Zero-Error Capacity of a Class of Timing Channels

We analyze the problem of zero-error communication through timing channels that can be interpreted as discrete-time queues with bounded waiting times. The channel model includes the following assumptions: 1) Time is slotted, 2) at most $N$ "particles" are sent in each time slot, 3) every particle is delayed in the channel for a number of slots chosen randomly from the set $\{0, 1, \ldots, K\}$, and 4) the particles are identical. It is shown that the zero-error capacity of this channel is $\log r$, where $r$ is the unique positive real root of the polynomial $x^{K+1} - x^{K} - N$. Capacity-achieving codes are explicitly constructed, and a linear-time decoding algorithm for these codes devised. In the particular case $N = 1$, $K = 1$, the capacity is equal to $\log \phi$, where $\phi = (1 + \sqrt{5}) / 2$ is the golden ratio, and the constructed codes give another interpretation of the Fibonacci sequence.Comment: 5 pages (double-column), 3 figures. v3: Section IV.1 from v2 is replaced with Remark 1, and Section IV.2 is removed. Accepted for publication in IEEE Transactions on Information Theor

Universal Privacy Gurantees for Smart Meters

Smart meters (SMs) provide advanced monitoring of consumer energy usage, thereby enabling optimized management and control of electricity distribution systems. Unfortunately, the data collected by SMs can reveal information about consumer activity, such as the times at which they run individual appliances. Two approaches have been proposed to tackle the privacy threat posed by such information leakage. One strategy involves manipulating user data before sending it to the utility provider (UP); this approach improves privacy at the cost of reducing the operational insight provided by the SM data to the UP. The alternative strategy employs rechargeable batteries or local energy sources at each consumer site to try decouple energy usage from energy requests. This thesis investigates the latter approach. Understanding the privacy implications of any strategy requires an appropriate privacy metric. A variety of metrics are used to study privacy in energy distribution systems. These include statistical distance metrics, differential privacy, distortion metrics, maximal leakage, maximal $\alpha$-leakage and information measures like mutual information. We here use mutual information to measure privacy both because its well understood fundamental properties and because it provides a useful bridge to adjacent fields such as hypothesis testing, estimation, and statistical or machine learning. Privacy leakage under mutual information measures has been studied under a variety of assumptions on the energy consumption of the user with a strong focus on i.i.d. and some exploration of markov processes. Since user energy consumption may be non-stationary, here we seek privacy guarantees that apply for general random process models of energy consumption. Moreover, we impose finite capacity bounds on batteries and include the price of the energy requested from the grid, thus minimizing the information leakage subject to a bound on the resulting energy bill. To that aim we model the energy management unit (EMU) as a deterministic finite-state channel, and adapt the Ahlswede-Kaspi coding strategy proposed for permuting channels to the SM privacy setting. Within this setting, we derive battery policies providing privacy guarantees that hold for any bounded process modelling the energy consumption of the user, including non-ergodic and non-stationary processes. These guarantees are also presented for bounded processes with a known expected average consumption. The optimality of the battery policy is characterized by presenting the probability law of a random process that is tight with respect to the upper bound. Moreover, we derive single letter bounds characterizing the privacy-cost trade off in the presence of variable market price. Finally it is shown that the provided results hold for mutual information, maximal leakage, maximal-alpha leakage and the Arimoto and Sibson channel capacity

Cooperative communications in wireless networks.

Zhang Jun.Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.Includes bibliographical references (leaves 82-92).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Multipath Fading Channels --- p.1Chapter 1.2 --- Diversity --- p.3Chapter 1.3 --- Outline of the Thesis --- p.6Chapter 2 --- Background and Related Work --- p.8Chapter 2.1 --- Cooperative Diversity --- p.8Chapter 2.1.1 --- User Cooperation --- p.9Chapter 2.1.2 --- Cooperative Diversity --- p.10Chapter 2.1.3 --- Coded Cooperation --- p.12Chapter 2.2 --- Information-Theoretic Studies --- p.13Chapter 2.3 --- Multihop Cellular Networks --- p.15Chapter 2.3.1 --- MCN: Multihop Cellular Network --- p.15Chapter 2.3.2 --- iCAR: Integrated Cellular and Ad Hoc Relaying Systems --- p.17Chapter 2.3.3 --- UCAN: Unified Cellular and Ad Hoc Network Architecture --- p.17Chapter 2.4 --- Wireless Ad Hoc Networks --- p.18Chapter 2.5 --- Space-Time Processing --- p.20Chapter 3 --- Single-Source Multiple-Relay Cooperation System --- p.23Chapter 3.1 --- System Model --- p.23Chapter 3.2 --- Fixed Decode-and-Forward Cooperation System --- p.26Chapter 3.2.1 --- BER for system with errors at the relay --- p.28Chapter 3.2.2 --- General BER formula for single-source nr-relay cooperation system --- p.30Chapter 3.2.3 --- Discussion of Interuser Channels --- p.31Chapter 3.3 --- Relay Selection Protocol --- p.33Chapter 3.3.1 --- Transmission Protocol --- p.34Chapter 3.3.2 --- BER Analysis for Relay Selection Protocol --- p.34Chapter 4 --- Multiple-Source Multiple-Relay Cooperation System --- p.40Chapter 4.1 --- Transmission Protocol --- p.41Chapter 4.2 --- Fixed Cooperative Coding System --- p.43Chapter 4.2.1 --- Performance Analysis --- p.43Chapter 4.2.2 --- Numerical Results and Discussion --- p.48Chapter 4.3 --- Adaptive Cooperative Coding --- p.49Chapter 4.3.1 --- Performance Analysis of Adaptive Cooperative Coding System --- p.50Chapter 4.3.2 --- Analysis of p2(2) --- p.52Chapter 4.3.3 --- Numerical Results and Discussion --- p.53Chapter 5 --- Cooperative Multihop Transmission --- p.56Chapter 5.1 --- System Model --- p.57Chapter 5.1.1 --- Conventional Multihop Transmission --- p.58Chapter 5.1.2 --- Cooperative Multihop Transmission --- p.59Chapter 5.2 --- Performance Evaluation --- p.59Chapter 5.2.1 --- Conventional Multihop Transmission --- p.60Chapter 5.2.2 --- Cooperative Multihop Transmission --- p.60Chapter 5.2.3 --- Numerical Results --- p.64Chapter 5.3 --- Discussion --- p.64Chapter 5.3.1 --- Cooperative Range --- p.64Chapter 5.3.2 --- Relay Node Distribution --- p.67Chapter 5.3.3 --- Power Allocation and Distance Distribution (2-hop Case) --- p.68Chapter 5.4 --- Cooperation in General Wireless Ad Hoc Networks --- p.70Chapter 5.4.1 --- Cooperation Using Linear Network Codes --- p.71Chapter 5.4.2 --- Single-Source Single-Destination Systems --- p.74Chapter 5.4.3 --- Multiple-Source Single-Destination Systems --- p.75Chapter 6 --- Conclusion --- p.80Bibliography --- p.82Chapter A --- Proof of Proposition 1-4 --- p.93Chapter A.1 --- Proof of Proposition 1 --- p.93Chapter A.2 --- Proof of Proposition 2 --- p.95Chapter A.3 --- Proof of Proposition 3 --- p.95Chapter A.4 --- Proof of Proposition 4 --- p.9