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We describe and explore so-called linear hash functions and show how they can be used to build error detection and correction codes. The method can be applied for different types of errors (for example, burst errors). When the method is…
We investigate machine learning based on clustering techniques that are suitable for the detection of encoded strings of q-ary symbols transmitted over a noisy channel with partially unknown characteristics. We consider the detection of the…
We consider the problem of computing a binary linear transformation using unreliable components when all circuit components are unreliable. Two noise models of unreliable components are considered: probabilistic errors and permanent errors.…
Having a clean dataset has been the foundational assumption of most natural language processing (NLP) systems. However, properly written text is rarely found in real-world scenarios and hence, oftentimes invalidates the aforementioned…
We obtain exact expressions for the asymptotic behaviour of the average probability of the block decoding error for ensembles of regular low density parity check error correcting codes, by employing diagrammatic techniques. Furthermore, we…
Binary memristive crossbars have gained huge attention as an energy-efficient deep learning hardware accelerator. Nonetheless, they suffer from various noises due to the analog nature of the crossbars. To overcome such limitations, most…
In this work, we prove new results concerning the combinatorial properties of random linear codes. Firstly, we prove a lower bound on the list-size required for random linear codes over $\mathbb F_q$ $\varepsilon$-close to capacity to…
Probabilistic language models, e.g. those based on an LSTM, often face the problem of finding a high probability prediction from a sequence of random variables over a set of tokens. This is commonly addressed using a form of greedy decoding…
We propose a quantized decoding algorithm for low- density parity-check codes where the variable node update rule of the standard min-sum algorithm is replaced with a look-up table (LUT) that is designed using an information-theoretic…
Modern software relies on a multitude of automated testing and quality assurance tools to prevent errors, bugs and potential vulnerabilities. This study sets out to provide a head-to-head, quantitative and qualitative evaluation of six…
In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve…
A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on the soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering…
Guessing Random Additive Noise Decoding (GRAND) is a family of hard- and soft-detection error correction decoding algorithms that provide accurate decoding of any moderate redundancy code of any length. Here we establish a method through…
We consider the problem of slotted asynchronous coded communication, where in each time frame (slot), the transmitter is either silent or transmits a codeword from a given (randomly selected) codebook. The task of the decoder is to decide…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
We establish that during the execution of any Guessing Random Additive Noise Decoding (GRAND) algorithm, an interpretable, useful measure of decoding confidence can be evaluated. This measure takes the form of a log-likelihood ratio (LLR)…
Linear Programming (LP) decoding is emerging as an attractive alternative to decode Low-Density Parity-Check (LDPC) codes. However, the earliest LP decoders proposed for binary and nonbinary LDPC codes are not suitable for use at moderate…
Label noise may affect the generalization of classifiers, and the effective learning of main patterns from samples with noisy labels is an important challenge. Recent studies have shown that deep neural networks tend to prioritize the…
Exact queueing analysis of erasure networks with network coding in a finite buffer regime is an extremely hard problem due to the large number of states in the network. In such networks, packets are lost due to either link erasures or due…