Related papers: Construction Methods Based on Minimum Weight Distr…
Binary neural networks (BNNs) have been widely adopted to reduce the computational cost and memory storage on edge-computing devices by using one-bit representation for activations and weights. However, as neural networks become…
Neural networks with synaptic weights constructed according to the weighted Hebb rule, a variant of the familiar Hebb rule, are studied in the presence of noise(finite temperature), when the number of stored patterns is finite and in the…
In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums.…
Permutation codes of length $n$ and distance $d$ is a set of permutations on $n$ symbols, where the distance between any two elements in the set is at least $d$. Subgroup permutation codes are permutation codes with the property that the…
This paper is concerned with bounds on the maximum-likelihood (ML) decoding error probability of Reed-Solomon (RS) codes over additive white Gaussian noise (AWGN) channels. To resolve the difficulty caused by the dependence of the Euclidean…
Recalibrating probabilistic classifiers is vital for enhancing the reliability and accuracy of predictive models. Despite the development of numerous recalibration algorithms, there is still a lack of a comprehensive theory that integrates…
For the additive white Gaussian noise channel with average codeword power constraint, new coding methods are devised in which the codewords are sparse superpositions, that is, linear combinations of subsets of vectors from a given design,…
A closed form formula of the partition weight enumerator of maximum distance separable (MDS) codes is derived for an arbitrary number of partitions. Using this result, some properties of MDS codes are discussed. The results are extended for…
Polar codes are of great interest since they are the first provably capacity-achieving forward error correction codes. To improve throughput and to reduce decoding latency of polar decoders, maximum likelihood (ML) decoding units are used…
We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to…
An erasure channel with a fixed alphabet size $q$, where $q \gg 1$, is studied. It is proved that over any erasure channel (with or without memory), Maximum Distance Separable (MDS) codes achieve the minimum probability of error (assuming…
It is well known that Space-Time Block Codes (STBCs) from orthogonal designs (ODs) are single-symbol decodable/symbol-by-symbol decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes…
A pruned variant of polar coding is reinvented for all binary erasure channels. For small $\varepsilon>0$, we construct codes with block length $\varepsilon^{-5}$, code rate $\text{Capacity}-\varepsilon$, error probability $\varepsilon$,…
Following an analysis of the advantages of SQL-based Machine Learning (ML) and a short literature survey of the field, we describe a novel method for In-Database Machine Learning (IDBML). We contribute a process for SQL-code generation in…
Maximum distance separable (MDS) are constructed to required specifications. The codes are explicitly given over finite fields with efficient encoding and decoding algorithms. Series of such codes over finite fields with ratio of distance…
Linear programming approaches have been applied to derive upper bounds on the size of classical codes and quantum codes. In this paper, we derive similar results for general quantum codes with entanglement assistance, including nonadditive…
This paper investigates a novel lossy compression framework operating under logarithmic loss, designed to handle situations where the reconstruction distribution diverges from the source distribution. This framework is especially relevant…
The evaluation of the minimum distance of linear block codes remains an open problem in coding theory, and it is not easy to determine its true value by classical methods, for this reason the problem has been solved in the literature with…
In this paper non-trivial non-linear binary systematic AMDS codes are classified in terms of their weight distributions, employing only elementary techniques. In particular, we show that their length and minimum distance completely…
Polar codes were introduced in 2009 and proven to achieve the symmetric capacity of any binary-input discrete memoryless channel under low-complexity successive cancellation decoding. In this thesis, we construct cyclic polar codes based on…