Related papers: Recursive/Iterative unique Projection-Aggregation …
We study robust PCA for the fully observed setting, which is about separating a low rank matrix $\boldsymbol{L}$ and a sparse matrix $\boldsymbol{S}$ from their sum $\boldsymbol{D}=\boldsymbol{L}+\boldsymbol{S}$. In this paper, a new…
A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes based on successive permutations (SP) of the codeword is presented. A low-complexity SP scheme applied to a subset of the symmetry group of RM codes is first…
Recent work have shown that Reed-Muller (RM) codes achieve the erasure channel capacity. However, this performance is obtained with maximum-likelihood decoding which can be costly for practical applications. In this paper, we propose an…
Partial Unit Memory (PUM) codes are a special class of convolutional codes, which are often constructed by means of block codes. Decoding of PUM codes may take advantage of existing decoders for the block code. The Dettmar--Sorger algorithm…
Coded polynomial aggregation (CPA) in distributed computing systems enables the master to directly recover a weighted aggregation of polynomial computations without individually decoding each term, thereby reducing the number of required…
We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.
Weighted projective spaces are natural generalizations of projective spaces with a rich structure. Projective Reed-Muller codes are error-correcting codes that played an important role in reliably transmitting information on digital…
Massive machine-type communications (mMTC) demand robust solutions to support extensive connectivity efficiently. Unsourced random access (URA) has emerged as a promising approach, delivering high spectral and energy efficiency. Among URA…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
Reed-Muller (RM) codes exhibit good performance under maximum-likelihood (ML) decoding due to their highly-symmetric structure. In this paper, we explore the question of whether the code symmetry of RM codes can also be exploited to achieve…
With the availability of more powerful computers, iterative reconstruction algorithms are the subject of an ongoing work in the design of more efficient reconstruction algorithms for X-ray computed tomography. In this work, we show how two…
Visual anomaly detection aims at classifying and locating the regions that deviate from the normal appearance. Embedding-based methods and reconstruction-based methods are two main approaches for this task. However, they are either not…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…
In this paper we present a comprehensive framework for learning robust low-rank representations by combining and extending recent ideas for learning fast sparse coding regressors with structured non-convex optimization techniques. This…
We propose a novel framework for retinal feature point alignment, designed for learning cross-modality features to enhance matching and registration across multi-modality retinal images. Our model draws on the success of previous…
We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some conditions for the weights, and we use it to derive bounds…
Unsourced random access (URA) is an increasingly popular communication paradigm attuned to machine driven data transfers in \textit{Internet-of-Things} (IoT) networks. In a typical URA setting, a small subset of active devices within a very…
Mixed precision Runge--Kutta methods have been recently developed and used for the time-evolution of partial differential equations. Two-derivative Runge--Kutta schemes may offer enhanced stability and accuracy properties compared to…
Accurate cloud property retrieval is vital for understanding cloud behavior and its impact on climate, including applications in weather forecasting, climate modeling, and estimating Earth's radiation balance. The Independent Pixel…
The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Also, a special class of generalized concatenated codes (GCC) can be…