Mohammad Naghshvar

Adaptive opportunistic routing for wireless ad hoc networks

A distributed adaptive opportunistic routing scheme for multihop wireless ad hoc networks is proposed. The proposed scheme utilizes a reinforcement learning framework to opportunistically route the packets even in the absence of reliable knowledge about channel statistics and network model. This scheme is shown to be optimal with respect to an expected average per-packet reward criterion. The proposed routing scheme jointly addresses the issues of learning and routing in an opportunistic context, where the network structure is characterized by the transmission success probabilities. In particular, this learning framework leads to a stochastic routing scheme that optimally “explores” and “exploits” the opportunities in the network.

Opportunistic Routing with Congestion Diversity in Wireless Multi-hop Networks

This paper considers the problem of routing packets across a multi-hop network consisting of multiple sources of traffic and wireless links with stochastic reliability while ensuring bounded expected delay. Each packet transmission can be overheard by a random subset of receiver nodes among which the next relay is selected opportunistically. The main challenge in the design of minimum-delay routing policies is balancing the trade-off between routing the packets along the shortest paths to the destination and distributing traffic across the network. Opportunistic variants of shortest path routing may, under heavy traffic scenarios, result in severe congestion and unbounded delay. While the opportunistic variants of backpressure, which ensure a bounded expected delay, are known to exhibit poor delay performance at low to medium traffic conditions. Combining important aspects of shortest path routing with those of backpressure routing, this paper provides an opportunistic routing policy with congestion diversity (ORCD). ORCD uses a measure of draining time to opportunistically identify and route packets along the paths with an expected low overall congestion. Previously, ORCD was proved to ensure a bounded expected delay for all networks and under any admissible traffic (without any knowledge of traffic statistics). This paper proposes practical implementations and discusses criticality of various aspects of the algorithm. Furthermore, the expected delay encountered by the packets in the network under ORCD is compared against known existing routing policies via simulations where substantial improvements are observed.

Sequentiality and Adaptivity Gains in Active Hypothesis Testing

Consider a decision maker who is responsible to collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest. The policies under which the decision maker selects sensing actions can be categorized based on the following two factors: i) sequential versus non-sequential; ii) adaptive versus non-adaptive. Non-sequential policies collect a fixed number of observation samples and make the final decision afterwards; while under sequential policies, the sample size is not known initially and is determined by the observation outcomes. Under adaptive policies, the decision maker relies on the previous collected samples to select the next sensing action; while under non-adaptive policies, the actions are selected independent of the past observation outcomes. In this paper, performance bounds are provided for the policies in each category. Using these bounds, sequentiality gain and adaptivity gain, i.e., the gains of sequential and adaptive selection of actions are characterized.

Extrinsic Jensen–Shannon Divergence: Applications to Variable-Length Coding

This paper considers the problem of variable-length coding over a discrete memoryless channel with noiseless feedback. This paper provides a stochastic control view of the problem whose solution is analyzed via a newly proposed symmetrized divergence, termed extrinsic Jensen-Shannon (EJS) divergence. It is shown that strictly positive lower bounds on EJS divergence provide nonasymptotic upper bounds on the expected code length. This paper presents strictly positive lower bounds on EJS divergence, and hence nonasymptotic upper bounds on the expected code length, for the following two coding schemes: 1) variable-length posterior matching and 2) MaxEJS coding scheme that is based on a greedy maximization of the EJS divergence. As an asymptotic corollary of the main results, this paper also provides a rate-reliability test. Variable-length coding schemes that satisfy the condition(s) of the test for parameters R and E are guaranteed to achieve a rate R and an error exponent E. The results are specialized for posterior matching and MaxEJS to obtain deterministic one-phase coding schemes achieving capacity and optimal error exponent. For the special case of symmetric binary-input channels, simpler deterministic schemes of optimal performance are proposed and analyzed.

A General Class of Throughput Optimal Routing Policies in Multi-Hop Wireless Networks

This paper considers the problem of throughput optimal routing/scheduling in a multi-hop constrained queueing network with random connectivity whose special cases include opportunistic multi-hop wireless networks and input-queued switch fabrics. The main challenge in the design of throughput optimal routing policies is closely related to identifying appropriate and universal Lyapunov functions with negative expected drift. The few well-known throughput optimal policies in the literature are constructed using simple quadratic or exponential Lyapunov functions of the queue backlogs and as such they seek to balance the queue backlogs across network independent of the topology. By considering a class of continuous, differentiable, and piece-wise quadratic Lyapunov functions, this paper provides a large class of throughput optimal routing policies. The proposed class of Lyapunov functions allow for the routing policy to control the traffic along short paths for a large portion of state-space while ensuring a negative expected drift. This structure enables the design of a large class of routing policies. In particular, and in addition to recovering the throughput optimality of the well-known backpressure routing policy, an opportunistic routing policy with congestion diversity is proved to be throughput optimal.

Extrinsic Jensen-Shannon divergence with application in active hypothesis testing

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest while accounting for the penalty of wrong declarations. In this paper, Extrinsic Jensen-Shannon (EJS) divergence is introduced as a measure of information. Using EJS as an information utility, a heuristic policy for selecting actions is proposed. Via numerical and asymptotic optimality analysis, the performance of the proposed policy, hence the applicability of the EJS divergence in the context of the active hypothesis testing is investigated.

An adaptive opportunistic routing scheme for wireless ad-hoc networks

In this paper, an adaptive opportunistic routing scheme for multi-hop wireless ad-hoc networks is proposed. The proposed scheme utilizes a reinforcement learning framework to achieve the optimal performance even in the absence of reliable knowledge about channel statistics and network model. This scheme is shown to be optimal with respect to an expected average per packet cost criterion. The proposed routing scheme jointly addresses the issues of learning and routing in an opportunistic context, where the network structure is characterized by the transmission success probabilities. In particular, this learning framework leads to a stochastic routing scheme which optimally “explores” and “exploits” the opportunities in the network.

Performance bounds for active sequential hypothesis testing

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest while accounting for the cost of data collection. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively (re-)evaluate the tradeoff between the cost of various sensing actions and the precision of their outcomes. In this paper, using results in dynamic programming, a lower bound for the optimal total cost is established. Moreover, an upper bound is obtained using a heuristic policy for dynamic selection of actions. Using the obtained bounds, the closed loop (feedback) gain is shown to be at least logarithmic in the penalty associated with wrong declarations. Furthermore, it is shown that the proposed heuristic achieves asymptotic optimality in many practically relevant problems such as variable-length coding with feedback and noisy dynamic search.

Information utility in active sequential hypothesis testing

This paper considers a broad spectrum of applications in cognition, communications, design of experiments, and sensor management. In all of these applications, a decision maker is responsible to control the system dynamically so as to enhance his information in a speedy manner about an underlying phenomena of interest while accounting for the cost of communication, sensing, or data collection. In addition, due to the sequential nature of the problem, the decision maker relies on his current information state to constantly (re-)evaluate the information utility of various actions. In this paper, using a dynamic programming interpretation, an optimal notion of information utility is derived. Inspired by this view of the problem, a set of heuristic policies for dynamic selection of actions are proposed. The construction of these heuristics relate various notions of information utility with the statistical properties of the outcome, such as Kullback-Leibler divergence and mutual information. Via numerical and asymptotic analysis, the performance of these policies, hence the utility of the statistical quantities such as divergence and mutual information, in the context of the active hypothesis testing is investigated.

Opportunistic routing with congestion diversity and tunable overhead

This paper considers the problem of routing packets across a multi-hop network consisting of multiple sources of traffic and wireless links with stochastic reliability and a broadcast nature. Opportunistic routing relies on the following principle. Each packet transmission can be overheard by a random subset of receiver nodes among which the next relay can be selected opportunistically. This paper surveys and revisits known opportunistic routing policies: Opportunistic variants of shortest path routing, such as extremely opportunistic routing (ExOR) and stochastic routing (SR), select the relay on the shortest path to the destination. The opportunistic variants of backpressure routing, such as diversity backpressure routing (DIVBAR), select the relay with the least queue backlog. In an enhanced version of DIVBAR (E-DIVBAR), a combination of queue backlogs and expected number of transmissions is used as the selection criterion. Finally, combining important aspects of shortest path routing with those of backpressure routing, opportunistic routing with congestion diversity (ORCD) uses a measure of draining time to opportunistically identify and route packets along the paths with an expected low overall congestion. One of the critical aspects of the design of opportunistic routing policies is the issue of control overhead. This paper considers the issue of performance in conjunction with the additional overhead cost. In particular, modifications of the routing policies for which overhead cost is traded-off with the performance, i.e. delay, are provided and compared via simulations. In addition to the overhead associated with opportunism, ORCD requires a high computation/control overhead associated with estimating the draining time. Various modifications to ORCD are also proposed and their performance and overhead are evaluated.