Related papers: Constrained Error Pattern Generation for GRAND
Large Language Models (LLMs) struggle with reliably generating highly structured outputs, such as program code, mathematical formulas, or well-formed markup. Constrained decoding approaches mitigate this problem by greedily restricting what…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible…
The design and implementation of error correcting codes has long been informed by two fundamental results: Shannon's 1948 capacity theorem, which established that long codes use noisy channels most efficiently; and Berlekamp, McEliece, and…
Channel decoding is a challenging task in communication channels exhibiting memory effects. In this work, we apply the recently proposed decoding paradigm of guessing random additive noise decoding (GRAND) to channels with memory, focusing…
Parallelism has become a central concern in modern decoding frameworks aiming to meet stringent throughput and latency requirements. Guessing Random Additive Noise Decoding (GRAND) is a recently proposed decoding paradigm that tests…
Guessing Random Additive Noise Decoding (GRAND) is a recently proposed approximate Maximum Likelihood (ML) decoding technique that can decode any linear error-correcting block code. Ordered Reliability Bits GRAND (ORBGRAND) is a powerful…
Large language models (LLMs) have achieved notable success in code generation. However, they still frequently produce uncompilable output because their next-token inference procedure does not model formal aspects of code. Although…
Guessing Random Additive Noise Decoding (GRAND) is a family of universal decoding algorithms suitable for decoding any moderate redundancy code of any length. We establish that, through the use of list decoding, soft-input variants of GRAND…
Guessing Random Additive Noise Decoding (GRAND) is a universal decoding algorithm that can be used to perform maximum likelihood decoding. It attempts to find the errors introduced by the channel by generating a sequence of possible error…
Proposals have been made to reduce the guesswork of Guessing Random Additive Noise Decoding (GRAND) for binary linear codes by leveraging codebook structure at the expense of degraded block error rate (BLER). We establish one can preserve…
Constrained decoding enables Language Models (LMs) to produce samples that provably satisfy hard constraints. However, existing constrained-decoding approaches often distort the underlying model distribution, a limitation that is especially…
Error correcting codes are a fundamental component in modern day communication systems, demanding extremely high throughput, ultra-reliability and low latency. Recent approaches using machine learning (ML) models as the decoders offer both…
Optimal modulation (OM) schemes for Gaussian channels with peak and average power constraints are known to require nonuniform probability distributions over signal points, which presents practical challenges. An established way to map…
Guessing Random Additive Noise Decoding (GRAND) is a universal framework for decoding all block codes by testing candidate error patterns (EPs). Ordered Reliability Bits GRAND (ORBGRAND) facilitates parallel implementation of GRAND by…
This paper studies maximum likelihood(ML) decoding in error-correcting codes as rational maps and proposes an approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion, which will be denoted by $p$ in the…
We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the 2D surface code with a noiseless syndrome extraction. First, we show how to implement MLD exactly in time…
This paper introduces a new approach to generating strongly constrained texts. We consider standardized sentence generation for the typical application of vision screening. To solve this problem, we formalize it as a discrete combinatorial…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
Guessing random additive noise decoding (GRAND) is a universal maximum-likelihood decoder that recovers code-words by guessing rank-ordered putative noise sequences and inverting their effect until one or more valid code-words are obtained.…