Related papers: On Erasure Combinatorial Batch Codes
Repair operations in distributed storage systems potentially expose the data to malicious acts of passive eavesdroppers or active adversaries, which can be detrimental to the security of the system. This paper presents erasure codes and…
We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage.…
The paper introduces ensembles of accumulate-repeat-accumulate (ARA) codes which asymptotically achieve capacity on the binary erasure channel (BEC) with {\em bounded complexity}, per information bit, of encoding and decoding. It also…
We consider the rack-aware storage system where \(n\) nodes are organized in \(\bar{n}\) racks each containing \(u\) nodes, and any \(k\) nodes can retrieve the stored file. Moreover, any single node erasure can be recovered by downloading…
The problem of joint universal source coding and identification is considered in the setting of fixed-rate lossy coding of continuous-alphabet memoryless sources. For a wide class of bounded distortion measures, it is shown that any…
This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable…
Coded caching schemes are used to reduce computer network traffics in peak time. To determine the efficiency of the schemes, \cite{MN} defined the information rate of the schemes and gave a construction of optimal coded caching schemes.…
Classical coded caching setting avails each user to have one dedicated cache. This is generalized to a more general shared cache scheme and the exact expression for the worst case rate was derived in [E. Parrinello, A. Unsal, P. Elia,…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications and data storage systems. SC codes are constructed by partitioning an…
This article describes lossless compression algorithms for multisets of sequences, taking advantage of the multiset's unordered structure. Multisets are a generalisation of sets where members are allowed to occur multiple times. A multiset…
We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$. Then we give an improved construction of binary codes capable…
In a single hop broadcast packet erasure network, we demonstrate that it is possible to provide multirate packet delivery outside of what is given by the network min-cut. This is achieved by using a deterministic non-block-based network…
In this work, lossy distributed compression of pairs of correlated sources is considered. Conventionally, Shannon's random coding arguments -- using randomly generated unstructured codebooks whose blocklength is taken to be asymptotically…
A generic $(r,m)$-erasure correcting set is a collection of vectors in $\bF_2^r$ which can be used to generate, for each binary linear code of codimension $r$, a collection of parity check equations that enables iterative decoding of all…
Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the…
Coded distributed batch computation distributes a computation task, such as matrix multiplication, $N$-linear computation, or multivariate polynomial evaluation, across $S$ servers through a coding scheme, such that the response from any…
In this paper, we study the minimum distances of binary linear codes with parity check matrices formed from subset inclusion matrices $W_{t,n,k}$, representing $t$-element subsets versus $k$-element subsets of an $n$-element set. We provide…
Let $n, r, k$ be positive integers such that $3\leq k < n$ and $2\leq r \leq k-1$. Let $m(n, r, k)$ denote the maximum number of edges an $r$-uniform hypergraph on $n$ vertices can have under the condition that any collection of $i$ edges,…
We consider the problem of erasure/list decoding using certain classes of simplified decoders. Specifically, we assume a class of erasure/list decoders, such that a codeword is in the list if its likelihood is larger than a threshold. This…
We consider irregular product codes.In this class of codes, each codeword is represented by a matrix. The entries in each row (column) of the matrix should come from a component row (column) code. As opposed to (standard) product codes, we…