相关论文: Bounds on Fractional Repetition Codes using Hyperg…
Recently, a number of variants of the notion of cut-preserving hypergraph sparsification have been studied in the literature. These variants include directed hypergraph sparsification, submodular hypergraph sparsification, general notions…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
A systematic convolutional encoder of rate $(n-1)/n$ and maximum degree $D$ generates a code of free distance at most ${\cal D} = D+2$ and, at best, a column distance profile (CDP) of $[2,3,\ldots,{\cal D}]$. A code is \emph{Maximum…
This paper introduces a sparse projection matrix composed of discrete (digital) periodic lines that create a pseudo-random (p.frac) sampling scheme. Our approach enables random Cartesian sampling whilst employing deterministic and…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
As consumers are increasingly engaged in social networking and E-commerce activities, businesses grow to rely on Big Data analytics for intelligence, and traditional IT infrastructures continue to migrate to the cloud and edge, these trends…
Heterogeneous Distributed Storage Systems (DSS) are close to real world applications for data storage. Internet caching system and peer-to-peer storage clouds are the examples of such DSS. In this work, we calculate the capacity formula for…
Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered…
The pivotal storage density win achieved by solid-state devices over magnetic devices recently is a result of multiple innovations in physics, architecture, and signal processing. Constrained coding is used in Flash devices to increase…
We investigate the problem of maintaining an encoded distributed storage system when some nodes contain adversarial errors. Using the error-correction capabilities that are built into the existing redundancy of the system, we propose a…
The process of DNA-based data storage (DNA storage for short) can be mathematically modelled as a communication channel, termed DNA storage channel, whose inputs and outputs are sets of unordered sequences. To design error correcting codes…
In this paper, we investigate maximum distance separable (MDS) codes based group coded caching in fog radio access networks (F-RANs). The goal is to minimize the average fronthaul rate under nonuniform file popularity. Firstly, an MDS codes…
We consider the problem of coding for computing with maximal distortion, where the sender communicates with a receiver, which has its own private data and wants to compute a function of their combined data with some fidelity constraint…
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 consider private information retrieval (PIR) for distributed storage systems (DSSs) with noncolluding nodes where data is stored using a non maximum distance separable (MDS) linear code. It was recently shown that if data is stored using…
\emph{Information Dispersal Algorithms (IDAs)} have been widely applied to reliable and secure storage and transmission of data files in distributed systems. An IDA is a method that encodes a file $F$ of size $L=|F|$ into $n$ unrecognizable…
We study finite-sum nonlinear programs with localized variable coupling encoded by a (hyper)graph. We introduce a graph-compliant decomposition framework that brings message passing into continuous optimization in a rigorous, implementable,…
In federated learning (FL) with top $r$ sparsification, millions of users collectively train a machine learning (ML) model locally, using their personal data by only communicating the most significant $r$ fraction of updates to reduce the…
Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF). This decoder displays sub-optimal performance in practice and requires very…
Index coding is often studied with the assumption that a single source has all the messages requested by the receivers. We refer to this as \emph{centralized} index coding. In contrast, this paper focuses on \emph{distributed} index coding…