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  1. A status updating system is considered in which a variable length code is used to transmit messages to a receiver over a noisy channel. The goal is to optimize the codewords lengths such that successfully-decoded messages are timely. That is, such that the age-of-information (AoI) at the receiver is minimized. A hybrid ARQ (HARQ) scheme is employed, in which variable-length incremental redundancy (IR) bits are added to the originally-transmitted codeword until decoding is successful. With each decoding attempt, a non-zero processing delay is incurred. The optimal codewords lengths are analytically derived utilizing a sequential differential optimization (SDO) framework. The framework is general in that it only requires knowledge of an analytical expression of the positive feedback (ACK) probability as a function of the codeword length. 
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  2. In this paper, we study a fresh data acquisition problem to acquire fresh data and optimize the age-related performance when strategic data sources have private market information. We consider an information update system in which a destination acquires, and pays for, fresh data updates from a source. The destination incurs an age-related cost, modeled as a general increasing function of the age-of-information (AoI). The source is strategic and incurs a sampling cost, which is its private information and may not be truthfully reported to the destination. To this end, we design an optimal (economic) mechanism for timely information acquisition by generalizing Myerson's seminal work. The goal is to minimize the sum of the destination's age-related cost and its payment to the source, while ensuring that the source truthfully reports its private information and will voluntarily participate in the mechanism. Our results show that, under some distributions of the source's cost, our proposed optimal mechanism can lead to an unbounded benefit, compared against a benchmark that naively trusts the source's report and thus incentivizes its maximal over-reporting. 
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  3. The notion of timely status updating is investigated in the context of cloud computing. Measurements of a time-varying process of interest are acquired by a sensor node, and uploaded to a cloud server to undergo some required computations. These computations have random service times that are independent and identically distributed across different uploads. After the computations are done, the results are delivered to a monitor, constituting an update. The goal is to keep the monitor continuously fed with fresh updates over time, which is assessed by an age-of-information(AoI) metric. A scheduler is employed to optimize the measurement acquisition times. Following an update, an idle waiting period may be imposed by the scheduler before acquiring a new measurement. The scheduler also has the capability to preempt a measurement in progress if its service time grows above a certain cutoff time, and upload a fresher measurement in its place. Focusing on stationary deterministic policies, in which waiting times are deterministic functions of the instantaneous AoI and the cutoff time is fixed for all uploads, it is shown that the optimal waiting policy that minimizes the long term average AoI has a threshold structure, in which a new measurement is uploaded following an update only if the AoI grows above a certain threshold that is a function of the service time distribution and the cutoff time. The optimal cutoff is then found for standard and shifted exponential service times. While it has been previously reported that waiting before updating can be beneficial for AoI, it is shown in this work that preemption of late updates can be even more beneficial. 
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