Pulkit Grover

Shannon meets Tesla: Wireless information and power transfer

The problem considered here is that of wireless information and power transfer across a noisy coupled-inductor circuit, which is a frequency-selective channel with additive white Gaussian noise. The optimal tradeoff between the achievable rate and the power transferred is characterized given the total power available. The practical utility of such systems is also discussed.

Energy Harvesting Wireless Communications: A Review of Recent Advances

This paper summarizes recent contributions in the broad area of energy harvesting wireless communications. In particular, we provide the current state of the art for wireless networks composed of energy harvesting nodes, starting from the information-theoretic performance limits to transmission scheduling policies and resource allocation, medium access, and networking issues. The emerging related area of energy transfer for self-sustaining energy harvesting wireless networks is considered in detail covering both energy cooperation aspects and simultaneous energy and information transfer. Various potential models with energy harvesting nodes at different network scales are reviewed, as well as models for energy consumption at the nodes.

Fundamental limits on the power consumption of encoding and decoding

We provide fundamental information-theoretic bounds on the required circuit wiring complexity and power consumption for encoding and decoding of error-correcting codes. These bounds hold for all codes and all encoding and decoding algorithms implemented within the paradigm of our VLSI model. This model essentially views computation on a 2-D VLSI circuit as a computation on a network of connected nodes. The bounds are derived based on analyzing information flow in the circuit. They are then used to show that there is a fundamental tradeoff between the transmit and encoding/decoding power, and that the total (transmit + encoding + decoding) power must diverge to infinity at least as fast as cube-root of log 1/pe, where Pe is the average block-error probability. On the other hand, for bounded transmit-power schemes, the total power must diverge to infinity at least as fast as square-root of log 1/Pe due to the burden of encoding/decoding.

The finite-dimensional Witsenhausen counterexample

Recently, we considered a vector version of Witsenhausens counterexample and used a new lower bound to show that in that limit of infinite vector length, certain quantization-based strategies are provably within a constant factor of the optimal cost for all possible problem parameters. In this paper, finite vector lengths are considered with the vector length being viewed as an additional problem parameter. By applying the “sphere-packing” philosophy, a lower bound to the optimal cost for this finite-length problem is derived that uses appropriate shadows of the infinite-length bounds. We also introduce latticebased quantization strategies for any finite length. Using the new finite-length lower bound, we show that the lattice-based strategies achieve within a constant factor of the optimal cost uniformly over all possible problem parameters, including the vector length. For Witsenhausens original problem — which corresponds to the scalar case — lattice-based strategies attain within a factor of 8 of the optimal cost. Based on observations in the scalar case and the infinite-dimensional case, we also conjecture what the optimal strategies could be for any finite vector length.

Green codes: Energy-efficient short-range communication

A green code attempts to minimize the total energy per-bit required to communicate across a noisy channel. The classical information-theoretic approach neglects the energy expended in processing the data at the encoder and the decoder and only minimizes the energy required for transmissions. Since there is no cost associated with using more degrees of freedom, the traditionally optimal strategy is to communicate at rate zero. In this work, we use our recently proposed model for the power consumed by iterative message passing. Using generalized sphere-packing bounds on the decoding power, we find lower bounds on the total energy consumed in the transmissions and the decoding, allowing for freedom in the choice of the rate. We show that contrary to the classical intuition, the rate for green codes is bounded away from zero for any given error probability. In fact, as the desired bit-error probability goes to zero, the optimizing rate for our bounds converges to 1.

Information Friction and Its Implications on Minimum Energy Required for Communication

Just as there are frictional losses associated with moving masses on a surface, what if there were frictional losses associated with moving information on a substrate? Indeed, many modes of communication suffer from such frictional losses. 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. We use this information-friction model to understand the fundamental energy requirements on encoding and decoding in communication circuitry. First, for communication across a binary input additive white Gaussian noise channel, we arrive at fundamental limits on bit-meters (and thus energy consumption) for decoding implementations that have a predetermined input-independent length of messages. For encoding, we relax the fixed-length assumption and derive bounds for flexible-message-length implementations. Using these lower bounds, we show that the total (transmit + encoding + decoding) energy-per-bit must diverge to infinity as the target error probability is lowered to zero. Furthermore, the closer the communication rate is maintained to the channel capacity (as the target error probability is lowered to zero), the fast required decoding energy diverges to infinity.

Coded convolution for parallel and distributed computing within a deadline

We consider the problem of computing the convolution of two long vectors using parallel processors in the presence of “stragglers”. Stragglers refer to the small fraction of faulty or slow processors that delays the entire computation in time-critical distributed systems. We first show that splitting the vectors into smaller pieces and using a linear code to encode these pieces provides improved resilience against stragglers than replication-based schemes under a simple, worst-case straggler analysis. We then demonstrate that under commonly used models of computation time, coding can dramatically improve the probability of finishing the computation within a target “deadline” time. As opposed to the more commonly used technique of expected computation time analysis, we quantify the exponents of the probability of failure in the limit of large deadlines. Our exponent metric captures the probability of failing to finish before a specified deadline time, i.e., the behavior of the “tail”. Moreover, our technique also allows for simple closed form expressions for more general models of computation time, e.g. shifted Weibull models instead of only shifted exponentials. Thus, through this problem of coded convolution, we establish the utility of a novel asymptotic failure exponent analysis for distributed systems.

Computing Linear Transformations With Unreliable Components

We consider the problem of computing a binary linear transformation when all circuit components are unreliable. Two models of unreliable components are considered: probabilistic errors and permanent errors. We introduce the “ENCODED” technique that ensures that the error probability of the computation of the linear transformation is kept bounded below a small constant independent of the size of the linear transformation even when all logic gates in the computation are noisy. By deriving a lower bound, we show that in some cases, the computational complexity of the ENCODED technique achieves the optimal scaling in error probability. Further, we examine the gain in energy-efficiency from the use of a “voltage-scaling” scheme, where gate-energy is reduced by lowering the supply voltage. We use a gate energy-reliability model to show that tuning gate-energy appropriately at different stages of the computation (“dynamic” voltage scaling), in conjunction with ENCODED, can lead to orders of magnitude energy-savings over the classical “uncoded” approach. Finally, we also examine the problem of computing a linear transformation when noiseless decoders can be used, providing upper and lower bounds to the problem.

Information embedding meets distributed control

We consider the problem of information embedding where the encoder modifies a white Gaussian host signal in a power-constrained manner to encode the message, and the decoder recovers both the embedded message and the modified host signal. This extends the recent work of Sumszyk and Steinberg to the continuous-alphabet Gaussian setting. We show that a dirty-paper coding based strategy achieves the optimal rate for perfect recovery of the modified host and the message. We also provide bounds for the extension wherein the modified host signal is recovered only to within a specified distortion. Our results specialized to the zero-rate case provide the tightest known lower bounds on the asymptotic costs for the vector version of a famous open problem in distributed control - the Witsenhausen counterexample. Using this bound, we 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.

Can a noisy encoder be used to communicate reliably

In this paper the problem of reliable communication with a noisy encoder is examined. We explicitly provided the construction of the encoder and show that even when all logic gates that constitute the encoder are noisy, reliable communication with a positive rate is still possible. The encoding complexity is shown to be O(log 1/ptar/log1/ε) per bit to achieve a target bit error rate ptar, where ε denotes the error probability of each noisy gate. This complexity upper bound is shown to coincide with a lower bound in order sense, and is hence tight. The key technique in the proposed construction is to embed noisy decoders inside the noisy encoder, which are utilized repeatedly to prevent the bit error rate from escalating. The proposed noisy encoder has a direct application in noisy computing of a linear transform.