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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…
In this paper, we present error-correcting codes which are the results of our research on the sub-exceeding functions. For a short and medium distance data transmission (wifi network, bluetooth, cable, ...), we see that these codes…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
Error correction code is a major part of the communication physical layer, ensuring the reliable transfer of data over noisy channels. Recently, neural decoders were shown to outperform classical decoding techniques. However, the existing…
This paper investigates data compression that simultaneously allows local decoding and local update. The main result is a universal compression scheme for memoryless sources with the following features. The rate can be made arbitrarily…
This paper explores the design of convolutional codes for varying constraint lengths, focusing on their role in error correction in digital communication systems. Convolutional codes are essential in achieving reliable data transmission…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of single-user memoryless channels. Recently Polyanskiy et al. studied the benefit of variable-length feedback with termination (VLFT)…
Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possible altered vectorspace. Ralf Koetter and Frank R. Kschischang in Coding for errors and erasures in…
In this work, we investigate the problem of neural-based error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We…
Function-correcting codes (FCCs) protect specific function evaluations of a message against errors. This condition imposes a less stringent distance requirement than classical error-correcting codes (ECCs), allowing for reduced redundancy.…
Broadcast networks allow one to model networks of identical nodes communicating through message broadcasts. Their parameterized verification aims at proving a property holds for any number of nodes, under any communication topology, and on…
Link and node failures are common two fundamental problems that affect operational networks. Hence, protection of communication networks is essential to increase their reliability, performance, and operations. Much research work has been…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
Emerging edge intelligence applications require the server to retrain and update deep neural networks deployed on remote edge nodes to leverage newly collected data samples. Unfortunately, it may be impossible in practice to continuously…
Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node,…
Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating…
The index coding problem is a fundamental transmission problem which occurs in a wide range of multicast networks. Network coding over a large finite field size has been shown to be a theoretically efficient solution to the index coding…
In this work, we consider adaptive linear programming (ALP) decoding of linear codes over the finite field $\mathbb{F}_p$ of size $p$ where $p$ is a prime. In particular, we provide a general construction of valid inequalities for the…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…