Fundamental Limits of Lossless Data Compression With Side Information

The problem of lossless data compression with side information available to both the encoder and decoder is considered. finite-blocklength fundamental limits best achievable performance are defined, in two different versions problem: Reference-based compression, when a single string used repeatedly compressing source messages, pair-based where for each message. General achievability converse theorems established arbitrary source-side pairs. Nonasymptotic normal approximation expansions proved optimal rate reference-based settings, memoryless sources. These stated terms explicit, bounds, that tight up third-order terms. Extensions go significantly beyond class sources obtained. relevant dispersion identified its relationship conditional varentropy established. Interestingly, it general smaller.