Strategic Quantization Over a Noisy Channel.

This paper is concerned with the strategic quantization setting where the encoder and the decoder have misaligned objectives and communicate over a noisy channel, extending the work on classical channel-optimized quantization. This problem without the quantization constraint has been well-studied under the theme of information design problems in Economics. It is more appealing and relevant to engineering applications with a constraint on the cardinality of the message space. We consider a scalar source $X$ and develop a gradient-descent based solution in conjunction with random index assignment, which has been used in prior literature on classical channel-optimized quantizaton. In our prior work, we used dynamic programming for this problem. Here, we employ gradient descent to reduce the complexity of the algorithm. We finally present numerical results obtained via the proposed algorithm that suggest its validity and demonstrate the strategic quantization features that differentiate it from its classical counterpart. The codes are available at: https://tinyurl.com/asilomar2023.