相关论文: Codes for Correcting Localized Deletions
Modern large-scale distributed storage systems use erasure codes to protect against node failures with low storage overhead. In practice, the failure rate and other factors of storage devices in the system may vary significantly over time,…
Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error…
In this paper, we investigate binary reconstruction codes capable of correcting one deletion and one substitution. We define the \emph{single-deletion single-substitution ball} function $ \mathcal{B} $ as a mapping from a sequence to the…
Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,\delta)$-locally balanced constraint requires that the weight of any…
Locally repairable codes have become a key instrument in large-scale distributed storage systems. This paper focuses on the construction of locally repairable codes with $(r,\delta)$-locality that achieve the equality in the Singleton-type…
We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code…
For a systematic erasure code, update complexity (UC) is defined as the maximum number of parity blocks needed to be changed when some information blocks are updated. Locally repairable codes (LRCs) have been recently proposed and used in…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
Locally decodable codes (LDCs) are error-correcting codes $C : \Sigma^k \to \Sigma^n$ that admit a local decoding algorithm that recovers each individual bit of the message by querying only a few bits from a noisy codeword. An important…
We improve Levenshtein's upper bound for the cardinality of a code of length four that is capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we construct…
Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…
We classify all binary error correcting completely regular codes of length $n$ with minimum distance $\delta>n/2$.
Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code. However, the lack of a practical decoding algorithm remains a barrier to…
This manuscript is an extended abstract version of the paper entitled ``Quantum Deletion Codes derived from Classical Deletion Codes.'' The paper contributes to the fundamental theory for quantum deletion error-correcting codes. The paper…
This paper develops a new family of locally recoverable codes for distributed storage systems, Sequential Locally Recoverable Codes (SLRCs) constructed to handle multiple erasures in a sequential recovery approach. We propose a new…
Distributed and cloud storage systems are used to reliably store large-scale data. Erasure codes have been recently proposed and used in real-world distributed and cloud storage systems such as Google File System, Microsoft Azure Storage,…
We consider error decoding of locally repairable codes (LRC) and partial MDS (PMDS) codes through interleaved decoding. For a specific class of LRCs we investigate the success probability of interleaved decoding. For PMDS codes we show that…
In this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is…
A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the "help-by-transfer" property where…
We consider the locally repairable codes (LRC), aiming at sequential recovering multiple erasures. We define the (n,k,r,t)-SLRC (Sequential Locally Repairable Codes) as an [n,k] linear code where any t'(>= t) erasures can be sequentially…