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Asymptotically Optimal Joint Sampling and Compression for Timely Status Updates: AgeDistortion Tradeoff
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DOI：10.1109/TVT.2024.3479242.png)
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Abstract
En 中文
We consider a joint sampling and compression system for timely status updates. Samples are taken, quantized and encoded into binary sequences, which are sent to the destination. According to the timeliness requirement represented by an age penalty function at the destination, we formulate an optimization problem to jointly design sampler, quantizer and encoder, optimizing data freshness on the basis of satisfying a mean-squared error (MSE) distortion constraint of the samples. We use average nonlinear age (ANA) to measure data freshness and study linear, squared and exponential penalty functions. We prove that the zero-wait sampling, the uniform quantization, and the ANA- optimal coding policies together provide an asymptotically optimal solution, in the sense that, as the average distortion approaches zero, the solution achieves the minimum ANA asymptotically, for the linear and squared penalty functions. When the probability density function (pdf) is weakly unimodal, we also prove that the zero-wait sampling, the K-L quantization which is asymptotically optimal for the quantization with R & eacute;nyi entropy constraint, and the ANA-optimal coding policies are asymptotically optimal for the exponential penalty function. Furthermore, we prove that the optimal ANA is asymptotically linear with respect to the log MSE distortion with a slope of - 3/4 , - root 7|12 and -1, corresponding to the linear, squared and exponential penalty functions, respectively.
Keywords:
Symbols
Encoding
Nonlinear distortion
Receivers
Quantization (signal)
Channel coding
Real-time systems
Probability density function
Data integrity
Accuracy
Age of information
average nonlinear age (ANA)
data compression
high-resolution quantization
timely status updates
Journal
IF:
7.1
Papers:
1.8W
Citations:
6.6W