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A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the encoding is a function of a small number (at most $r$) other symbols. We present a family of LRC codes that attain the maximum possible value of the…
Large-scale machine learning and data mining applications require computer systems to perform massive matrix-vector and matrix-matrix multiplication operations that need to be parallelized across multiple nodes. The presence of straggling…
In distributed computing, slower nodes (stragglers) usually become a bottleneck. Gradient Coding (GC), introduced by Tandon et al., is an efficient technique that uses principles of error-correcting codes to distribute gradient computation…
A cumbersome operation in many scientific fields, is inverting large full-rank matrices. In this paper, we propose a coded computing approach for recovering matrix inverse approximations. We first present an approximate matrix inversion…
The reliability of erasure-coded distributed storage systems, as measured by the mean time to data loss (MTTDL), depends on the repair bandwidth of the code. Repair-efficient codes provide reliability values several orders of magnitude…
An adaptive delay-tolerant distributed space-time coding (DSTC) scheme that exploits feedback is proposed for two-hop cooperative MIMO networks. Maximum likelihood (ML) receivers and adjustable code matrices are considered subject to a…
Matrix-parametrized models, including multiclass logistic regression and sparse coding, are used in machine learning (ML) applications ranging from computer vision to computational biology. When these models are applied to large-scale ML…
Matrix-parametrized models, including multiclass logistic regression and sparse coding, are used in machine learning (ML) applications ranging from computer vision to computational biology. When these models are applied to large-scale ML…
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and…
In this paper, we extend the work of (Abbondati et al., 2024) on decoding simultaneous rational number codes by addressing two important scenarios: multiplicities and the presence of bad primes (divisors of denominators). First, we…
In a distributed computing system for the master-worker framework, an erasure code can mitigate the effects of slow workers, also called stragglers. The distributed computing system combined with coding is referred to as coded computation.…
Petabyte-scale distributed storage systems are currently transitioning to erasure codes to achieve higher storage efficiency. Classical codes like Reed-Solomon are highly sub-optimal for distributed environments due to their high overhead…
Rateless/fountain codes are designed so that all input symbols can be recovered from a slightly larger number of coded symbols, with high probability using an iterative decoder. In this paper we investigate the number of input symbols that…
The continuously increasing amount of digital data generated by today's society asks for better storage solutions. This survey looks at a new generation of coding techniques designed specifically for the needs of distributed networked…
Locally repairable codes have become a key instrument in large-scale distributed storage systems. This paper focuses on the construction of locally repairable codes with $(r,\delta)$-locality that achieve the equality in the Singleton-type…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
Local Reconstruction Codes (LRCs) allow for recovery from a small number of erasures in a local manner based on just a few other codeword symbols. A maximally recoverable (MR) LRC offers the best possible blend of such local and global…
Inexpensive cloud services, such as serverless computing, are often vulnerable to straggling nodes that increase end-to-end latency for distributed computation. We propose and implement simple yet principled approaches for straggler…
Deep polar codes are pre-transformed polar codes that employ a multi-layered polar kernel transformation strategy to enhance code performance in short blocklength regimes. However, like conventional polar codes, their block length is…
With the rapid evolution of large language models (LLM), reinforcement learning (RL) has emerged as a pivotal technique for code generation and optimization in various domains. This paper presents a systematic survey of the application of…