相关论文: Information Set Decoding for Lee-Metric Codes usin…

Recursive list decoding is considered for Reed-Muller (RM) codes. The algorithm repeatedly relegates itself to the shorter RM codes by recalculating the posterior probabilities of their symbols. Intermediate decodings are only performed…

We study analytically and numerically decoding properties of finite rate hypergraph-product quantum LDPC codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several non-trival lower…

We introduce a new quantum decoder based on a variant of the pretty good measurement, but defined via an alternative matrix quotient. We use this decoder to show new lower bounds on the error exponent both in the one-shot and asymptotic…

Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…

Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon…

We investigate dense coding by imposing various locality restrictions to our decoder by employing the resource theory of asymmetry framework. In this task, the sender Alice and the receiver Bob share an entangled state. She encodes the…

In this work we explore possibilities for coding and decoding tailor-made for mean squared error evaluation of error in contexts such as image transmission. To do so, we introduce a loss function that expresses the overall performance of a…

We introduce a new rank-based key encapsulation mechanism (KEM) with public key and ciphertext sizes around 3.5 Kbytes each, for 128 bits of security, without using ideal structures. Such structures allow to compress objects, but give…

Maximum-likelihood (ML) decoding for arbitrary block codes remains fundamentally hard, with worst-case time complexity-measured by the total number of multiplications-being no better than straightforward exhaustive search, which requires…

The Permutation Equivalence Problem (PEP) for linear codes is a fundamental problem in coding theory and cryptography. A recent reduction shows that PEP for Linear Complementary Dual (LCD) codes reduces to Graph Isomorphism (GI) via…

We consider the quantum decoding problem. It consists in recovering a codeword given a superposition of noisy versions of this codeword. By measuring the superposition, we get back to the classical decoding problem. It appears for the first…

LDPC codes play a vital role in coding theory and practical error correction. A central problem in this direction is to understand their rate--distance tradeoff. In this paper, we introduce a new framework for estimating ball sizes in the…

Maximum-likelihood decoding is one of the central algorithmic problems in coding theory. It has been known for over 25 years that maximum-likelihood decoding of general linear codes is NP-hard. Nevertheless, it was so far unknown whether…

A novel channel coding scheme for progressive transmission of large images is proposed. The transmission time, low distortion reconstructed image and low complexity are most concerned in this paper. In the case of medical data transmission,…

Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…

In this paper, we introduce the syndrome loss, an alternative loss function for neural error-correcting decoders based on a relaxation of the syndrome. The syndrome loss penalizes the decoder for producing outputs that do not correspond to…

Consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible.…

We present a list decoding algorithm for quaternary negacyclic codes over the Lee metric. To achieve this result, we use a Sudan-Guruswami type list decoding algorithm for Reed-Solomon codes over certain ring alphabets. Our decoding…

We consider the problem of computing the convolution of two long vectors using parallel processing units in the presence of "stragglers". Stragglers refer to the small fraction of faulty or slow processors that delays the entire computation…

The minimum distance is one of the most important combinatorial characterizations of a code. The maximum likelihood decoding problem is one of the most important algorithmic problems of a code. While these problems are known to be hard for…