A rate-compatible solution to the set reconciliation problem (2211.05472v2)

Abstract: We consider a set reconciliation setting in which two parties hold similar sets which they would like to reconcile In particular, we focus on set reconciliation based on invertible Bloom lookup tables (IBLTs), a probabilistic data structure inspired by Bloom filters but allowing for more complex operations. IBLT-based set reconciliation schemes have the advantage of exhibiting a low complexity, however, the schemes available in literature are known to be far from optimal in terms of communication complexity (overhead). The inefficiency of IBLT-based set reconciliation can be attributed to two facts. First, it requires an estimate of the cardinality of the set difference between the sets, which implies an increase in overhead. Second, in order to cope with errors in the aforementioned estimation of the cardinality of the set difference, IBLT schemes in literature make a worst-case assumption and oversize the data structures, thus further increasing the overhead. In this work, we present a novel IBLT-based set reconciliation protocol that does not require estimating the cardinality of the set difference. The scheme we propose relies on what we term multi-edge-type (MET) IBLTs. The simulation results shown in this paper show that the novel scheme outperforms previous IBLT-based approaches to set reconciliation