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This paper is concerned with a search-number-reduced guessing random additive noise decoding (GRAND) algorithm for linear block codes, called partially constrained GRAND (PC-GRAND). In contrast to the original GRAND, which guesses error…
CRC codes have long since been adopted in a vast range of applications. The established notion that they are suitable primarily for error detection can be set aside through use of the recently proposed Guessing Random Additive Noise…
To facilitate applications in IoT, 5G, and beyond, there is an engineering need to enable high-rate, low-latency communications. Errors in physical channels typically arrive in clumps, but most decoders are designed assuming that channels…
GRAND features both soft-input and hard-input variants that are well suited to efficient hardware implementations that can be characterized with achievable average and worst-case decoding latency. This paper introduces step-GRAND, a…
Guessing random additive noise decoding (GRAND) is a code-agnostic decoding method that iteratively guesses the noise pattern affecting the received codeword. The number of noise sequences to test depends on the noise realization. Thus,…
In this paper, we propose an efficient ordered-statistics decoding (OSD) algorithm with an adaptive Gaussian elimination (GE) reduction technique. The proposed decoder utilizes two decoding conditions to adaptively remove GE in OSD. The…
The high computational cost of approaching the performance of Maximum-likelihood (ML) decoding has limited its practical use for decades. Because the complexity grows exponentially with the message length, researchers have spent years…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
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)…
We establish that a large, flexible class of long, high redundancy error correcting codes can be efficiently and accurately decoded with guessing random additive noise decoding (GRAND). Performance evaluation demonstrates that it is…
We propose a reduced complexity approach to pattern-based soft decoding of block codes. We start from the ORDEPT decoding algorithm which tests a list of partial error patterns organized in the order of their likelihood and attempts to…
In this paper, we distinguish two guessing algorithms for decoding binary linear codes. One is the guessing noise decoding (GND) algorithm, and the other is the guessing codeword decoding (GCD) algorithm. We prove that the GCD is a maximum…
Supporting ultra-reliable and low-latency communication (URLLC) is a challenge in current wireless systems. Channel codes that generate large codewords improve reliability but necessitate the use of interleavers, which introduce undesirable…
We introduce a novel universal soft-decision decoding algorithm for binary block codes called ordered reliability direct error pattern testing (ORDEPT). Our results, obtained for a variety of popular short high-rate codes, demonstrate that…
Guessing Codeword Decoding (GCD) is a recently proposed soft-input forward error correction decoder for arbitrary binary linear codes. Inspired by recent proposals that leverage binary linear codebook structure to reduce the number of…
Learning with noisy labels is an important topic for scalable training in many real-world scenarios. However, few previous research considers this problem in the online setting, where the arrival of data is streaming. In this paper, we…
Global routing is a critical stage in electronic design automation (EDA) that enables early estimation and optimization of the routability of modern integrated circuits with respect to congestion, power dissipation, and design complexity.…
This article introduces randomized block Gram-Schmidt process (RBGS) for QR decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm and inherits its key characteristics such as being more efficient and having…
Retrieval-Augmented Generation (RAG) has become a widely adopted approach to enhance Large Language Models (LLMs) by incorporating external knowledge and reducing hallucinations. However, noisy or irrelevant documents are often introduced…
Efficient and scalable decoding of quantum codes is essential for high-performance quantum error correction. In this work, we introduce Reliable Subset Reduction (RSR), a reliability-driven preprocessing framework that leverages belief…