Related papers: Erasure codes with symbol locality and group decod…
Batch codes are a useful notion of locality for error correcting codes, originally introduced in the context of distributed storage and cryptography. Many constructions of batch codes have been given, but few lower bound (limitation)…
When a node in a distributed storage system fails, it needs to be promptly repaired to maintain system integrity. While typical erasure codes can provide a significant storage advantage over replication, they suffer from poor repair…
Erasure codes provide a storage efficient alternative to replication based redundancy in (networked) storage systems. They however entail high communication overhead for maintenance, when some of the encoded fragments are lost and need to…
A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the encoding is a function of a small number (at most $r$) other symbols. We present a family of LRC codes that attain the maximum possible value of the…
Maximally Recoverable Local Reconstruction Codes (LRCs) are codes designed for distributed storage to provide maximum resilience to failures for a given amount of storage redundancy and locality. An $(n,r,h,a,g)$-MR LRC has $n$ coordinates…
We introduce a new erasure decoder that applies to arbitrary quantum LDPC codes. Dubbed the cluster decoder, it generalizes the decomposition idea of Vertical-Horizontal (VH) decoding introduced by Connelly et al. in 2022. Like the VH…
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…
In this paper, we consider a few iterative decoding schemes for the joint source-channel coding of correlated sources. Specifically, we consider the joint source-channel coding of two erasure correlated sources with transmission over…
Erasure codes are being increasingly used in distributed-storage systems in place of data-replication, since they provide the same level of reliability with much lower storage overhead. We consider the problem of constructing explicit…
Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing…
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…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
We investigate adaptive single-trial error/erasure decoding of binary codes whose decoder is able to correct e errors and t erasures if le+t<=d-1. Thereby, d is the minimum Hamming distance of the code and 1<l<=2 is the tradeoff parameter…
A distributed quantum storage code maps a quantum message to N storage nodes, of arbitrary specified sizes, such that the stored message is robust to an arbitrary specified set of erasure patterns. The sizes of the storage nodes, and…
The concept of group divisible codes, a generalization of group divisible designs with constant block size, is introduced in this paper. This new class of codes is shown to be useful in recursive constructions for constant-weight and…
Two new rate-one full-diversity space-time block codes (STBC) are proposed. They are characterized by the \emph{lowest decoding complexity} among the known rate-one STBC, arising due to the complete separability of the transmitted symbols…
Maximum-distance-separable (MDS) codes are a class of erasure codes that are widely adopted to enhance the reliability of distributed storage systems (DSS). In (n, k) MDS coded DSS, the original data are stored into n distributed nodes in…
Distributed data storage systems are essential to deal with the need to store massive volumes of data. In order to make such a system fault-tolerant, some form of redundancy becomes crucial, incurring various overheads - most prominently in…
Locally decodable channel codes form a special class of error-correcting codes with the property that the decoder is able to reconstruct any bit of the input message from querying only a few bits of a noisy codeword. It is well known that…
We consider the problem of constructing codes that can correct $\delta$ deletions occurring in an arbitrary binary string of length $n$ bits. Varshamov-Tenengolts (VT) codes, dating back to 1965, are zero-error single deletion $(\delta=1)$…