Related papers: Coded Iterative Computing using Substitute Decodin…
An efficient decoding algorithm for horizontally u-interleaved LRPC codes is proposed and analyzed. Upper bounds on the decoding failure rate and the computational complexity of the algorithm are derived. It is shown that interleaving…
A general class of polynomial remainder codes is considered. Such codes are very flexible in rate and length and include Reed-Solomon codes as a special case. As an extension of previous work, two joint error-and-erasure decoding approaches…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
Quantum low-density parity-check (LDPC) codes are a promising family of quantum error-correcting codes for fault tolerant quantum computing with low overhead. Decoding quantum LDPC codes on quantum erasure channels has received more…
In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted…
In support of applications involving multiview sources in distributed object recognition using lightweight cameras, we propose a new method for the distributed coding of sparse sources as visual descriptor histograms extracted from…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
In a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information…
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error…
We propose a method for modifying orthogonal sparse matrix pairs used in CSS codes while preserving their matrix row and column weight distributions, which play a crucial role in determining the performance of belief-propagation decoding.…
The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and control. Traditionally, low-rank approximations are constructed…
This paper proposes an enhanced list-aided successive cancellation stack (ELSCS) decoding algorithm with adjustable decoding complexity. In addition, a logarithmic likelihood ratio (LLR)-threshold based path extension scheme is designed to…
Sparse coding of images is traditionally done by cutting them into small patches and representing each patch individually over some dictionary given a pre-determined number of nonzero coefficients to use for each patch. In lack of a way to…
Generative retrieval has emerged as a powerful paradigm for LLM-based recommendation. However, industrial recommender systems often benefit from restricting the output space to a constrained subset of items based on business logic (e.g.…
Product codes (PCs) and staircase codes (SCCs) are conventionally decoded based on bounded distance decoding (BDD) of the component codes and iterating between row and column decoders. The performance of iterative BDD (iBDD) can be improved…
Sparse representations of images are useful in many computer vision applications. Sparse coding with an $l_1$ penalty and a learned linear dictionary requires regularization of the dictionary to prevent a collapse in the $l_1$ norms of the…
MapReduce is a commonly used framework for executing data-intensive jobs on distributed server clusters. We introduce a variant implementation of MapReduce, namely "Coded MapReduce", to substantially reduce the inter-server communication…
Many parallel algorithms which solve basic problems in computer science use auxiliary space linear in the input to facilitate conflict-free computation. There has been significant work on improving these parallel algorithms to be in-place,…