Rate loss in distributed functional source coding

For point-to-point and distributed communication of continuous sources, high-resolution quantization theory provides an achievable rate-distortion trade-off that is simple to compute and motivates practical compression architectures. Moreover, high-resolution analysis gives good inner bounds for the Shannon rate-distortion region when a more general characterization is difficult. In this paper, we analyze the sum-rate gap between coded nonuniform scalar quantization and the Shannon rate- distortion region for a system that requires fidelity in a computation applied to the source variables. We find that the loss can be as low as 0.255 bits/sample, which has previously been observed in the point-to-point setting, and it is achieved using a simple architecture of nonuniform quantization followed by Slepian-Wolf coding.