Fundamental limits in Gaussian channels with feedback: confluence of communication, estimation, and control

The emerging study of integrating information theory and control systems theory has attracted tremendous attention, mainly motivated by the problems of control under communication constraints, feedback information theory, and networked systems. An often overlooked element is the estimation aspect; however, estimation cannot be studied isolatedly in those problems. Therefore, it is natural to investigate systems from the perspective of unifying communication, estimation, and control;This thesis is the first work to advocate such a perspective. To make Matters concrete, we focus on communication systems over Gaussian channels with feedback. For some of these channels, their fundamental limits for communication have been studied using information theoretic methods and control-oriented methods but remain open. In this thesis, we address the problems of characterizing and achieving the fundamental limits for these Gaussian channels with feedback by applying the unifying perspective;We establish a general equivalence among feedback communication, estimation, and feedback stabilization over the same Gaussian channels. As a consequence, we see that the information transmission (communication), information processing (estimation), and information utilization (control), seemingly different and usually separately treated, are in fact three sides of the same entity. We then reveal that the fundamental limitations in feedback communication, estimation, and control coincide: The achievable communication rates in the feedback communication problems can be alternatively given by the decay rates of the Cramer-Rao bounds (CRB) in the associated estimation problems or by the Bode sensitivity integrals in the associated control problems. Utilizing the general equivalence, we design optimal feedback communication schemes based on the celebrated Kalman filtering algorithm; these are the first deterministic, optimal communication schemes for these channels with feedback (except for the degenerated AWGN case). These schemes also extend the Schalkwijk-Kailath (SK) coding scheme and inherit its useful features, such as reduced coding complexity and improved performance. Hence, this thesis demonstrates that the new perspective plays a significant role in gaining new insights and new results in studying Gaussian feedback communication systems. We anticipate that the perspective could be extended to more general problems and helpful in building a theoretically and practically sound paradigm that unifies information, estimation, and control

Universal decoding for noisy channels

Cover title.Includes bibliographical references (p. 49-51).Supported in part by the Advanced Concepts Committee, Lincoln Laboratory.Feder, M., Lapidoth, A

Efficient UC Commitment Extension with Homomorphism for Free (and Applications)

Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment. We obtain amortized linear computational complexity in the length of the input messages and rate 1. Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters. While the previously best constructions use UC oblivious transfer as the main building block, our constructions only require extractable commitments and PRGs, achieving better concrete efficiency and offering new insights into the sufficient conditions for obtaining homomorphic UC commitments. Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic. These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments. Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge

Hardware-Limited Task-Based Quantization

Quantization plays a critical role in digital signal processing systems. Quantizers are typically designed to obtain an accurate digital representation of the input signal, operating independently of the system task, and are commonly implemented using serial scalar analog-to-digital converters (ADCs). In this work, we study hardware-limited task-based quantization, where a system utilizing a serial scalar ADC is designed to provide a suitable representation in order to allow the recovery of a parameter vector underlying the input signal. We propose hardware-limited task-based quantization systems for a fixed and finite quantization resolution, and characterize their achievable distortion. We then apply the analysis to the practical setups of channel estimation and eigen-spectrum recovery from quantized measurements. Our results illustrate that properly designed hardware-limited systems can approach the optimal performance achievable with vector quantizers, and that by taking the underlying task into account, the quantization error can be made negligible with a relatively small number of bits

COVERT COMMUNICATIONS IN CONTINUOUS-TIME SYSTEMS

This dissertation studies covert wireless communications where a transmitter (Alice) intends to transmit messages to a legitimate receiver (Bob) such that the presence of the message is hidden from an attentive warden (Willie). Here we consider pertinent aspects of covert communications that focus on moving such systems closer to implementation. For example, previous studies use the standard discrete-time communication model when analyzing covert communications, since this is commonly assumed without loss of generality in standard communication theory. However, it is not clear that such a model captures the salient aspects of the continuous-time covert communications problem. A power detector that is optimal for the warden in a discrete-time covert communications scenario may not be optimal on a continuous- time model. Thus, it is of interest to consider this more realistic model for physical channels. After analyzing a power optimization problem using the standard discrete-time model, we move to the key part of system implementation: the instantiation in true continuous-time systems of the discrete-time models studied to this point in the literature. A key goal is to examine Willie’s detection capability on a continuous-time model and study how the limits of covert communications change from the discrete-time case. In particular, we show that detectors for Willie can benefit from the continuous-time setting and outperform detectors based on the discrete-time model; not surprisingly, this has a significant impact on the true covert throughput of the system. Nevertheless, we establish constructions such that efficient covert communications can still be achieved in a continuous-time model, and prove the fundamental limit on the covert communication rate. After considering the continuous-time problem in detail, we then turn to addressing another limitation of previous work - the requirement for an intentional jammer to facilitate efficient covert communication. Instead, we consider how to exploit a pre-existing interference source – a radar - to achieve covert communication. We establish a covert communication scheme in such an environment, and analyze the corresponding covert rate. Finally, we consider the use of a detection technique similar to that in the covert communications problem, in the area of quantized signal detection

Efficient Importance sampling Simulations for Digital Communication Systems

Importance sampling is a- modified. Monte Carlo simulation technique which can dramatically reduce the computational cost of the Monte Carlo method. A complete development is presented for its use in the estimation of bit error rates /V for digital communication systems with small Gaussian noise inputs. Emphasis is on the optimal mean-translation Gaussian simulation density function design and the event simulation method as applied to systems which employ quasi-regular trellis codes. These codes include the convolutional codes and many TCM (Ungerboeck) codes. Euclidean distance information of a code is utilized to facilitate the simulation. Also, the conditional importance sampling technique is presented which can handle many non-Gaussian system inputs. Theories as well as numerical examples are given. In particular, we study the simulations of an uncoded MSK and a trellis-coded 8- PSK transmissions over a general bandlimited nonlinear satellite channel model. Our algorithms are shown to be very efficient at low Pb compared to the ordinary Monte Carlo method. Many techniques we have developed are applicable to other system simulations as building blocks for their particular system configurations and channels

Channel coding for high speed links

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2008.Includes bibliographical references (p. 139-144).This thesis explores the benefit of channel coding for high-speed backplane or chip-to-chip interconnects, referred to as the high-speed links. Although both power-constrained and bandwidth-limited, the high-speed links need to support data rates in the Gbps range at low error probabilities. Modeling the high-speed link as a communication system with noise and intersymbol interference (ISI), this work identifies three operating regimes based on the underlying dominant error mechanisms. The resulting framework is used to identify the conditions under which standard error control codes perform optimally, incur an impractically large overhead, or provide the optimal performance in the form of a single parity check code. For the regime where the standard error control codes are impractical, this thesis introduces low-complexity block codes, termed pattern-eliminating codes (PEC), which achieve a potentially large performance improvement over channels with residual ISI. The codes are systematic, require no decoding and allow for simple encoding. They can also be additionally endowed with a (0, n - 1) run-length-limiting property. The simulation results show that the simplest PEC can provide error-rate reductions of several orders of magnitude, even with rate penalty taken into account. It is also shown that channel conditioning, such as equalization, can have a large effect on the code performance and potentially large gains can be derived from optimizing the equalizer jointly with a pattern-eliminating code. Although the performance of a pattern-eliminating code is given by a closed-form expression, the channel memory and the low error rates of interest render accurate simulation of standard error-correcting codes impractical. This work proposes performance estimation techniques for coded high-speed links, based on the underlying regimes of operation.(cont)It also introduces an efficient algorithm for computing accurate marginal probability distributions of signals in a coded high-speed link.by Natasa Blitvic.S.M

Quantum channels and memory effects

Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information. Quantum information provides a theoretical framework and the proper mathematical tools to accomplish this. In this context the notion of codes and communication capacities have been introduced by generalizing them from the classical Shannon theory of information transmission and error correction. The underlying assumption of this approach is to consider the channel not as acting on a single system, but on sequences of systems, which, when properly initialized allow one to overcome the noisy effects induced by the physical process under consideration. While most of the work produced so far has been focused on the case in which a given channel transformation acts identically and independently on the various elements of the sequence (memoryless configuration in jargon), correlated error models appear to be a more realistic way to approach the problem. A slightly different, yet conceptually related, notion of correlated errors applies to a single quantum system which evolves continuously in time under the influence of an external disturbance which acts on it in a non-Markovian fashion. This leads to the study of memory effects in quantum channels: a fertile ground where interesting novel phenomena emerge at the intersection of quantum information theory and other branches of physics. A survey is taken of the field of quantum channels theory while also embracing these specific and complex settings.Comment: Review article, 61 pages, 26 figures; 400 references. Final version of the manuscript, typos correcte