Source Coding for Synthesizing Correlated Randomness

We consider a scenario wherein two parties Alice and Bob are provided $X_{1}^{n}$ notation="LaTeX">$X_{2}^{n}$ – samples that IID from PMF notation="LaTeX">$P_{X_{1} X_{2}}$ . can communicate to Charlie over (noiseless) communication links of rates notation="LaTeX">$R_{1}$ notation="LaTeX">$R_{2}$ , respectively. Their goal is enable generate notation="LaTeX">$Y^{n}$ such the triple notation="LaTeX">$(X_{1}^{n},X_{2}^{n},Y^{n})$ has close, in total variation, notation="LaTeX">$\prod P_{X_{1} X_{2} Y}$ enabling three achieve strong coordination. In addition, may posses pairwise shared common randomness at notation="LaTeX">$C_{1}$ notation="LaTeX">$C_{2}$ address problem characterizing set rate quadruples notation="LaTeX">$(R_{1},R_{2},C_{1},C_{2})$ for which above be accomplished. propose new coding scheme based on random algebraic codes–coset codes particular–of asymptotically large block-length. analyze its performance derive single-letter information-theoretic inner bound. This bound subsumes largest known improves upon it strictly identified examples. Our findings build variant soft-covering generalizes applicability code ensembles. we provide an outer region this party distributed setup.