Two-terminal source coding with common sum reconstruction
This work addresses a specific coding problem in information theory, but it is incremental as it builds on existing results for related problems.
The paper tackles the problem of two-terminal source coding where both terminals must reconstruct the sum of two correlated sources with identical reconstructions under distortion constraints, and it develops inner and outer bounds for the achievable rate distortion region for a doubly symmetric binary source.
We present the problem of two-terminal source coding with Common Sum Reconstruction (CSR). Consider two terminals, each with access to one of two correlated sources. Both terminals want to reconstruct the sum of the two sources under some average distortion constraint, and the reconstructions at two terminals must be identical with high probability. In this paper, we develop inner and outer bounds to the achievable rate distortion region of the CSR problem for a doubly symmetric binary source. We employ existing achievability results for Steinberg's common reconstruction and Wyner-Ziv's source coding with side information problems, and an achievability result for the lossy version of Korner-Marton's modulo-two sum computation problem.