In this talk, I will talk about our recent work (jointly with Prof. Tong) on the capacity of wireless networks. We will look at the effects of multipacket reception (MPR) capability on the capacity of regular wireless networks. We have obtained the maximum stable packet generation rate for the MPR Manhattan networks under uniform traffic and minimum connectivity. For a network of size N, it is shown that the capacity is K_1 / sqrt{N}, and adding MPR affects the coefficient K_1 of a non-MPR network by no more than 1.6 times. For the same network the stability region of the slotted ALOHA random access protocol with MPR is shown to be K_2 / sqrt{N}, for some constant K_2 < K_1.
For increased connectivity, it is shown that the capacity can be increased further by adding MPR. In the limiting case, in a fully connected network, MPR increases the capacity linearly. These results indicate that minimum connectivity for MPR networks is not necessarily optimal which is in constrast to the results obtained by Gupta and Kumar for the conventional collision channel.
For more information, download our paper.
In this talk, a bidirectional decision feedback equalizer (BiDFE) structure that combines the outputs of a normal mode DFE and a time-reversal mode DFE will be introduced. The performance gains achievable by the use of a BiDFE will be quantified and simulation results demonstrating BER improvements will be provided. The optimization of the tap coefficients of the BiDFE will be considered and closed form solutions provided. It will be shown that an MMSE optimized infinite length BiDFE, under the ideal feedback assumption, attains the matched filter bound.
In response to a sensory stimulus, the brain chain attempts to "classify" or "identify" said stimulus by traversing a path in state space that converges in several probabilistic senses toward a (unique?) equilibrium distribution associated with the stimulus. This is done in a way that reduces the conditional entropy of the stimulus given the response (equivalently, increases the Shannon mutual information between the stimulus and the response) by as much as possible subject an energy constraint. Here, "energy" is metabolic energy plus perhaps certain other valuable resources. More importantly, during this process the local response of relatively densely connected regions of the brain (e.g., V1 in visual cortex) is characterized by maximization of the mutual information between the joint binary spiking processes of the region's afferent and efferent neurons subject to an energy consumption profile constraint.
Widely accepted models consider the spiking, or not, by each efferent neuron in each time slot in such a relatively dense neuronal coalition to be a consequence of whether or not its post-synaptic potential (PSP) exceeds a certain threshold during this slot. Said PSP is modeled as a fixed linear combination of r.v. associated with each of the neuron's synapses, with each of these r.v. multiplied in turn by two independent binary r.v. The first binary r.v. represents a spike, or not, on the axon afferent to the synapse; the second is a so-called "quantal failure" r.v. which, whenever it assumes the value 0, annihilates the would-be contribution to the PSP from a spiking afferent neuron. In a typical relatively dense coalition of neurons, roughly half the synapses are between pairs of neurons in the coalition, one quarter involve afferent neurons that are "bottom up" (i.e., feeding forward) and the reamining quarter involve afferent neurons that are "top down" (i.e., feeding back).
We show that the information-rate-maximizing joint binary process on the afferent neurons produces a joint binary process on the efferent neurons that is effectively first-order Markov, though generally non-homogeneous. This elucidates how latency in neural processing is kept small despite the sizable number of coalitions along the bottom-up and top-down paths. Moreover, each coalition operates at a saddle point in the sense that, although its afferent-to-efferent information rate is maximized subject to the imposed mean energy consumption schedule, said information rate also simultaneously is minimized subject to the achievement of a specified level of fidelity with respect to the aforementioned global goal of equivocation reduction.
Game theory has been developed primarily by the economics research community. As a result, it is optimized for modeling problems in the realm of economics. Applying game theory to telecommunications network design and analysis will require the development of a new set of game theoretic tools. We have developped one such tool which we denote "Games of Population Transition." Games of Population Transition are games in which the set of players is not fixed. New players enter the game via an exogenous stochastic process; the departure of active players is also stochastic, but depends on the actions of the players. This type of game models a communications network scenario in which players enter the network randomly and depart when they have finished their intended task.
In this talk, I will define a game of population transition, motivate and define an equilibrium of such a game, present sufficient conditions for the existence of an equilibrium, and define a notion of stability for these games. I will then apply this game model to a model of Aloha, proving conditions under which Aloha with selfish users is stable. I will then describe our ongoing work examining a more sophisticated Aloha model and developping a model for CSMA within the same framework. Finally I will describe the future directions of this research.
In this talk, the problem of efficiently partitioning forward error protected, pre-encoded video data is introduced for transmission over multiple channels. The partitioning formulation will be clearly defined, which exploits the structure of MPEG video while taking into account the varying channel conditions. Considerations such as latency for video applications will be discussed and approximation algorithms are shown to be well feasible for the problem. Simulation results are to be presented for a variety of channel conditions and for a broad range of source material.
This talk presents a blind, adaptive channel shortening algorithm that is globally convergent, and has a complexity similar to LMS. We relate the cost function to that of the Shortening SNR solution of Melsa et al., and provide simulations to demonstrate the performance of the algorithm.
From standard results in the theory of controlled Markov chains, we know that the optimal controller for this problem satisfies a "separation" property: first compute a probability measure on the state space of the chain (the probability of the system being in any state given the entire history of observations and control actions), then use this measure as the new state based on which the best possible control action is chosen. This measure is sometimes referred to as an "information state". Note that the information state is a random quantity itself, since it is a function of past (random) observations and controls. In this talk, we show how the ergodic behavior of our queueing model is characterized by an invariant measure over all possible information states, and then construct that measure. This last step is not trivial: because of the feedback control loop, none of the standard theorems on the existence of invariant measures for Markov chains are applicable in our context.
To the best of our knowledge, not much is known about controlled queues. The problem is simple: control introduces dependencies that render classical queueing models (based on arrivals and services rates with independent increments) inappropriate. The significance of our results lies in the fact that, by conditioning on information states, we are able to break those dependencies, thus rendering our model analytically tractable.
If time permits, we will also discuss new ongoing work, on applications of these results in the derivation of minimum-delay controllers to stabilize the slotted Aloha protocol, on the design of verifiable MAC protocols for large scale sensor networks, and on performance bounds for TCP/AQM systems.
Joint work with Razvan Cristescu.