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Consider two remote nodes (encoder and decoder), each with a binary sequence. The encoder's sequence $X$ differs from the decoder's sequence $Y$ by a small number of edits (deletions and insertions). The goal is to construct a message $M$,…
This paper considers the problem of variable-length coding over a discrete memoryless channel (DMC) with noiseless feedback. The paper provides a stochastic control view of the problem whose solution is analyzed via a newly proposed…
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…
Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of data. In this work we show that orthogonality relations…
Under the emerging network coding paradigm, intermediate nodes in the network are allowed not only to store and forward packets but also to process and mix different data flows. We propose a low-complexity cryptographic scheme that exploits…
Physical-layer network coding (PNC) is now well-known as a potential candidate for delay-sensitive and spectrally efficient communication applications, especially in two-way relay channels (TWRCs). In this paper, we present the error…
As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes,…
The question of list decoding error-correcting codes over finite fields (under the Hamming metric) has been widely studied in recent years. Motivated by the similar discrete structure of linear codes and point lattices in R^N, and their…
Network embedding has attracted an increasing attention over the past few years. As an effective approach to solve graph mining problems, network embedding aims to learn a low-dimensional feature vector representation for each node of a…
Error correction code (ECC) is an integral part of the physical communication layer, ensuring reliable data transfer over noisy channels. Recently, neural decoders have demonstrated their advantage over classical decoding techniques.…
The universal secure network coding presented by Silva et al. realizes secure and reliable transmission of a secret message over any underlying network code, by using maximum rank distance codes. Inspired by their result, this paper…
We consider a communication problem in which an update of the source message needs to be conveyed to one or more distant receivers that are interested in maintaining specific linear functions of the source message. The setting is one in…
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
The growing demand for highly reliable communication systems drives the research and development of algorithms that identify and correct errors during data transmission and storage. This need becomes even more critical in hard-to-access or…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
In "On Coding for Reliable Communication over Packet Networks" (Lun, Medard, and Effros, Proc. 42nd Annu. Allerton Conf. Communication, Control, and Computing, 2004), a capacity-achieving coding scheme for unicast or multicast over lossy…
We study two fundamental problems in communication, Document Exchange (DE) and Error Correcting Code (ECC). In the first problem, two parties hold two strings, and one party tries to learn the other party's string through communication. In…
A new class of exact-repair regenerating codes is constructed by stitching together shorter erasure correction codes, where the stitching pattern can be viewed as block designs. The proposed codes have the "help-by-transfer" property where…
We develop a network coding technique based on flags of subspaces and a corresponding network channel model. To define error correcting codes we introduce a new distance on the flag variety, the Grassmann distance on flags and compare it to…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…