Showing papers by "Pulkit Grover published in 2013"

Approximately Optimal Solutions to the Finite-Dimensional Witsenhausen Counterexample

Abstract: Recently, a vector version of Witsenhausen's counterexample was considered and it was shown that in the asymptotic limit of infinite vector length, certain vector-quantization-based control strategies are provably within a constant factor of the asymptotically optimal cost for all possible problem parameters. While suggestive, a constant factor result for the finite-dimensional problem has remained elusive. In this paper, we provide a resolution to this issue. By applying a large-deviation “sphere-packing” philosophy, we derive a lower bound to the optimal cost for the finite dimensional case that uses appropriate shadows of an existing vector lower bound that is the same for all dimensions. Using this new lower bound, we show that good lattice-quantization-based control strategies achieve within a constant factor of the optimal cost uniformly over all possible problem parameters, including the vector length. For Witsenhausen's original problem-which is the scalar case-the gap between regular lattice-quantization-based strategies and the lower bound is provably never more than a factor of 100, and computer calculations strongly suggest that the factor in fact may be no larger than 8. Finally, to obtain a numerical understanding of the possible room for improvement in costs using alternative strategies, we also include numerical comparison with strategies that are conjectured to be optimal. Using this comparison, we posit that there is more room for improvement in our lower bounds than in our upper bounds.

“Information-friction” and its impact on minimum energy per communicated bit

Abstract: Just as there are frictional losses associated with moving masses on a surface, what if there are frictional losses associated with moving information on a substrate? We propose to model these losses as proportional to “bit-meters” i.e., the product of mass of information (i.e., the number of bits) and the distance of information transport. For communication across a binary input AWGN channel decoded by decoders implemented using a simple circuit model, we derive unavoidable lower bounds on bit-meters for decoding computation. These bounds are translated into limits on energy consumption in decoding under the information-friction model. Using these lower bounds we show that the total (transmit + decoding) energy-per-bit must diverge to infinity as the target error probability is lowered.

Information embedding and the triple role of control

Abstract: We consider the problem of information embedding where the encoder modifies a white Gaussian host signal in a power-constrained manner to encode a message, and the decoder recovers both the embedded message and the modified host signal. This partially extends the recent work of Sumszyk and Steinberg to the continuous-alphabet Gaussian setting. Through a control-theoretic lens, we observe that the problem is a minimalist example of what is called the "triple role" of control actions. We show that a dirty-paper-coding strategy achieves the optimal rate for perfect recovery of the modified host and the message for any message rate. For imperfect recovery of the modified host, by deriving bounds on the minimum mean-square error (MMSE) in recovering the modified host signal, we show that DPC-based strategies are guaranteed to attain within a uniform constant factor of 16 of the optimal weighted sum of power required in host signal modification and the MMSE in the modified host signal reconstruction for all weights and all message rates. When specialized to the zero-rate case, our results provide the tightest known lower bounds on the asymptotic costs for the vector version of a famous open problem in decentralized control: the Witsenhausen counterexample. Numerically, this tighter bound helps us characterize the asymptotically optimal costs for the vector Witsenhausen problem to within a factor of 1.3 for all problem parameters, improving on the earlier best known bound of 2.

What do we need to do to “green” data-center networks? A fundamental perspective

Abstract: While traditional information theory has driven the choice of communication strategies for most of today's communication systems, it focuses almost exclusively on minimizing the transmit power of the system. In modern short-distance applications, including high-speed data-center networks, the energy consumed in the circuitry to enable reliable between servers can dominate the transmit energy across the links. Recent theoretical results and empirical observations show that in such situations, operating close to the traditional information-theoretic limits can be highly inefficient from a system-level energy-perspective. In this position paper, we use these results to propose a way forward for obtaining energy-efficient strategies for future Ethernet, including the NGBASE Ethernet which is currently being standardized. We also introduce our Total Energy Minimization platform, TotEM, that will collect information to enable communication system designers to make the most energy-efficient choices.

Intrusion detection for wireless power networks, near-field communication, and side-channel attacks

Abstract: Near-field approximations to Maxwell's equations reveal an interesting property of inductively-coupled links that are so frequently used in wireless power transfer: observation disturbs the system. We propose theoretical strategies and include preliminary practical implementations that demonstrate how this property can be used to detect presence of an adversary/intruder/eavesdropper, and thereby secure (a) wireless power transfer from power-stealing; (b) near-field information transfer; and (c) circuits from hardware probing attacks. These strategies rely on detecting the distortions in the electro-magnetic field induced by the presence of an extraneous element. We implement two of such circuits and compare them on their stability to detect such eavesdroppers.