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A new property which relies on the linear programming (LP) decoder, the approximate maximum-likelihood certificate (AMLC), is introduced. When using the belief propagation decoder, this property is a measure of how close the decoded…

Information Theory · Computer Science 2011-05-17 Idan Goldenberg , David Burshtein

In this work it is shown that locally repairable codes (LRCs) can be list-decoded efficiently beyond the Johnson radius for a large range of parameters by utilizing the local error-correction capabilities. The corresponding decoding radius…

Information Theory · Computer Science 2020-09-16 Lukas Holzbaur , Sven Puchinger , Antonia Wachter-Zeh

In natural language processing (NLP), the likelihood ratios (LRs) of N-grams are often estimated from the frequency information. However, a corpus contains only a fraction of the possible N-grams, and most of them occur infrequently. Hence,…

Computation and Language · Computer Science 2022-04-15 Masato Kikuchi , Mitsuo Yoshida , Kyoji Umemura , Tadachika Ozono

A key component of generating text from modern language models (LM) is the selection and tuning of decoding algorithms. These algorithms determine how to generate text from the internal probability distribution generated by the LM. The…

Machine Learning · Computer Science 2023-12-05 Ali Naseh , Kalpesh Krishna , Mohit Iyyer , Amir Houmansadr

We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…

Information Theory · Computer Science 2016-11-15 Constantinos Daskalakis , Alexandros G. Dimakis , Richard M. Karp , Martin J. Wainwright

Quantum error correction requires decoders that are both accurate and efficient. To this end, union-find decoding has emerged as a promising candidate for error correction on the surface code. In this work, we benchmark a weighted variant…

Quantum Physics · Physics 2020-07-22 Shilin Huang , Michael Newman , Kenneth R. Brown

We introduce new reliability definitions for bit and check nodes. Maximizing global reliability, which is the sum reliability of all bit nodes, is shown to be equivalent to minimizing a decoding metric which is closely related to the…

Information Theory · Computer Science 2010-01-15 Chi-Yuan Chang , Yu T. Su , Yu-Liang Chen , Yin-Chen Liu

Graph Neural Networks (GNNs) have emerged as a powerful, data-driven approach for Quantum Error Correction (QEC) decoding, capable of learning complex noise characteristics directly from syndrome data. However, the robustness of these…

Quantum Physics · Physics 2025-08-08 Ryota Ikeda

The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of…

Cryptography and Security · Computer Science 2022-10-18 Kevin Carrier , Thomas Debris-Alazard , Charles Meyer-Hilfiger , Jean-Pierre Tillich

We present a new model for LT codes which simplifies the analysis of the error probability of decoding by belief propagation. For any given degree distribution, we provide the first rigorous expression for the limiting error probability as…

Information Theory · Computer Science 2007-07-13 Elitza N. Maneva , Amin Shokrollahi

Speculative Decoding (SD) accelerates autoregressive large language model (LLM) inference by decoupling generation and verification. While recent methods improve draft quality by tightly coupling the drafter with the target model, the…

Machine Learning · Computer Science 2026-04-14 Jingwei Song , Xinyu Wang , Hanbin Wang , Xiaoxuan Lei , Bill Shi , Shixin Han , Eric Yang , Xiao-Wen Chang , Lynn Ai

Designing robust algorithms capable of training accurate neural networks on uncurated datasets from the web has been the subject of much research as it reduces the need for time consuming human labor. The focus of many previous research…

Computer Vision and Pattern Recognition · Computer Science 2022-10-18 Paul Albert , Eric Arazo , Tarun Krishna , Noel E. O'Connor , Kevin McGuinness

flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…

Quantum Physics · Physics 2023-08-30 T. R. Scruby , K. Nemoto

Quantum error correction is of crucial importance for fault-tolerant quantum computers. As an essential step towards the implementation of quantum error-correcting codes, quantum non-demolition (QND) measurements are needed to efficiently…

Soft demodulation of received symbols into bit log-likelihood ratios (LLRs) is at the very heart of multiple-input-multiple-output (MIMO) detection. However, the optimal maximum a posteriori (MAP) detector is complicated and infeasible to…

Signal Processing · Electrical Eng. & Systems 2022-08-18 Jiankun Zhang , Hao Wang , Jing Qian , Zhenxing Gao

\textbf{RE}trieval-\textbf{A}ugmented \textbf{L}LM-based \textbf{M}achine \textbf{T}ranslation (REAL-MT) shows promise for knowledge-intensive tasks like idiomatic translation, but its reliability under noisy retrieval contexts remains…

Computation and Language · Computer Science 2025-11-18 Yanming Sun , Runzhe Zhan , Chi Seng Cheang , Han Wu , Xuebo Liu , Yuyao Niu , Fengying Ye , Kaixin Lan , Lidia S. Chao , Derek F. Wong

We propose a novel soft-aided iterative decoding algorithm for product codes (PCs). The proposed algorithm, named iterative bounded distance decoding with combined reliability (iBDD-CR), enhances the conventional iterative bounded distance…

Information Theory · Computer Science 2021-09-08 Alireza Sheikh , Alexandre Graell i Amat , Gianluigi Liva , Alex Alvarado

Strong authentication in an interconnected wireless environment continues to be an important, but sometimes elusive goal. Research in physical-layer authentication using channel features holds promise as a technique to improve network…

Signal Processing · Electrical Eng. & Systems 2020-09-01 Ken St. Germain , Frank Kragh

Products codes (PCs) are conventionally decoded with efficient iterative bounded-distance decoding (iBDD) based on hard-decision channel outputs which entails a performance loss compared to a soft-decision decoder. Recently, several hybrid…

Information Theory · Computer Science 2022-11-22 Sisi Miao , Lukas Rapp , Laurent Schmalen

Large Language Models (LLMs) are increasingly employed in real-world applications, driving the need to evaluate the trustworthiness of their generated text. To this end, reliable uncertainty estimation is essential. Leading uncertainty…

Machine Learning · Computer Science 2026-04-21 Lukas Aichberger , Kajetan Schweighofer , Sepp Hochreiter