Matthew S. Nokleby

Cooperative Power Scheduling for Wireless MIMO Networks

We examine signaling strategies for wireless MIMO networks with interference. Previous approaches have focused on maximizing either individual or total throughput, resulting in an inefficient or potentially unfair allocation of resources. We propose two methods motivated by game-theoretic results. First, we extend the non-cooperative Nash equilibrium proposed in previous literature. Second, we present a cooperative method based on the Nash bargaining solution which provides an axiomatic arbitration scheme. Simulation results show that the Nash bargaining solution provides a fair allocation of resources without significantly sacrificing total throughput.

Lattice Coding over the Relay Channel

It has been conjectured that lattice codes are good for (almost) everything. As an additional bit of evidence for this claim, we offer a few results showing the utility of lattice codes for the AWGN relay channel. We show that the decode-and-forward rates of the relay channel can be achieved using lattice encoding and decoding. We present an encoding/decoding technique that uses a doubly-nested lattice code. Encoding is accomplished using a combination of superposition encoding and block Markov encoding, while decoding is accomplished using a strategy reminiscent of Cover and El Gamals list decoding. Our technique can be extended to a wide variety of relay topologies, including the half-duplex relay channel and the cooperative multiple-access channel.

Toward Resource-Optimal Consensus Over the Wireless Medium

We carry out a comprehensive study of the resource cost of averaging consensus in wireless networks. Most previous approaches suppose a graphical network, which abstracts away crucial features of the wireless medium, and measure resource consumption only in terms of the total number of transmissions required to achieve consensus. Under a path-loss model, we study the resource requirements of consensus with respect to three wireless-appropriate metrics: total transmit energy, elapsed time, and time-bandwidth product. First, we characterize the performance of several popular gossip algorithms, showing that they may be order-optimal with respect to transmit energy but are strictly suboptimal with respect to elapsed time and time-bandwidth product. Further, we propose a new consensus scheme, termed hierarchical averaging, and show that it is nearly order-optimal with respect to all three metrics. Finally, we examine the effects of quantization, showing that hierarchical averaging provides a nearly order-optimal tradeoff between resource consumption and quantization error.

Cooperative Compute-and-Forward

We propose a class of signaling schemes that leverage transmitter cooperation in wireless networks employing compute-and-forward or physical-layer network coding. We devise a lattice-coding approach to superposition block Markov encoding from which we construct a cooperative lattice coding strategy. Transmitters broadcast lattice codewords, decode each others messages, and then cooperatively transmit resolution information which aids relays in decoding finite-field linear combinations of the incoming messages. We show that cooperation provides a substantial improvement in achievable computation rate and outage probability over noncooperative strategies. Using this strategy, we derive a new achievability scheme for the multiway relay channel, the rates of which are near capacity in many regimes and enjoy a diversity advantage over noncooperation.

Low density lattice codes for the relay channel

We study practical, efficient codes for the Gaussian relay channel. It has been demonstrated that low-density lattice codes (LDLCs) can provide near-capacity performance for point-to-point Gaussian channels. We present an LDLC formulation that provides performance near the decode-and-forward inner bound of the relay channel capacity. We employ a superposition block Markov strategy tailored to LDLCs and design an appropriate iterative decoder. We characterize the error performance via simulations, showing that our scheme achieves performance only 2dB away from the decode-and-forward bound.

Learning Deep Networks from Noisy Labels with Dropout Regularization

Large datasets often have unreliable labels—such as those obtained from Amazons Mechanical Turk or social media platforms—and classifiers trained on mislabeled datasets often exhibit poor performance. We present a simple, effective technique for accounting for label noise when training deep neural networks. We augment a standard deep network with a softmax layer that models the label noise statistics. Then, we train the deep network and noise model jointly via end-to-end stochastic gradient descent on the (perhaps mislabeled) dataset. The augmented model is underdetermined, so in order to encourage the learning of a non-trivial noise model, we apply dropout regularization to the weights of the noise model during training. Numerical experiments on noisy versions of the CIFAR-10 and MNIST datasets show that the proposed dropout technique outperforms state-of-the-art methods.

Discrimination on the Grassmann Manifold: Fundamental Limits of Subspace Classifiers

Repurposing tools and intuitions from Shannon theory, we derive fundamental limits on the reliable classification of high-dimensional signals from low-dimensional features. We focus on the classification of linear and affine subspaces and suppose the features to be noisy linear projections. Leveraging a syntactic equivalence of discrimination between subspaces and communications over vector wireless channels, we derive asymptotic bounds on classifier performance. First, we define the classification capacity, which characterizes necessary and sufficient relationships between the signal dimension, the number of features, and the number of classes to be discriminated, as all three quantities approach infinity. Second, we define the diversitydiscrimination tradeoff, which characterizes relationships between the number of classes and the misclassification probability as the signal-to-noise ratio approaches infinity. We derive inner and outer bounds on these measures, revealing precise relationships between signal dimension and classifier performance.

Relays that cooperate to compute

This paper proposes a new coding scheme that combines the advantages of statistical cooperation and algebraic structure. Consider a multiple-access relay channel where two transmitters attempt to send the modulo sum of their finite field messages to the receiver with the help of the relay. The transmitters use nested lattice codes to ensure that sums of codewords are protected against noise and to preserve the modulo operation of the finite field. We develop a block Markov coding scheme where the relay recovers the real sum of the codewords and retransmits it coherently with the two transmitters.

Low-Density Lattice Codes for Full-Duplex Relay Channels

We propose a class of practical efficient lattice codes for real-valued full-duplex one- and two-way relay channels. First, we investigate the problem from a theoretical perspective, proposing lattice-coding instantiations of superposition block Markov encoding. Our encoding/decoding strategies recover the well-known decode-and-foward rates for the one-way relay channel and a previously-proven rate region for the two-way relay channel. Then, we construct practical, low-complexity implementations of these schemes using low-density lattice codes. Simulations show that our schemes achieve performance as close as 2.5 dB away from theoretical limits. Finally, we show that, due to features inherent to full-duplex relaying and practical codes, the gap to theoretical limits depends on the channel gains and transmit power of the relay relative to the source(s). We characterize this gap analytically, providing insight into the design of practical full-duplex relay systems.

Multicriterion Decision Making with Depen ent Preferences

If preferential independence is assumed inappropriately when developing multicriterion search methods, biased results may occur. A new axiomatic approach to defining conditional preference orderings that naturally accounts for preferential dependencies is presented and illustrated. This approach applies both to scalar optimization techniques that identify a best solution and to evolutionary optimization approaches that approximate the Pareto frontier