Related papers: Block Circulant Codes with Application to Decentra…
A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants in the parity-check matrix of a block code into several components and piecing copies of these components in a diagonal structure. By connecting…
We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {\alpha; \beta; k; t}, where k is the number of information symbols, each codeword of an…
We consider the concatenation of a convolutional code (CC) with an optimized cyclic redundancy check (CRC) code as a promising paradigm for good short blocklength codes. The resulting CRC-aided convolutional code naturally permits the use…
Block codes are considered for improving the reliability of messages stored in a computer memory with both stuck-at defects and random errors. It is assumed that the side information about the state of the defects is available to the…
A circulant-based spatially-coupled (SC) code is constructed by partitioning the circulants of an underlying block code into a number of components, and then coupling copies of these components together. By connecting (coupling) several SC…
We consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We…
Low density parity check (LDPC) codes, initially discovered by Gallager, exhibit excellent performance in iterative decoding, approaching the Shannon limit. MDS array codes, with favorable algebraic structures, are codes suitable for…
In order to accommodate the ever-growing data from various, possibly independent, sources and the dynamic nature of data usage rates in practical applications, modern cloud data storage systems are required to be scalable, flexible, and…
Rollups have emerged as a promising solution to enhance blockchain scalability, offering increased throughput, reduced latency, and lower transaction fees. However, they currently rely on a centralized sequencer to determine transaction…
We introduce a family of balanced locally repairable codes (BLRCs) $[n, k, d]$ for arbitrary values of $n$, $k$ and $d$. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low…
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A.…
We prove that 3-query linear locally correctable codes over the Reals of dimension $d$ require block length $n>d^{2+\lambda}$ for some fixed, positive $\lambda >0$. Geometrically, this means that if $n$ vectors in $R^d$ are such that each…
We consider the problem of encoding information in a system of N=K+R processors that operate in a decentralized manner, i.e., without a central processor which orchestrates the operation. The system involves K source processors, each…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Coded computing has proved to be useful in distributed computing. We have observed that almost all coded computing systems studied so far consider a setup of one master and some workers. However, recently emerging technologies such as…
Blockchain design involves many tradeoffs, and much debate has focused on tradeoffs related to scaling parameters such as blocksize. To address some of the confusion around this subject, we present a probability proof of the DCS Triangle.…
We analyze permutation routing of rigid blocks representing surface code patches of $d_C^2$ atoms on a reconfigurable lattice with hypergraph transformations. For a hypergraph $H$, code distance $d_C$, $s=d_C^2$, number of blocks $N_L$, and…
Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a…
We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes…
SC-LDPC codes with sub-block locality can be decoded locally at the level of sub-blocks that are much smaller than the full code block, thus providing fast access to the coded information. The same code can also be decoded globally using…