XML query processing based on labeling schemes has been thoroughly studied in the past several years. Recently efficient processing of updates in dynamic XML data has gained more attention. However, all the existing techniques have high update cost, they cannot completely avoid re-labeling in XML updates, and they will increase the label size which will influence the query performance. Thus, in this paper we propose a novel Compact Dynamic Binary String (CDBS) encoding to efficiently process updates. CDBS has two important properties which form the foundations of this paper: (1) CDBS supports that CDBS codes can be inserted between any two consecutive CDBS codes with orders kept and without re-encoding the existing codes; (2) CDBS is orthogonal to specific labeling schemes; thus it can be applied broadly to different labeling schemes or other applications to efficiently process updates. Moreover, because CDBS will encounter the overflow problem, we improve CDBS to Compact Dynamic Quaternary String (CDQS) encoding which can completely avoid re-labeling in XML leaf node updates no matter what the labeling schemes are. Meanwhile, we also discuss how to efficiently process internal node updates. We report the experimental results to show that our CDBS and CDQS are superior to previous approaches to process both leaf node and internal node updates.