Upper Bounds on Multiple $b$-Burst Deletion-Correcting Codes
For researchers in coding theory and DNA storage, this work provides tighter theoretical bounds on codes correcting consecutive deletions, improving upon prior results.
This paper investigates the fundamental limits of multiple b-burst deletion-correcting codes, deriving improved upper and lower bounds on the maximum code size. The bounds are asymptotically optimal for certain parameter regimes.
Motivated by their applications in DNA-based storage systems, codes capable of correcting consecutive deletions have attracted significant attention. An important class of such codes consists of those that can correct multiple consecutive deletion errors, commonly referred to as multiple $b$-burst deletion-correcting codes. In this paper, we investigate the fundamental limits of multiple $b$-burst deletion-correcting codes. Specifically, we first characterize several structural properties of the associated deletion balls. Then, leveraging these properties, we derive several upper bounds and a combinatorial lower bound on the maximum size of such codes. As a consequence, our bounds improve upon the previously known results for general parameter regimes and are shown to be asymptotically optimal for certain cases.