 among all deterministic search strategies. In this paper, we show that by using randomized strategies (i.e., successive TTL values are chosen from certain probability distributions rather than deterministic values), this ratio is asymptotically lower bounded by e. We derive an optimal strategy that achieves this lower bound, and discuss its performance under other criteria. We further introduce a class of randomized strategies that are sub-optimal but potentially more useful in practice

Competitive Analysis of Opportunistic Spectrum Access Strategies

We consider opportunistic spectrum access (OSA) strategies for a transmitter in a multichannel wireless system, where a channel may or may not be available and the transmitter must sense/probe the channel to find out before transmission. Applications for this work include joint probing and transmission for a secondary user in a cognitive radio network. Limited by resources, e.g., energy and time, the transmitter must decide on a subset of a potentially very large number of channels to probe and can only use for transmission those that have been found to be available. In contrast to previous works, we do not assume the user has a priori knowledge regarding the statistics of channel states. The main goal of this work is to design strategies that decide, based only on knowledge of the channel bandwidths/data rates, which channels to probe. We derive optimal strategies that maximize the total expected bandwidth/data rate in the worst-case, via a performance measure in the form of a competitive regret (ratio) between the average performance of a strategy and a genie (or omniscient observer). We examine the performance of these optimal strategies under a wide range of system parameters and practical channel models via numerical studies.

MIMO wireless communication channel phenomenology

Wireless communication using multiple-input multiple-output (MIMO) systems enables increased spectral efficiency and link reliability for a given total transmit power. Increased capacity is achieved by introducing additional spatial channels which are exploited using space-time coding. The spatial diversity improves the link reliability by reducing the adverse effects of link fading and shadowing. The choice of coding and the resulting performance improvement are dependent upon the channel phenomenology. In this paper, experimental channel-probing estimates are reported for outdoor environments near the personal communication services frequency allocation (1790 MHz). A simple channel parameterization is introduced. Channel distance metrics are introduced. Because the bandwidth of the channel-probing signal (1.3 MHz) is sufficient to resolve some delays in outdoor environments, frequency-selective fading is also investigated. Channel complexity and channel stationarity are investigated. Complexity is associated with channel-matrix singular value distributions. Stationarity is associated with the stability of channel singular value and singular vector structure over time.

Optimal controlled flooding search in a large wireless network

In this paper we consider the problem of searching for a node or an object (i.e., piece of data, file, etc.) in a large wireless network. We consider the class of controlled flooding search strategies where query/search packets are broadcast and propagated in the network until a preset TTL (time-to-live) value carried in the packet expires. Every unsuccessful search attempt results in an increased TTL value (i.e., larger search area) and the same process is repeated. We derive search strategies that minimize the search cost in the worst-case, via a performance measure in the form of the competitive ratio between the average search cost of a strategy and that of an omniscient observer. This ratio is shown in prior work to be lower bounded by 4 among all deterministic search strategies. In this paper we show that by using randomized strategies this ratio is lower bounded by e. We derive an optimal strategy that achieves this lower bound, and discuss its performance under other performance criteria.

Rate adaptive non-binary LDPC codes with low encoding complexity

For error-correction codes, the optimal coding rate can vary and depend on factors including channel, time-varying fading, environmental interference, power, bandwidth allocation, communication content, and application. Rate adaptive coding schemes are thus important for robust communications. This writeup proposes and studies a rate adaptive low density parity check (LDPC) coding scheme using non-binary Galois fields (GF). The algorithm uses a single low complexity encoding structure, but maintains strong near-capacity performance at arbitrary rational rates. The rate adaptive encoder can be used in a space-time code for multiple-input multiple-output (MIMO) communication systems and is shown to achieve near capacity performance at various rates and different MIMO configurations.

Optimal Competitive Algorithms for Opportunistic Spectrum Access

We consider opportunistic spectrum access (OSA) strategies for a transmitter in a multichannel wireless system, where a channel may or may not be available and the transmitter must sense/probe the channel to find out before transmission. Applications for this work include joint probing and transmission for a secondary user in a cognitive radio network. Limited by resources, e.g., energy and time, the transmitter must decide on a subset of a potentially very large number of channels to probe and can only use for transmission those that have been found to be available. In contrast to previous works, we do not assume the user has a priori knowledge regarding the statistics of channel states. The main goal of this work is to design robust strategies that decide, based only on knowledge of the channel bandwidths/data rates, which channels to probe. We derive optimal strategies that maximize the total expected bandwidth/data rate in the worst-case, via a performance measure in the form of a competitive regret (ratio) between the average performance of a strategy and a genie (or omniscient observer). This formulation can also be viewed as a two-player zero-sum game between the user and an adversary which chooses the channel state that minimizes the useriquests gain. We show that our results correspond to a Nash equilibrium (in the form of a mixed strategy) in this game. We examine the performance of the optimal strategies under a wide range of system parameters and practical channel models via numerical studies.

Sequential decoding of non-binary LDPC codes on graphics processing units

Non-binary low-density parity-check (LDPC) codes have been shown to attain near capacity error correcting performance in noisy wireless communication channels. It is well known that these codes require a very large number of operations per-bit to decode. This high computational complexity along with a parallel decoder structure makes graphics processing units (GPUs) an attractive platform for acceleration of the decoding algorithm. The seemingly random memory access patterns associated with decoding are generally beneficial to error-correcting performance but present a challenge to designers who want to leverage the computational capabilities of the GPU. In this paper we describe the design of an efficient decoder implementation based on GPUs and a corresponding set of powerful non-binary LDPC codes. Using the belief propagation algorithm with a sequential message updating scheme it is shown that we are able to exploit parallelism inherent in the decoding algorithm while decreasing the number of decoding iterations required for convergence.

Controlled Flooding Search with Delay Constraints

In this paper we consider the problem of query and search in a network, e.g., searching for a specific node or a piece of data. We limit our attention to the class of TTL (time-to-live) based controlled flooding search strategies where query/search packets are broadcast and relayed in the network until a preset TTL value carried in the packet expires. Every unsuccessful search attempt results in an increased TTL value (i.e., larger search area) and the same process is repeated. Every search attempt also incurs a cost (in terms of packet transmissions and receptions) and a delay (time till timeout or till the target is found). The primary goal is to derive search strategies (i.e., sequences of TTL values) that minimize a worstcase cost measure subject to a worst-case delay constraint. We present a constrained optimization framework and derive a class of optimal strategies, shown to be randomized strategies, and obtain their performance as a function of the delay constraint. We also use these results to discuss the trade-off between search cost and delay within the context of flooding search.