The Estimation-Compression Separation in Semantic Communication Systems

We study an estimation-compression (EC) separation scheme in a semantic communication system. Therein, the semantic information is intrinsic and not observable. The EC scheme first estimates the semantic information from the observed message and then compresses the estimation subject to a rate-distortion regime. The corresponding EC rate-distortion tradeoff is obtained. In particular, the EC separation scheme achieves the semantic rate-distortion function if the estimation is a sufficient statistic of the semantic information based on the observed message. Moreover, the extra distortion incurred by the compression in addition to the irreducible error in semantic estimation problems is also analyzed. A binary classification of vector Gaussian observations is investigated. We design an optimal soft decision estimator which is a sufficient statistic and show that it strictly outperforms the Bayesian decision estimator in terms of rate-distortion tradeoff. As the dimension of the observed Gaussian vector increases, the performance gap between the Bayesian decision estimator and the soft decision estimator becomes smaller and smaller until it is negligible.