Age of information (AoI) is a fundamentally important metric to characterize the freshness of information in real-time Internet of Things (IoT) monitoring systems. Another important metric is the energy cost for information sensing and transmission. In this paper, we investigate the average AoI and energy cost for low-density parity-check coded status update with and without automatic repeat request (ARQ), where the fixed redundancy scheme is employed. The non-ARQ, classical ARQ, truncated ARQ, and truncated hybrid ARQ with Chase combining (HARQ-CC) schemes are analyzed and compared. By using the renewal processes theory, the expressions for the average AoI as well as the average energy cost of each considered scheme are derived. Both the lower bound of age and the upper bound of energy are provided. It is shown through simulation results that the average AoI and energy cost are mainly influenced by network parameters in the low signal-to-noise ratio (SNR) region. With short code, the smaller average AoI can be obtained at the cost of more energy consumption. Compared with other schemes, the truncated HARQ-CC achieves the best average AoI and the moderate average energy cost, which is a compromise between the age and energy.

Age of information (AoI) and energy efficiency (EE), as two important performance metrics in status update systems, usually cannot be simultaneously optimized. This paper investigates the age and energy tradeoff for multicast networks with retransmissions, where each sensed status update is encoded as a short blocklength packet and is broadcasted to multiple destinations via independent and identically distributed error-prone channels. By considering the stopping threshold, the average AoI and EE expressions for stopping at earliest- l , stopping at preselected- l , and wait-for-all schemes are derived as a function of the packet length. On this basis, the average AoI-EE ratio is introduced and is minimized to trade off age and energy by optimizing the packet length. Numerical results indicate that among the three schemes, earliest- l scheme attains the minimum AoI when the packet length is small, and preselected- l scheme attains the maximum EE when the packet length is large. An optimal packet length can always be found for each scheme to minimize age-energy ratio. Moreover, the selection of stopping threshold l will also impact the age and energy performance.

Age of information (AoI) and energy cost (EC) are two key metrics in real-time remote monitoring systems. In this letter, we investigate the age-energy tradeoff for a short packet-based two-hop status update system, where the packet transmission may fail because of channel errors. In this case, the source can either retransmit the failed update to save EC for sensing, or generate a new one to maintain the AoI. Accordingly, we consider the truncated automatic repeat request (ARQ) scheme in both the first and second hops with different retransmission thresholds. Closed-form average AoI and average EC are given as a function of the failure probability and the thresholds of two hops. Moreover, a weighted sum of AoI and EC is minimized to tradeoff the age and energy. Numerical results demonstrate that increasing the difference between the thresholds of two hops can reduce the average AoI but increase the average EC, and an optimal packet length can always be identified to achieve age-energy tradeoff.

A novel status update information system is designed by jointly considering wireless energy harvesting diversity, status update transmission diversity, and hybrid automatic repeat request with chase combining (HARQ-CC) diversity, which consists of two sensors and one destination. The two sensors, which have finite-sized batteries, harvest energy from a Bernoulli process, and cooperatively deliver the status update to the destination by sharing a common information source. In addition, the two sensors synchronously operate in half-duplex (HD) mode and are triggered by a common control center. We first propose the sensor energy harvesting model that can be represented by Markov chain (MC) and develop the construction method of the transition matrix of sensor battery energy states as well as the stationary distributions. Secondly, the average age of information (AoI) of the proposed dual-sensor status update system is derived in terms of a closed-form expression by accurately calculating the statistical descriptions of the maximal number of the retransmissions of an update packet and the service time of one packet. Compared with traditional single-sensor system, the proposed dual-sensor system not only harvests more energy, but also has a smaller average AoI.

This paper focuses on the timely delivery of status updates for a multi-relay assisted energy harvesting (EH) Internet of Things system with short packet communications (SPC), where an EH-powered source transmits status updates to a destination with the aid of multiple EH-powered relays. To improve the energy efficiency and information freshness, an earliest-ℓ partial relay selection scheme is proposed, in which the earliest ℓ relays that successfully receive the status update from the source will be selected to forward the status update to the destination, and the selection combining (SC) and maximal-ratio combining (MRC) schemes are used at the destination. Firstly, we investigate the update packet delivery schemes of source-relay (S-R) and relay-destination (R-D) links, and present the packet error probabilities under the SC and MRC schemes based on SPC theory. Secondly, after characterizing the full charge time durations of both the source and relay, we investigate the statistical description of the number of the packet transmission attempts from the source to relay as well as the one from the relay to destination by using order statistics. With the analysis of the evolution of the instantaneous age of information (AoI), the expression for average AoI is derived. Finally, we investigate the average AoI minimization, which is formulated as a coupled triplet problem of the packet lengths at the source and relays and the value of ℓ. To overcome the coupling, we present the convexity approximation of the average AoI as well as the concise proof. Then, an efficient gradient-based two-step optimal search algorithm is proposed to solve the optimization problem, which searches the local optimal packet lengths for S-R and R-D links by iteratively updating the value of ℓ until the global optimal objective parameters are found. Numerical analyses give the effect of the key parameters on the average AoI, and the comparison demonstrates that the proposed gradient-based method converges quickly than the conventional greedy search method.

In the Internet of Things monitoring systems, the fresh information delivery and efficient energy usage are two significant design concerns. However, they generally cannot be simultaneously achieved. In this paper, we investigate the fundamental tradeoff between the age of information (AoI) and energy consumption (EC) for a generalized $\ell$ th best relay selection policy in two-hop cooperative status update systems with automatic repeat request (ARQ), where the source delivers the sensed status update to the destination through multiple decode-and-forward relays. Among these relays, the $\ell$ th best relay (i.e., the $\ell$ -th earliest one that correctly decodes the update packet) will be selected as a forwarder to relay the data to the sink. When a decoding failure occurs, we can either retransmit the old packet to save sensing EC or sense and transmit a new one to reduce AoI. Accordingly, the classical ARQ and truncated ARQ protocols are employed in the second hop. By considering short packet-based transmissions, the average AoI and average EC expressions are derived, and the weighted combination of them is minimized to attain the tradeoff. Numerical results demonstrate that an optimal packet size that can trade off age and energy always exists. Moreover, the best relay does not always minimize the weighted combination, and the truncated ARQ is superior to the classical one. As a promising candidate, the $\ell$ th best relay selection can be implemented when either the system energy resource is limited or the best relay is unavailable.