Related papers: Construction and redundancy of codes for correctin…
In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements,…
Codes correcting bursts of deletions and localized deletions have garnered significant research interest in recent years. One of the primary objectives is to construct codes with minimal redundancy. Currently, the best known constructions…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
The explosion of the amount of data stored in cloud systems calls for more efficient paradigms for redundancy. While replication is widely used to ensure data availability, erasure correcting codes provide a much better trade-off between…
The noise model of deletions poses significant challenges in coding theory, with basic questions like the capacity of the binary deletion channel still being open. In this paper, we study the harder model of worst-case deletions, with a…
The coded trace reconstruction problem asks to construct a code $C\subset \{0,1\}^n$ such that any $x\in C$ is recoverable from independent outputs ("traces") of $x$ from a binary deletion channel (BDC). We present binary codes of rate…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
A binary 1-error-correcting code can always be embedded in a 1-perfect code of some larger length
We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms…
We classify all binary error correcting completely regular codes of length $n$ with minimum distance $\delta>n/2$.
We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…
Distributed storage systems often introduce redundancy to increase reliability. When coding is used, the repair problem arises: if a node storing encoded information fails, in order to maintain the same level of reliability we need to…
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…
The construction of deletion codes for the Levenshtein metric is reduced to the construction of codes over the integers for the Manhattan metric by run length coding. The latter codes are constructed by expurgation of translates of…
We improve the upper bound of Levenshtein for the cardinality of a code of length 4 capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we will construct an…
We give an explicit construction of length-$n$ binary codes capable of correcting the deletion of two bits that have size $2^n/n^{4+o(1)}$. This matches up to lower order terms the existential result, based on an inefficient greedy choice…
Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…
We explain how to optimize finite-length LDPC codes for transmission over the binary erasure channel. Our approach relies on an analytic approximation of the erasure probability. This is in turn based on a finite-length scaling result to…
Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating…