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A Viterbi-like decoding algorithm is proposed in this paper for generalized convolutional network error correction coding. Different from classical Viterbi algorithm, our decoding algorithm is based on minimum error weight rather than the…
Unsourced random access is a novel communication paradigm designed for handling a large number of uncoordinated users that sporadically transmit very short messages. Under this model, coded compressed sensing (CCS) has emerged as a…
We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that…
The security of code-based cryptosystems such as the McEliece cryptosystem relies primarily on the difficulty of decoding random linear codes. The best decoding algorithms are all improvements of an old algorithm due to Prange: they are…
In this paper, we consider the problem of remote vector Gaussian source coding for a wireless acoustic sensor network. Each node receives messages from multiple nodes in the network and decodes these messages using its own measurement of…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
We study a lossy source coding problem with secrecy constraints in which a remote information source should be transmitted to a single destination via multiple agents in the presence of a passive eavesdropper. The agents observe noisy…
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…
We consider the problem of distributed lossy linear function computation in a tree network. We examine two cases: (i) data aggregation (only one sink node computes) and (ii) consensus (all nodes compute the same function). By quantifying…
We introduce a general framework that constructs estimators with reduced variance for random walk Metropolis and Metropolis-adjusted Langevin algorithms. The resulting estimators require negligible computational cost and are derived in a…
Various studies that address the compressed sensing problem with Multiple Measurement Vectors (MMVs) have been recently carried. These studies assume the vectors of the different channels to be jointly sparse. In this paper, we relax this…
Distributed optimization methods are often applied to solving huge-scale problems like training neural networks with millions and even billions of parameters. In such applications, communicating full vectors, e.g., (stochastic) gradients,…
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…
We consider a distributed source coding problem of $L$ correlated Gaussian observations $Y_i, i=1,2,...,L$. We assume that the random vector $Y^{L}={}^{\rm t} (Y_1,Y_2,$ $...,Y_L)$ is an observation of the Gaussian random vector…
We consider a coded compressed sensing approach for the unsourced random access and replace the outer tree code proposed by Amalladinne et al. with the list recoverable code capable of correcting t errors. A finite-length random coding…
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this…
Motivated by storage applications, we study the following data structure problem: An encoder wishes to store a collection of jointly-distributed files $\overline{X}:=(X_1,X_2,\ldots, X_n) \sim \mu$ which are \emph{correlated}…
The sum-rank metric generalizes the Hamming and rank metric by partitioning vectors into blocks and defining the total weight as the sum of the rank weights of these blocks, based on their matrix representation. In this work, we explore…
Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…
We consider the following communication scenario. An encoder causally observes the Wiener process and decides when and what to transmit about it. A decoder makes real-time estimation of the process using causally received codewords. We…