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A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
Flash memory devices are winning the competition for storage density against magnetic recording devices. This outcome results from advances in physics that allow storage of more than one bit per cell, coupled with advances in signal…
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…
Coded caching systems have been widely studied to reduce the data transmission during the peak traffic time. In practice, two important parameters of a coded caching system should be considered, i.e., the rate which is the maximum amount of…
Large language models (LLMs) have achieved notable success in code generation. However, they still frequently produce uncompilable output because their next-token inference procedure does not model formal aspects of code. Although…
The two-dimensional magnetic recording (TDMR) technology promises storage densities of $10$ terabits per square inch. However, when tracks are squeezed together, a bit stored in the two-dimensional (TD) grid suffers inter-symbol…
Finding desired information from large data set is a difficult problem. Information retrieval is concerned with the structure, analysis, organization, storage, searching, and retrieval of information. Index is the main constituent of an IR…
The pivotal storage density win achieved by solid-state devices over magnetic devices in 2015 is a result of multiple innovations in physics, architecture, and signal processing. One of the most important innovations in that regard is…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
We introduce a new family of codes, termed weighted superimposed codes (WSCs). This family generalizes the class of Euclidean superimposed codes (ESCs), used in multiuser identification systems. WSCs allow for discriminating all bounded,…
The paper is devoted to the problem of erasure coding in distributed storage. We consider a model of storage that assumes that nodes are organized into equally sized groups, called racks, that within each group the nodes can communicate…
We consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We…
Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from…
Spatially-coupled (SC) codes, known for their threshold saturation phenomenon and low-latency windowed decoding algorithms, are ideal for streaming applications. They also find application in various data storage systems because of their…
Coded caching is a technique that generalizes conventional caching and promises significant reductions in traffic over caching networks. However, the basic coded caching scheme requires that each file hosted in the server be partitioned…
A new family of codes, called clustering-correcting codes, is presented in this paper. This family of codes is motivated by the special structure of data that is stored in DNA-based storage systems. The data stored in these systems has the…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
We propose computationally efficient encoders and decoders for lossy compression using a Sparse Regression Code. The codebook is defined by a design matrix and codewords are structured linear combinations of columns of this matrix. The…
Code Large Language Models (Code LLMs) have been increasingly used by developers to boost productivity, but they often generate vulnerable code. Thus, there is an urgent need to ensure that code generated by Code LLMs is correct and secure.…
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…