Decoding Errors in Difference-Invertible Bloom Filters: Analysis and Resolution

An invertible Bloom filter (IBF) is a useful data structure for various network applications because the difference IBF (d-IBF) of two IBFs programmed by two separate sets effectively identifies distinct elements unique to each set. d-IBF eliminates common elements, and unique elements are listed through a decoding process that utilizes pure cells, each of which stores a single element in a cell. However, the definition of pure cells used for decoding an IBF is insufficient to decode a d-IBF. Composite cells in a d-IBF can also satisfy the pure cell conditions defined for an IBF, and decoding composite cells adversely affects d-IBF performance. This study mathematically analyzes the probability of decoding errors in a d-IBF and proposes a new decoding method to resolve these errors. Experimental results confirm that the proposed decoding method successfully detects and resolves the decoding errors. This enables accurate identification of the difference between the two sets without generating any incorrect elements, even with a small IBF of m =
$2d$
regardless of set sizes, where m is the number of cells in the IBF and d is the size of the difference.