Bits through Time

In any communication system, there exist two dimensions through which the information at the source becomes distorted before reaching the destination: the noisy channel and time. Messages transmitted through a noisy channel are susceptible to modification in their content, due to the action of the noise of the channel. Claude E. Shannon, in his seminal paper of 1948 "A Mathematical Theory of Communication", introduces the bit as a unit of measure of information, and he lays down the theoretical foundations needed to understand the problem of sending bits reliably through a noisy channel. The distortion measure, which he used to quantify reliability, is the error probability. In his paper, Shannon shows that any channel is characterized by a number that he calls capacity: It represents the highest transmission rate that can be used to communicate information with, through this same channel, while guaranteeing a negligible error probability. Whereas, even if the messages are sent through a perfect channel, the time they take to reach their destination causes the receiver to acquire a distorted view of the status of the source that generated these messages. For instance, take the case of a monitor interested in the status of a distant process. A sender observes this process and, to keep the monitor up-to-date, sends updates to it. However, if, at any time t, the last received update at the monitor was generated at time u(t), then the information at the receiver reflects the status of the process at time u(t), not at time t. Hence, the monitor has a distorted version of reality. In fact, it has an obsolete version with an age of t-u(t). The concept of age as a distortion measure in communication systems was first used in 2011 by Kaul et al., in order to assess the performance of a given vehicular network. The aim of the authors was to come up with a transmission scheme that would minimize an age-related metric: the average age. Since then, a growing body of works has used this metric to evaluate the performance of multiple communication systems. The drive behind this interest lies in the importance that status-update applications are gaining in today's life (in vehicular networks, warehouse and environment surveillance, news feed,etc.). In this thesis, we choose age as a distortion measure and derive expressions for the average age and the average peak-age (another age-related metric) for different communication systems. Therefore, we divide this dissertation into two parts: In the first part, we assume that the the updates are transmitted through a noiseless channel that has a random service time. In the second part, we consider a special category of noisy channels, namely the erasure channel. In the first part of this thesis, in order to compute the age-related metrics, we employ queue-theoretic concepts. We study and compare the performance of various transmission schemes under different settings.We show that the optimal transmission scheme when the monitor is interested in a single source loses its optimality when another source of higher priority shares the system. In the second part of this thesis, we introduce, in our age calculations, the distortion caused by the erasure channel on the transmitted updates. In order to combat the erasures of the channel, we first consider two flavors of the hybrid automatic repeat request (HARQ). Finally, we focus on the optimal average age that could be achieved over an erasure channel

Timely Estimation Using Coded Quantized Samples

The effects of quantization and coding on the estimation quality of a Gauss-Markov, namely Ornstein-Uhlenbeck, process are considered. Samples are acquired from the process, quantized, and then encoded for transmission using either infinite incremental redundancy or fixed redundancy coding schemes. A fixed processing time is consumed at the receiver for decoding and sending feedback to the transmitter. Decoded messages are used to construct a minimum mean square error (MMSE) estimate of the process as a function of time. This is shown to be an increasing functional of the age-of-information, defined as the time elapsed since the sampling time pertaining to the latest successfully decoded message. Such (age-penalty) functional depends on the quantization bits, codeword lengths and receiver processing time. The goal, for each coding scheme, is to optimize sampling times such that the long term average MMSE is minimized. This is then characterized in the setting of general increasing age-penalty functionals, not necessarily corresponding to MMSE, which may be of independent interest in other contexts.Comment: To appear in ISIT 202

Sample, Quantize and Encode: Timely Estimation Over Noisy Channels

The effects of quantization and coding on the estimation quality of Gauss-Markov processes are considered, with a special attention to the Ornstein-Uhlenbeck process. Samples are acquired from the process, quantized, and then encoded for transmission using either infinite incremental redundancy (IIR) or fixed redundancy (FR) coding schemes. A fixed processing time is consumed at the receiver for decoding and sending feedback to the transmitter. Decoded messages are used to construct a minimum mean square error (MMSE) estimate of the process as a function of time. This is shown to be an increasing functional of the age-of-information (AoI), defined as the time elapsed since the sampling time pertaining to the latest successfully decoded message. Such functional depends on the quantization bits, codewords lengths and receiver processing time. The goal, for each coding scheme, is to optimize sampling times such that the long-term average MMSE is minimized. This is then characterized in the setting of general increasing functionals of AoI, not necessarily corresponding to MMSE, which may be of independent interest in other contexts. We first show that the optimal sampling policy for IIR is such that a new sample is generated only if the AoI exceeds a certain threshold, while for FR it is such that a new sample is delivered just-in-time as the receiver finishes processing the previous one. Enhanced transmissions schemes are then developed in order to exploit the processing times to make new data available at the receiver sooner. For both IIR and FR, it is shown that there exists an optimal number of quantization bits that balances AoI and quantization errors, and hence minimizes the MMSE. It is also shown that for longer receiver processing times, the relatively simpler FR scheme outperforms IIR.Comment: Accepted for publication in the IEEE Transactions on Communications. arXiv admin note: substantial text overlap with arXiv:2004.1298

Timely Monitoring of Dynamic Sources with Observations from Multiple Wireless Sensors

Age of Information (AoI) has recently received much attention due to its relevance in IoT sensing and monitoring applications. In this paper, we consider the problem of minimizing the AoI in a system in which a set of sources are observed by multiple sensors in a many-to-many relationship, and the probability that a sensor observes a source depends on the state of the source. This model represents many practical scenarios, such as the ones in which multiple cameras or microphones are deployed to monitor objects moving in certain areas. We formulate the scheduling problem as a Markov Decision Process, and show how the age-optimal scheduling policy can be obtained. We further consider partially observable variants of the problem, and devise approximate policies for large state spaces. Our evaluations show that the approximate policies work well in the considered scenarios, and that the fact that sensors can observe multiple sources is beneficial, especially when there is high uncertainty of the source states.Comment: Submitted for publicatio

Age of Information in Random Access Channels

In applications of remote sensing, estimation, and control, timely communication is not always ensured by high-rate communication. This work proposes distributed age-efficient transmission policies for random access channels with $M$ transmitters. In the first part of this work, we analyze the age performance of stationary randomized policies by relating the problem of finding age to the absorption time of a related Markov chain. In the second part of this work, we propose the notion of \emph{age-gain} of a packet to quantify how much the packet will reduce the instantaneous age of information at the receiver side upon successful delivery. We then utilize this notion to propose a transmission policy in which transmitters act in a distributed manner based on the age-gain of their available packets. In particular, each transmitter sends its latest packet only if its corresponding age-gain is beyond a certain threshold which could be computed adaptively using the collision feedback or found as a fixed value analytically in advance. Both methods improve age of information significantly compared to the state of the art. In the limit of large $M$, we prove that when the arrival rate is small (below $\frac{1}{eM}$), slotted ALOHA-type algorithms are asymptotically optimal. As the arrival rate increases beyond $\frac{1}{eM}$, while age increases under slotted ALOHA, it decreases significantly under the proposed age-based policies. For arrival rates $\theta$, $\theta=\frac{1}{o(M)}$, the proposed algorithms provide a multiplicative factor of at least two compared to the minimum age under slotted ALOHA (minimum over all arrival rates). We conclude that, as opposed to the common practice, it is beneficial to increase the sampling rate (and hence the arrival rate) and transmit packets selectively based on their age-gain