Corrections to “Wyner’s Common Information Under Rényi Divergence Measures” [May 18 3616-3632

Abstract

In this correspondence, we correct an erroneous result on the achievability part of the Renyi common information with order $1+s\in (1,2]$ in (L. Yu and V. Y. F. Tan, “Wyner’s common information under Renyi divergence measures,” IEEE Trans. Inf. Theory, vol. 64, no. 5, pp. 3616–3632, May 2018). The new achievability result (upper bound) of the Renyi common information no longer coincides with Wyner’s common information. We also provide a new converse result (lower bound) in this correspondence for the Renyi common information with order $1+s\in (1,\infty]$ . Numerical results show that for doubly symmetric binary sources, the new upper and lower bounds coincide for the order $1+s\in (1,2]$ and they are both strictly larger than Wyner’s common information for this case.