Related papers: Construction and Encoding Algorithm for Maximum Ru…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
Locally Decodable Codes (LDCs) are error-correcting codes $C\colon\Sigma^n\rightarrow \Sigma^m,$ encoding \emph{messages} in $\Sigma^n$ to \emph{codewords} in $\Sigma^m$, with super-fast decoding algorithms. They are important mathematical…
This paper investigates the construction of linear network codes for broadcasting a set of data packets to a number of users. The links from the source to the users are modeled as independent erasure channels. Users are allowed to inform…
We present in this paper a special class of unit memory convolutional codes (UMCCs), called semi-random UMCCs (SRUMCCs), where the information block is first encoded by a short block code and then transmitted in a block Markov (random)…
Streaming codes (SCs) are packet-level codes that recover erased packets within a strict decoding-delay deadline. Streaming codes for various packet erasure channel models such as sliding-window (SW) channel models that admit random or…
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…
The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. On one end of this spectrum of…
This paper tackles two problems that fall under the study of coding for insertions and deletions. These problems are motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm,…
Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $\delta$ deletions occur in each of the concatenated strings.…
Lattice codes with optimal decoding coefficient are capacity-achieving when dimension $N \rightarrow \infty$. In communications systems, finite dimensional lattice codes are considered, where the optimal decoding coefficients may still fail…
This paper investigates the ultra reliable and low latency communication (URLLC) performance of the IRS-aided MIMO system. The upper and lower bounds of the optimal average error probability (OAEP) for the coding rate 1/sqrt(Mn) of the…
A locally repairable code (LRC) with locality $r$ allows for the recovery of any erased codeword symbol using only $r$ other codeword symbols. A Singleton-type bound dictates the best possible trade-off between the dimension and distance of…
We construct constant-sized ensembles of linear error-correcting codes over any fixed alphabet that can correct a given fraction of adversarial erasures at rates approaching the Singleton bound arbitrarily closely. We provide several…
We consider a real-time streaming system where messages are created sequentially at the source, and are encoded for transmission to the receiver over a packet erasure link. Each message must subsequently be decoded at the receiver within a…
We study data structures in the presence of adversarial noise. We want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object, even if the data structure has been…
In this paper, we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where data is represented by an unordered set of $M$ sequences, each of length $L$. Errors…
Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through…
We consider the locality of encoding and decoding operations in distributed storage systems (DSS), and propose a new class of codes, called locally encodable and decodable codes (LEDC), that provides a higher degree of operational locality…
Two-dimensional error-correcting codes, where codewords are represented as $n \times n$ arrays over a $q$-ary alphabet, find important applications in areas such as QR codes, DNA-based storage, and racetrack memories. Among the possible…
In this work, we investigate the problem of constructing codes capable of correcting two deletions. In particular, we construct a code that requires redundancy approximately 8 log n + O(log log n) bits of redundancy, where n is the length…