Strategic Quantization of a Noisy Source

This paper is concerned with strategic quantization of a noisy source where the encoder, which observes the remote source through a noisy channel, and the decoder, with distortions defined over the remote source, have misaligned objectives. We show that as in the classical noisy source setting, this indirect source coding problem can be transformed to direct source coding with an equivalent distortion measure defined as the conditional expectation of the original distortion measure conditioned over the sensing channel output. On the design side, we extend the gradient-descent based method developed to solve the noiseless problem in recent work to the associated noisy setting. Finally, we present the numerical results that confirm the theoretical analysis in this paper. The codes associated with our numerical results are available at: https://tinyurl.com/allerton2023.