相关论文: Uncertainty of Reconstruction with List-Decoding f…

We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…

We investigate the task of retrieving information from compositional distributed representations formed by Hyperdimensional Computing/Vector Symbolic Architectures and present novel techniques which achieve new information rate bounds.…

Inverse problems, such as accelerated MRI reconstruction, are ill-posed and an infinite amount of possible and plausible solutions exist. This may not only lead to uncertainty in the reconstructed image but also in downstream tasks such as…

In models to generate program source code from natural language, representing this code in a tree structure has been a common approach. However, existing methods often fail to generate complex code correctly due to a lack of ability to…

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…

In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…

The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. The common…

The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in applications of networked control systems. Although the work of Schulman and Sahai over the past two decades, and…

The problem of reconstructing evolutionary trees or phylogenies is of great interest in computational biology. A popular model for this problem assumes that we are given the set of leaves (current species) of an unknown binary tree and the…

Strings in the real world are often encoded with some level of uncertainty. In the character-level uncertainty model, an uncertain string $X$ of length $n$ on an alphabet $\Sigma$ is a sequence of $n$ probability distributions over…

In this paper, we study the tradeoffs between complexity and reliability for decoding large linear block codes. We show that using artificial neural networks to predict the required order of an ordered statistics based decoder helps in…

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…

Current vision systems typically assign fixed-length representations to images, regardless of the information content. This contrasts with human intelligence - and even large language models - which allocate varying representational…

This work constructs codes that are efficiently decodable from a constant fraction of \emph{worst-case} insertion and deletion errors in three parameter settings: (i) Binary codes with rate approaching 1; (ii) Codes with constant rate for…

The problem of learning a channel decoder is considered for two channel models. The first model is an additive noise channel whose noise distribution is unknown and nonparametric. The learner is provided with a fixed codebook and a dataset…

In this paper, we investigate the problem of designing $(n, N; \mathcal{B})$-reconstruction codes for $N\in \{14,11,9,5\}$, where $\mathcal{B}$ is the single-deletion single-substitution ball function that maps a sequence to the set of all…

Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size $m \times n$) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix…

Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…

We propose a decoding algorithm for the $(u\mid u+v)$-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one…

Decoding from the output distributions of large language models to produce high-quality text is a complex challenge in language modeling. Various approaches, such as beam search, sampling with temperature, $k-$sampling, nucleus…