Fixed-length compression for letter-based fidelity measures in the finite blocklength regime

This paper studies fixed-length compression with multiple constraints in the finite blocklength regime. We introduce two different average distortion measures and consider constraints for individual source outcomes. The concept of d-tilted information as well as recent finite-length bounds for the optimal coding rates are extended to this setting. We further particularise our results to the binary memoryless source and a sparse Gaussian source.