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Sample Quantize and Encode Timely Estimation Over Noisy Channels

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Document pages: 29 pages

Abstract: The effects of quantization and coding on the estimation quality ofGauss-Markov processes are considered, with a special attention to theOrnstein-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 isconsumed 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 anincreasing functional of the age-of-information (AoI), defined as the timeelapsed since the sampling time pertaining to the latest successfully decodedmessage. Such (age-penalty) functional depends on the quantization bits,codewords lengths and receiver processing time. The goal, for each codingscheme, is to optimize sampling times such that the long-term average MMSE isminimized. This is then characterized in the setting of general increasingage-penalty functionals, not necessarily corresponding to MMSE, which may be ofindependent interest in other contexts.The solution is first shown to be a threshold policy for IIR, and ajust-in-time policy for FR. Enhanced transmissions schemes are then developedin order to exploit the processing times to make new data available at thereceiver sooner. For both IIR and FR, it is shown that there exists an optimalnumber of quantization bits that balances AoI and quantization errors. It isalso shown that for longer receiver processing times, the relatively simpler FRscheme outperforms IIR.

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