Related papers: Linear Batch Codes
A functional $k$-batch code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information bits. These codes are designed to recover any multiset of $k$ requests, each being a linear combination…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Batch codes are a family of codes that represent a distributed storage system (DSS) of $n$ nodes so that any batch of $t$ data symbols can be retrieved by reading at most one symbol from each node. Fractional repetition codes are a family…
Many database applications perform complex data retrieval and update tasks. Nested queries, and queries that invoke user-defined functions, which are written using a mix of procedural and SQL constructs, are often used in such applications.…
We describe and explore so-called linear hash functions and show how they can be used to build error detection and correction codes. The method can be applied for different types of errors (for example, burst errors). When the method is…
This paper presents the first generic bi-objective binary linear branch-and-cut algorithm. Studying the impact of valid inequalities in solution and objective spaces, two cutting frameworks are proposed. The multi-point separation problem…
Private information retrieval (PIR) codes and batch codes are two important types of codes that are designed for coded distributed storage systems and private information retrieval protocols. These codes have been the focus of much…
We propose a new caching scheme where linear combinations of the file segments are cached at the users, for the cases where the number of files is no greater than the number of users. When a user requests a certain file in the delivery…
Network coding can significantly improve the transmission rate of communication networks with packet loss compared with routing. However, using network coding usually incurs high computational and storage costs in the network devices and…
In this paper, we quantify how much codes can reduce the data retrieval latency in storage systems. By combining a simple linear code with a novel request scheduling algorithm, which we call Blocking-one Scheduling (BoS), we show…
We consider load balancing problem in a cache network consisting of storage-enabled servers forming a distributed content delivery scenario. Previously proposed load balancing solutions cannot perfectly balance out requests among servers,…
Machine learning training pipelines consume data in batches. A single training step may require thousands of samples drawn from shards distributed across a storage cluster. Issuing thousands of individual GET requests incurs per-request…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
Linear batch codes and codes for private information retrieval (PIR) with a query size $t$ and a restricted size $r$ of the reconstruction sets are studied. New bounds on the parameters of such codes are derived for small values of $t$ or…
Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…
As large language models (LLMs) grow in popularity for their diverse capabilities, improving the efficiency of their inference systems has become increasingly critical. Batching LLM requests is a critical step in scheduling the inference…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
Coded distributed computing introduced by Li et al. in 2015 is an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. In particular, Li et al. show that…
Information theoretic analysis of a coded caching system is considered, in which a server with a database of N equal-size files, each F bits long, serves K users. Each user is assumed to have a local cache that can store M files, i.e.,…
A functional $k$-PIR code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information symbols. Any linear combination of the $s$ information symbols can be recovered by $k$ disjoint subsets…