50 research outputs found

    On the Entropy Region of Discrete and Continuous Random Variables and Network Information Theory

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    We show that a large class of network information theory problems can be cast as convex optimization over the convex space of entropy vectors. A vector in 2^(n) - 1 dimensional space is called entropic if each of its entries can be regarded as the joint entropy of a particular subset of n random variables (note that any set of size n has 2^(n) - 1 nonempty subsets.) While an explicit characterization of the space of entropy vectors is well-known for n = 2, 3 random variables, it is unknown for n > 3 (which is why most network information theory problems are open.) We will construct inner bounds to the space of entropic vectors using tools such as quasi-uniform distributions, lattices, and Cayley's hyperdeterminant

    Normalized Entropy Vectors, Network Information Theory and Convex Optimization

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    We introduce the notion of normalized entropic vectors -- slightly different from the standard definition in the literature in that we normalize entropy by the logarithm of the alphabet size. We argue that this definition is more natural for determining the capacity region of networks and, in particular, that it smooths out the irregularities of the space of non-normalized entropy vectors and renders the closure of the resulting space convex (and compact). Furthermore, the closure of the space remains convex even under constraints imposed by memoryless channels internal to the network. It therefore follows that, for a large class of acyclic memoryless networks, the capacity region for an arbitrary set of sources and destinations can be found by maximization of a linear function over the convex set of channel-constrained normalized entropic vectors and some linear constraints. While this may not necessarily make the problem simpler, it certainly circumvents the "infinite-letter characterization" issue, as well as the nonconvexity of earlier formulations, and exposes the core of the problem. We show that the approach allows one to obtain the classical cutset bounds via a duality argument. Furthermore, the approach readily shows that, for acyclic memoryless wired networks, one need only consider the space of unconstrained normalized entropic vectors, thus separating channel and network coding -- a result very recently recognized in the literature

    Wireless Throughput and Energy Efficiency under QoS Constraints

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    Mobile data traffic has experienced unprecedented growth recently and is predicted to grow even further over the coming years. As one of the main driving forces behind this growth, wireless transmission of multimedia content has significantly increased in volume and is expected to be the dominant traffic in data communications. Such wireless multimedia traffic requires certain quality-of-service (QoS) guarantees. With these motivations, in the first part of the thesis, throughput and energy efficiency in fading channels are studied in the presence of randomly arriving data and statistical queueing constraints. In particular, Markovian arrival models including discrete-time Markov, Markov fluid, and Markov-modulated Poisson sources are considered, and maximum average arrival rates in the presence of statistical queueing constraints are characterized. Furthermore, energy efficiency is analyzed by determining the minimum energy per bit and wideband slope in the low signal-to-noise ratio (SNR) regime. Following this analysis, energy-efficient power adaptation policies in fading channels are studied when data arrivals are modeled as Markovian processes and statistical QoS constraints are imposed. After formulating energy efficiency (EE) as maximum throughput normalized by the total power consumption, optimal power control policies that maximize EE are obtained for different source models. Next, throughput and energy efficiency of secure wireless transmission of delay sensitive data generated by random sources are investigated. A fading broadcast model in which the transmitter sends confidential and common messages to two receivers is considered. It is assumed that the common and confidential data, generated from Markovian sources, is stored in buffers prior to transmission, and the transmitter operates under constraints on buffer/delay violation probability. Under such statistical QoS constraints, the throughput is determined. In particular, secrecy capacity is used to describe the service rate of buffers containing confidential messages. Moreover, energy efficiency is studied in the low signal-to-noise (SNR) regime. In the final part of the thesis, throughput and energy efficiency are addressed considering the multiuser channel models. Five different channel models, namely, multiple access, broadcast, interference, relay and cognitive radio channels, are considered. In particular, throughput regions of multiple-access fading channels are characterized when multiple users, experiencing random data arrivals, transmit to a common receiver under statistical QoS constraints. Throughput regions of fading broadcast channels with random data arrivals in the presence of QoS requirements are studied when power control is employed at the transmitter. It is assumed that superposition coding with power control is performed at the transmitter with interference cancellation at the receivers. Optimal power control policies that maximize the weighted combination of the average arrival rates are investigated in the two-user case. Energy efficiency in two-user fading interference channels is studied when the transmitters are operating subject to QoS constraints. Specifically, energy efficiency is characterized by determining the corresponding minimum energy per bit requirements and wideband slope regions. Furthermore, transmission over a half-duplex relay channel with secrecy and QoS constraints is studied. Secrecy throughput is derived for the half duplex two-hop fading relay system operating in the presence of an eavesdropper. Fundamental limits on the energy efficiency of cognitive radio transmissions are analyzed in the presence of statistical quality of service (QoS) constraints. Minimum energy per bit and wideband slope expressions are obtained in order to identify the performance limits in terms of energy efficiency
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