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Register a new userOn Timely Channel Coding with Hybrid ARQ
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Added by
Ahmed Arafa
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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A status updating communication system is examined, in which a transmitter communicates with a receiver over a noisy channel. The goal is to realize timely delivery of fresh data over time, which is assessed by an age-of-information (AoI) metric. Channel coding is used to combat the channel errors, and feedback is sent to acknowledge updates reception. In case decoding is unsuccessful, a hybrid ARQ protocol is employed, in which incremental redundancy (IR) bits are transmitted to enhance the decoding ability. This continues for some amount of time in case decoding remains unsuccessful, after which a new (fresh) status update is transmitted instead. In case decoding is successful, the transmitter has the option to idly wait for a certain amount of time before sending a new update. A general problem is formulated that optimizes the codeword and IR lengths for each update, and the waiting times, such that the long term average AoI is minimized. Stationary deterministic policies are investigated, in which the codeword and IR lengths are fixed for each update, and the waiting time is a deterministic function of the AoI. The optimal waiting policy is then derived, and is shown to have a threshold structure, in which the transmitter sends a new update only if the AoI grows above a certain threshold that is a function of the codeword and IR lengths. Choosing the codeword and IR lengths is discussed in the context of binary symmetric channels.
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We consider a status update system in which the update packets need to be processed to extract the embedded useful information. The source node sends the acquired information to a computation unit (CU) which consists of a master node and $n$ worker nodes. The master node distributes the received computation task to the worker nodes. Upon computation, the master node aggregates the results and sends them back to the source node to keep it emph{updated}. We investigate the age performance of uncoded and coded (repetition coded, MDS coded, and multi-message MDS (MM-MDS) coded) schemes in the presence of stragglers under i.i.d.~exponential transmission delays and i.i.d~shifted exponential computation times. We show that asymptotically MM-MDS coded scheme outperforms the other schemes. Furthermore, we characterize the optimal codes such that the average age is minimized.
We consider two closely related problems: anomaly detection in sensor networks and testing for infections in human populations. In both problems, we have $n$ nodes (sensors, humans), and each node exhibits an event of interest (anomaly, infection) with probability $p$. We want to keep track of the anomaly/infection status of all nodes at a central location. We develop a $group$ $updating$ scheme, akin to group testing, which updates a central location about the status of each member of the population by appropriately grouping their individual status. Unlike group testing, which uses the expected number of tests as a metric, in group updating, we use the expected age of information at the central location as a metric. We determine the optimal group size to minimize the age of information. We show that, when $p$ is small, the proposed group updating policy yields smaller age compared to a sequential updating policy.
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.
We consider a system in which an information source generates independent and identically distributed status update packets from an observed phenomenon that takes $n$ possible values based on a given pmf. These update packets are encoded at the transmitter node to be sent to the receiver node. Instead of encoding all $n$ possible realizations, the transmitter node only encodes the most probable $k$ realizations and disregards whenever a realization from the remaining $n-k$ values occurs. We find the average age and determine the age-optimal real codeword lengths such that the average age at the receiver node is minimized. Through numerical evaluations for arbitrary pmfs, we show that this selective encoding policy results in a lower average age than encoding every realization and find the age-optimal $k$. We also analyze a randomized selective encoding policy in which the remaining $n-k$ realizations are encoded and sent with a certain probability to further inform the receiver at the expense of longer codewords for the selected $k$ realizations.
A status updating system is considered in which multiple data sources generate packets to be delivered to a destination through a shared energy harvesting sensor. Only one sources data, when available, can be transmitted by the sensor at a time, subject to energy availability. Transmissions are prune to erasures, and each successful transmission constitutes a status update for its corresponding source at the destination. The goal is to schedule source transmissions such that the collective long-term average age-of-information (AoI) is minimized. AoI is defined as the time elapsed since the latest successfully-received data has been generated at its source. To solve this problem, the case with a single source is first considered, with a focus on threshold waiting policies, in which the sensor attempts transmission only if the time until both energy and data are available grows above a certain threshold. The distribution of the AoI is fully characterized under such a policy. This is then used to analyze the performance of the multiple sources case under maximum-age-first scheduling, in which the sensors resources are dedicated to the source with the maximum AoI at any given time. The achievable collective long-term average AoI is derived in closed-form. Multiple numerical evaluations are demonstrated to show how the optimal threshold value behaves as a function of the system parameters, and showcase the benefits of a threshold-based waiting policy with intermittent energy and data arrivals.
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