Related papers: Combinatorial Batch Codes: A Lower Bound and Optim…
Unbounded SubsetSum is a classical textbook problem: given integers $w_1,w_2,\cdots,w_n\in [1,u],~c,u$, we need to find if there exists $m_1,m_2,\cdots,m_n\in \mathbb{N}$ satisfying $c=\sum_{i=1}^n w_im_i$. In its all-target version, $t\in…
In this work, we consider the multi-access combinatorial topology with $C$ caches where each user accesses a unique set of $r$ caches. For this setup, we consider secrecy, where each user should not know anything about the files it did not…
We study the inherent space requirements of shared storage algorithms in asynchronous fault-prone systems. Previous works use codes to achieve a better storage cost than the well-known replication approach. However, a closer look reveals…
Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in…
We consider the $(K,L,M,N)$ multi-access coded caching system introduced by Hachem et al., which consists of a central server with $N$ files and $K$ cache nodes, each of memory size $M$, where each user can access $L$ cache nodes in a…
To address the exponentially rising demand for wireless content, use of caching is emerging as a potential solution. It has been recently established that joint design of content delivery and storage (coded caching) can significantly…
Caching is a technique to reduce the communication load in peak hours by prefetching contents during off-peak hours. An information-theoretic framework for coded caching was introduced by Maddah-Ali and Niesen in a recent work, where it was…
We investigate the fundamental task of addition under uncertainty, namely, addends that are represented as intervals of numbers rather than single values. One potential source of such uncertainty can occur when obtaining discrete-valued…
This paper presents a construction for high-rate MDS codes that enable bandwidth-efficient repair of a single node. Such MDS codes are also referred to as the minimum storage regenerating (MSR) codes in the distributed storage literature.…
Coherent parity check (CPC) codes are a new framework for the construction of quantum error correction codes that encode multiple qubits per logical block. CPC codes have a canonical structure involving successive rounds of bit and phase…
We consider a cache-aided interference network which consists of a library of $N$ files, $K_T$ transmitters and $K_R$ receivers (users), each equipped with a local cache of size $M_T$ and $M_R$ files respectively, and connected via a…
We address a centralized caching problem with unequal cache sizes. We consider a system with a server of files connected through a shared error-free link to a group of cache-enabled users where one subgroup has a larger cache size than the…
Bounded context switching (BCS) is an under-approximate method for finding violations to safety properties in shared memory concurrent programs. Technically, BCS is a reachability problem that is known to be NP-complete. Our contribution is…
Batched network coding is a variation of random linear network coding which has low computational and storage costs. In order to adapt to random fluctuations in the number of erasures in individual batches, it is not optimal to recode and…
An $(n, M)$ vector code $\mathcal{C} \subseteq \mathbb{F}^n$ is a collection of $M$ codewords where $n$ elements (from the field $\mathbb{F}$) in each of the codewords are referred to as code blocks. Assuming that $\mathbb{F} \cong…
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…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
A cache-aided $K$-user Gaussian broadcast channel (BC) is considered. The transmitter has a library of $N$ equal-rate files, from which each user demands one. The impact of the equal-capacity receiver cache memories on the minimum required…
The coded caching problem with secrecy constraint i.e., the users should not be able to gain any information about the content of the files that they did not demand, is known as the secretive coded caching problem. This was proposed by…
We study the optimal design of heterogeneous Coded Elastic Computing (CEC) where machines have varying computation speeds and storage. CEC introduced by Yang et al. in 2018 is a framework that mitigates the impact of elastic events, where…