Related papers: On Extremal Rates of Storage over Graphs
This paper presents flexible storage codes, a class of error-correcting codes that can recover information from a flexible number of storage nodes. As a result, one can make a better use of the available storage nodes in the presence of…
By a locally recoverable code (LRC), we will in this paper, mean a linear code in which a given code symbol can be recovered by taking a linear combination of at most $r$ other code symbols with $r << k$. A natural extension is to the local…
We propose a novel technique for constructing a graph representation of a code through which we establish a significant connection between the service rate problem and the well-known fractional matching problem. Using this connection, we…
One of the primary objectives of a distributed storage system is to reliably store large amounts of source data for long durations using a large number $N$ of unreliable storage nodes, each with $c$ bits of storage capacity. Storage nodes…
The concept of the \textit{relative fractional packing number} between two graphs $G$ and $H$, initially introduced in arXiv:2307.06155 [math.CO], serves as an upper bound for the ratio of the zero-error Shannon capacity of these graphs.…
Caching at the wireless edge nodes is a promising way to boost the spatial and spectral efficiency, for the sake of alleviating networks from content-related traffic. Coded caching originally introduced by Maddah-Ali and Niesen…
This paper finds new tight finite-blocklength bounds for the best achievable lossy joint source-channel code rate, and demonstrates that joint source-channel code design brings considerable performance advantage over a separate one in the…
Maximally recoverable codes are codes designed for distributed storage which combine quick recovery from single node failure and optimal recovery from catastrophic failure. Gopalan et al [SODA 2017] studied the alphabet size needed for such…
This paper introduces the notion of cache-tapping into the information theoretic models of coded caching. The wiretap channel II in the presence of multiple receivers equipped with fixed-size cache memories, and an adversary which selects…
Let $\Gamma$ be a simple connected graph on $n$ vertices, and let $C$ be a code of length $n$ whose coordinates are indexed by the vertices of $\Gamma$. We say that $C$ is a \textit{storage code} on $\Gamma$ if for any codeword $c \in C$,…
We consider storage systems in which $K$ files are stored over $N$ nodes. A node may be systematic for a particular file in the sense that access to it gives access to the file. Alternatively, a node may be coded, meaning that it gives…
A cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle. An L-cycle cover is a cycle cover in which the length of every cycle is in the set L. The weight of a cycle cover of an edge-weighted graph is…
Machine learning models that take computer program source code as input typically use Natural Language Processing (NLP) techniques. However, a major challenge is that code is written using an open, rapidly changing vocabulary due to, e.g.,…
In this paper, we study the zero-error capacity of channels with memory, which are represented by graphs. We provide a method to construct code for any graph with one edge, thereby determining a lower bound on its zero-error capacity.…
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from all other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an identifying code of…
Coding techniques may be useful for data center data survivability as well as for reducing traffic congestion. We present a queued cross-bar network (QCN) method that can be used for traffic analysis of both replication/uncoded and coded…
The service rate region of a coded distributed storage system is the set of all achievable data access requests under the capacity constraints. This paper investigates the service rate regions of systematic Hamming codes using hypergraph…
Shaping codes are used to generate code sequences in which the symbols obey a prescribed probability distribution. They arise naturally in the context of source coding for noiseless channels with unequal symbol costs. Recently, shaping…
We describe and analyze the joint source/channel coding properties of a class of sparse graphical codes based on compounding a low-density generator matrix (LDGM) code with a low-density parity check (LDPC) code. Our first pair of theorems…
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…