Rate-Distortion Achievability via Event Threshold Quantizers for Planer Wiener Processes

We analyze the rate-distortion performance of two quantized event-based encoding paradigms estimating a two-dimensional Wiener process. Each encoder remains silent until the estimation error reaches a threshold and then transmits a packet from a finite codebook over a noiseless, zero-delay channel to a decoder that updates the estimate. Both encoding methods are parameterized by the radius of the event threshold and the size of the codebook. The first encoding scheme simply quantizes the error of the source process on the event threshold. The second scheme employs a dithered quantizer, which simplifies the derivation of an analytical rate-distortion upper bound. Each method is simulated in discrete time to inform the choice of the bitrate-optimal codebook size and event radius for a given distortion constraint. The rate-distortion performance of these encoding schemes are compared to a known lower bound and a conservative upper bound that we derive herein.