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In addition to their applications in data storage, communications systems, and consumer electronics, LCD codes -- a class of linear codes -- have been employed in cryptography recently. LCD cyclic codes were referred to as reversible cyclic…

This paper proposes a new family of recursive systematic convolutional codes, defined in the non-binary domain over different Galois fields GF(q) and intended to be used as component codes for the design of non-binary turbo codes. A general…

Radial basis function generated finite-difference (RBF-FD) methods have recently gained popularity due to their flexibility with irregular node distributions. However, the convergence theories in the literature, when applied to nonuniform…

This paper provides a comprehensive survey on recent advances in deep learning (DL) techniques for the channel coding problems. Inspired by the recent successes of DL in a variety of research domains, its applications to the physical layer…

We introduce a new paradigm for finite precision iterative decoding on low-density parity-check codes over the Binary Symmetric channel. The messages take values from a finite alphabet, and unlike traditional quantized decoders which are…

It is a long standing open problem to find search to decision reductions for structured versions of the decoding problem of linear codes. Such results in the lattice-based setting have been carried out using number fields: Polynomial-LWE,…

This is a survey article written for a workshop on L-functions and random matrix theory at the Newton Institute in July, 2004. The goal is to give some insight into how well-distributed sets of matrices in classical groups arise from…

We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…

Large language models (LLMs) trained on next-token prediction (NTP) paradigm have demonstrated powerful capabilities. However, the existing NTP paradigm contains several limitations, particularly related to planned task complications and…

Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over certain finite rings, more efficient physical-layer network coding…

In this paper, we propose a methodology to compute the optimal finite-length coding rate for random linear network coding schemes over a line network. To do so, we first model the encoding, reencoding, and decoding process of different…

An essential part of monitoring machine learning models in production is measuring input and output data drift. In this paper, we present a system for measuring distributional shifts in natural language data and highlight and investigate…

Large language models (LLM) are advanced AI systems trained on extensive textual data, leveraging deep learning techniques to understand and generate human-like language. Today's LLMs with billions of parameters are so huge that hardly any…

We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that…

This paper proposes LCFL, a novel clustering metric for evaluating clients' data distributions in federated learning. LCFL aligns with federated learning requirements, accurately assessing client-to-client variations in data distribution.…

In this paper, we study the performance of finite-length LDPC codes in the waterfall region. We propose an algorithm to predict the error performance of finite-length LDPC codes over various binary memoryless channels. Through numerical…

Recently, deep learning(DL) methods have been proposed for the low-dose computed tomography(LdCT) enhancement, and obtain good trade-off between computational efficiency and image quality. Most of them need large number of pre-collected…

Let $\mathbb{F}_{p^m}$ be a finite field with $p^m$ elements, where $p$ is an odd prime and $m$ is a positive integer. Recently, \cite{Hengar} and \cite{Wang2020} determined the weight distributions of subfield codes with the form…

Tabular deep-learning methods require embedding numerical and categorical input features into high-dimensional spaces before processing them. Existing methods deal with this heterogeneous nature of tabular data by employing separate…

This paper proposes a highly efficient global coded-multiplexing scheme, conceptualized as Orthogonal Frequency Division Multiplexing over a finite field (FF-OFDM), for reliable multiuser communications. By utilizing a prime length cyclic…