In this correspondence, we correct an erroneous result on the achievability part of the Rényi common information with order $1+s\in (1,2]$ in (L. Yu and V. Y. F. Tan, “Wyner’s common information under Rényi divergence measures,” IEEE Trans. Inf. Theory, vol. 64, no. 5, pp. 3616–3632, May 2018). The new achievability result (upper bound) of the Rényi common information no longer coincides with Wyner’s common information. We also provide a new converse result (lower bound) in this correspondence for the Rényi 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.

中文翻译：

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对“人一分歧测度下的Wyner公共信息”的更正

在这封信函中，我们用顺序更正了人一公共信息的可实现性部分的错误结果 $1+s\in (1,2]$ (L. Yu and VYF Tan, “Wyner's common information under Rényi divergence measure,” IEEE 翻译 信息 理论，卷 64，没有。5，第 3616-3632 页，2018 年 5 月）。Rényi 公共信息的新可实现性结果（上限）不再与 Wyner 公共信息重合。我们还在这个对应关系中为 Rényi 公共信息提供了一个新的逆结果（下界） $1+s\in (1,\infty]$ . 数值结果表明，对于双对称二进制源，阶次的新上下界重合 $1+s\in (1,2]$ 并且它们都严格大于 Wyner 在这种情况下的共同信息。