arXiv subjects

Pulkit Grover

Publications and source records attributed to Pulkit Grover.

44 records · Page 3Linked to original sources

arXiv2010

Implicit and explicit communication in decentralized control

There has been substantial progress recently in understanding toy problems of purely implicit signaling. These are problems where the source and the channel are implicit -- the message is generated endogenously by the system, and the plant itself is used as a channel. In this paper, we explore how implicit and explicit communication can be used synergistically to reduce control costs. The setting is an extension of Witsenhausen's counterexample where a rate-limited external channel connects the two controllers. Using a semi-deterministic version of the problem, we arrive at a binning-based strategy that can outperform the best known strategies by an arbitrarily large factor. We also show that our binning-based strategy attains within a constant factor of the optimal cost for an asymptotically infinite-length version of the problem uniformly over all problem parameters and all rates on the external channel. For the scalar case, although our results yield approximate optimality for each fixed rate, we are unable to prove approximately-optimality uniformly over all rates.

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arXiv2010

Is Witsenhausen's counterexample a relevant toy?

This paper answers a question raised by Doyle on the relevance of the Witsenhausen counterexample as a toy decentralized control problem. The question has two sides, the first of which focuses on the lack of an external channel in the counterexample. Using existing results, we argue that the core difficulty in the counterexample is retained even in the presence of such a channel. The second side questions the LQG formulation of the counterexample. We consider alternative formulations and show that the understanding developed for the LQG case guides the investigation for these other cases as well. Specifically, we consider 1) a variation on the original counterexample with general, but bounded, noise distributions, and 2) an adversarial extension with bounded disturbance and quadratic costs. For each of these formulations, we show that quantization-based nonlinear strategies outperform linear strategies by an arbitrarily large factor. Further, these nonlinear strategies also perform within a constant factor of the optimal, uniformly over all possible parameter choices (for fixed noise distributions in the Bayesian case). Fortuitously, the assumption of bounded noise results in a significant simplification of proofs as compared to those for the LQG formulation. Therefore, the results in this paper are also of pedagogical interest.

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arXiv2010

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. 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 distributed control -- the Witsenhausen counterexample. Using this bound, we characterize the asymptotically optimal costs for the vector Witsenhausen problem numerically to within a factor of 1.3 for all problem parameters, improving on the earlier best known bound of 2.

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arXiv2010

The finite-dimensional Witsenhausen counterexample

Recently, a vector version of Witsenhausen's counterexample was considered and it was shown that in that limit of infinite vector length, certain quantization-based control 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 dimension being viewed as an additional problem parameter. By applying a large-deviation "sphere-packing" philosophy, a lower bound to the optimal cost for the finite dimensional case is derived that uses appropriate shadows of the infinite-length bound. Using the new lower bound, we show that good lattice-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 -- the scalar case -- the gap between regular lattice-based strategies and the lower bound is numerically never more than a factor of 8.

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arXiv2008

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.

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arXiv2008

The price of certainty: "waterslide curves" and the gap to capacity

The classical problem of reliable point-to-point digital communication is to achieve a low probability of error while keeping the rate high and the total power consumption small. Traditional information-theoretic analysis uses `waterfall' curves to convey the revolutionary idea that unboundedly low probabilities of bit-error are attainable using only finite transmit power. However, practitioners have long observed that the decoder complexity, and hence the total power consumption, goes up when attempting to use sophisticated codes that operate close to the waterfall curve. This paper gives an explicit model for power consumption at an idealized decoder that allows for extreme parallelism in implementation. The decoder architecture is in the spirit of message passing and iterative decoding for sparse-graph codes. Generalized sphere-packing arguments are used to derive lower bounds on the decoding power needed for any possible code given only the gap from the Shannon limit and the desired probability of error. As the gap goes to zero, the energy per bit spent in decoding is shown to go to infinity. This suggests that to optimize total power, the transmitter should operate at a power that is strictly above the minimum demanded by the Shannon capacity. The lower bound is plotted to show an unavoidable tradeoff between the average bit-error probability and the total power used in transmission and decoding. In the spirit of conventional waterfall curves, we call these `waterslide' curves.

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arXiv2007

What is needed to exploit knowledge of primary transmissions?

Recently, Tarokh and others have raised the possibility that a cognitive radio might know the interference signal being transmitted by a strong primary user in a non-causal way, and use this knowledge to increase its data rates. However, there is a subtle difference between knowing the signal transmitted by the primary and the actual interference at our receiver since there is a wireless channel between these two points. We show that even an unknown phase results in a substantial decrease in the data rates that can be achieved, and thus there is a need to feedback interference channel estimates to the cognitive transmitter. We then consider the case of fading channels. We derive an upper bound on the rate for given outage error probability for faded dirt. We give a scheme that uses appropriate "training" to obtain such estimates and quantify this scheme's required overhead as a function of the relevant coherence time and interference power.

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arXiv2007

Tradeoff between decoding complexity and rate for codes on graphs

We consider transmission over a general memoryless channel, with bounded decoding complexity per bit under message passing decoding. We show that the achievable rate is bounded below capacity if there is a finite success in the decoding in a specified number of operations per bit at the decoder for some codes on graphs. These codes include LDPC and LDGM codes. Good performance with low decoding complexity suggests strong local structures in the graphs of these codes, which are detrimental to the code rate asymptotically. The proof method leads to an interesting necessary condition on the code structures which could achieve capacity with bounded decoding complexity. We also show that if a code sequence achieves a rate epsilon close to the channel capacity, the decoding complexity scales at least as O(log(1/epsilon).

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