Related papers: Linear Batch Codes
Secure codes are widely-studied combinatorial structures which were introduced for traitor tracing in broadcast encryption. To determine the maximum size of such structures is the main research objective. In this paper, we investigate the…
We consider the canonical {\em shared link network} formed by a source node, hosting a library of $m$ information messages (files), connected via a noiseless common link to $n$ destination nodes (users), each with a cache of size M files.…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
Data generation and analysis is a fundamental aspect of many industries and disciplines, from strategic decision making in business to research in the physical and social sciences. However, data generated using software and algorithms can…
In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices. The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes…
The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched…
In a digital communication system, information is sent from one place to another over a noisy communication channel using binary symbols (bits). Original information is encoded by adding redundant bits, which are then used by low--density…
This paper discusses the feasibility of using Large Language Models LLM for code generation with a particular application in designing an RISC. The paper also reviews the associated steps such as parsing, tokenization, encoding, attention…
Batched sparse (BATS) code is a class of batched network code that can achieve a close-to-optimal rate when an optimal degree distribution is provided. We observed that most probability masses in this optimal distribution are very small,…
Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0-1 problems via a…
Load balancing is critical for distributed storage to meet strict service-level objectives (SLOs). It has been shown that a fast cache can guarantee load balancing for a clustered storage system. However, when the system scales out to…
A \textit{functional $k$-batch} code of dimension $s$ consists of $n$ servers storing linear combinations of $s$ linearly independent information bits. Any multiset request of size $k$ of linear combinations (or requests) of the information…
We consider the distributed computing problem of multiplying a set of vectors with a matrix. For this scenario, Li et al. recently presented a unified coding framework and showed a fundamental tradeoff between computational delay and…
As text and code resources have expanded, large-scale pre-trained models have shown promising capabilities in code generation tasks, typically employing supervised fine-tuning with problem statement-program pairs. However, increasing model…
We show that expander codes, when properly instantiated, are high-rate list recoverable codes with linear-time list recovery algorithms. List recoverable codes have been useful recently in constructing efficiently list-decodable codes, as…
Guo, Kopparty and Sudan have initiated the study of error-correcting codes derived by lifting of affine-invariant codes. Lifted Reed-Solomon (RS) codes are defined as the evaluation of polynomials in a vector space over a field by requiring…
The majority of works in distributed storage networks assume a simple network model with a collection of identical storage nodes with the same communication cost between the nodes. In this paper, we consider a realistic multi-rack…
Large language models (LLMs) increasingly play an important role in a wide range of information processing and management tasks in industry. Many of these tasks are performed in large batches or even offline, and the performance indicator…
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…