Related papers: Dual-Code Bounds on Multiple Concurrent (Local) Da…
This paper studies the problem of code symbol availability: a code symbol is said to have $(r, t)$-availability if it can be reconstructed from $t$ disjoint groups of other symbols, each of size at most $r$. For example, $3$-replication…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes which affects code performance and ease of physical realization. For device architectures restricted to 2D local gates,…
We introduce the notion of the stopping redundancy hierarchy of a linear block code as a measure of the trade-off between performance and complexity of iterative decoding for the binary erasure channel. We derive lower and upper bounds for…
The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…
Locally repairable codes (LRCs) are considered with equal or unequal localities, local distances and local field sizes. An explicit two-layer architecture with a sum-rank outer code is obtained, having disjoint local groups and achieving…
Peer-to-peer distributed storage systems provide reliable access to data through redundancy spread over nodes across the Internet. A key goal is to minimize the amount of bandwidth used to maintain that redundancy. Storing a file using an…
This work considers the smart repeater network where a single source $s$ wants to send two independent packet streams to destinations $\{d_1,d_2\}$ with the help of relay $r$. The transmission from $s$ or $r$ is modeled by packet erasure…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
There is a growing interest in discovery of internet topology at the interface level. A new generation of highly distributed measurement systems is currently being deployed. Unfortunately, the research community has not examined the problem…
Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…
Performance modeling of parallel applications on multicore computers remains a challenge in computational co-design due to the complex design of multicore processors including private and shared memory hierarchies. We present a Scalable…
Classical locally recoverable codes, which permit highly efficient recovery from localized errors as well as global recovery from larger errors, provide some of the most useful codes for distributed data storage in practice. In this paper,…
This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the…
Regenerating codes are a class of codes proposed for providing reliability of data and efficient repair of failed nodes in distributed storage systems. In this paper, we address the fundamental problem of handling errors and erasures during…
We consider the storage-retrieval rate tradeoff in private information retrieval (PIR) systems using a Shannon-theoretic approach. Our focus is mostly on the canonical two-message two-database case, for which a coding scheme based on random…
In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
The problem of robustly reconstructing a large number from its erroneous remainders with respect to several moduli, namely the robust remaindering problem, may occur in many applications including phase unwrapping, frequency detection from…
Consider a linear [n,k,d]_q code C. We say that that i-th coordinate of C has locality r, if the value at this coordinate can be recovered from accessing some other r coordinates of C. Data storage applications require codes with small…