Related papers: Bounding Multiple Unicasts through Index Coding an…
Recent studies have delved into the construction of locally repairable codes (LRCs) with optimal minimum distance from function fields. In this paper, we present several novel constructions by extending the findings of optimally designed…
Recent years, several new types of codes were introduced to provide fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) have played an important role. A…
The index coding problem is a problem of efficient broadcasting with side-information. We look at the uniprior index coding problem, in which the receivers have disjoint side-information symbols and arbitrary demand sets. Previous work has…
List-decoding and list-recovery are important generalizations of unique decoding that received considerable attention over the years. However, the optimal trade-off among list-decoding (resp. list-recovery) radius, list size, and the code…
The problem of two-sender unicast index coding consists of two senders and a set of receivers. Each receiver demands a unique message and possesses some of the messages demanded by other receivers as its side-information. Every demanded…
We show that for the multi-antenna Gaussian multi-access channel (MAC) and broadcast channel (BC) with perfect feedback, the rate regions achieved by linear-feedback coding schemes (called linear-feedback capacity regions) coincide when the…
In this paper, we introduce a model of a distributed storage system that is locally recoverable from any single server failure. Unlike the usual local recovery model of codes for distributed storage, this model accounts for the fact that…
We suggest a new approach to obtain bounds on locally correctable and some locally testable binary linear codes, by arguing that these codes (or their subcodes) have coset leader graphs with high discrete Ricci curvature. The bounds we…
We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and introduce a class of invariants that refine the classical…
In the practical network communications, many internal nodes in the network are required to not only transmit messages but decode source messages. For different applications, four important classes of linear network codes in network coding…
Locally recoverable (LRC) codes provide ways of recovering erased coordinates of the codeword without having to access each of the remaining coordinates. A subfamily of LRC codes with hierarchical locality (H-LRC codes) provides added…
An index coding (IC) problem consisting of a server and multiple receivers with different side-information and demand sets can be equivalently represented using a fitting matrix. A scalar linear index code to a given IC problem is a matrix…
We revisit existing linear computation coding (LCC) algorithms, and introduce a new framework that measures the computational cost of computing multidimensional linear functions, not only in terms of the number of additions, but also with…
The problem of multilevel diversity coding with regeneration is considered in this work. Two new outer bounds on the optimal tradeoffs between the normalized storage capacity and repair bandwidth are established, by which the optimality of…
Self-Repairing Codes (SRC) are codes designed to suit the need of coding for distributed networked storage: they not only allow stored data to be recovered even in the presence of node failures, they also provide a repair mechanism where as…
We consider a wireless broadcast station that transmits packets to multiple users. The packet requests for each user may overlap, and some users may already have certain packets. This presents a problem of broadcasting in the presence of…
The groupcast index coding problem is the most general version of the classical index coding problem, where any receiver can demand messages that are also demanded by other receivers. Any groupcast index coding problem is described by its…
Maximally recoverable codes are a class of codes which recover from all potentially recoverable erasure patterns given the locality constraints of the code. In earlier works, these codes have been studied in the context of codes with…
We establish an equivalence between two important random ensembles of linear codes: random linear codes (RLCs) and random Reed-Solomon (RS) codes. Specifically, we show that these models exhibit identical behavior with respect to key…
We consider the communication capacity of wireline networks for a two-unicast traffic pattern. The network has two sources and two destinations with each source communicating a message to its own destination, subject to the capacity…