相关论文: Bridging Hamming Distance Spectrum with Coset Card…

Arithmetic codes are usually deemed as the most important means to implement lossless source coding, whose principle is mapping every source symbol to a sub-interval in [0, 1). For every source symbol, the length of its mapping sub-interval…

In this paper, we propose new coupled codes constructed by overlapping circular spatially-coupled low-density parity-check (SC-LDPC) codes, which show better asymptotic and finite-length decoding performance compared to the conventional…

We study covering problems in Hamming and Grassmann spaces through a unified coding-theoretic and information-theoretic framework. Viewing covering as a form of quantization in general metric spaces, we introduce the notion of the average…

We describe a novel extension of subspace codes for noncoherent networks, suitable for use when the network is viewed as a communication system that introduces both dimension and symbol errors. We show that when symbol erasures occur in a…

Coded distributed batch computation distributes a computation task, such as matrix multiplication, $N$-linear computation, or multivariate polynomial evaluation, across $S$ servers through a coding scheme, such that the response from any…

We present a novel way to encode compositional information in high-dimensional (HD) vectors. Inspired by chromosomal crossover, random HD vectors are recursively interwoven, with a fraction of one vector's components masked out and replaced…

In this paper, we study amplitude shaping schemes for the probabilistic amplitude shaping (PAS) framework as well as algorithms for constant-composition distribution matching (CCDM). Huffman-coded sphere shaping (HCSS) is discussed in…

We consider Slepian-Wolf (SW) coding of multiple sources and extend the packing bound and the notion of perfect code from conventional channel coding to SW coding with more than two sources. We then introduce Hamming Codes for Multiple…

An equidistant code is a code in the Hamming space such that two distinct codewords have the same Hamming distance. This paper investigates the bounds for equidistant codes in Hamming spaces.

We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes, and describe code surgery between such codes using a specific colimit in the category of chain complexes. As well as describing a surgery…

In this work, we study linear codes with the folded Hamming distance, or equivalently, codes with the classical Hamming distance that are linear over a subfield. This includes additive codes. We study MDS codes in this setting and define…

We propose an efficient algorithm to find a Reed-Solomon (RS) codeword at a distance within the covering radius of the code from any point in its ambient Hamming space. To the best of the authors' knowledge, this is the first attempt of its…

Unsupervised hashing methods typically aim to preserve the similarity between data points in a feature space by mapping them to binary hash codes. However, these methods often overlook the fact that the similarity between data points in the…

Cross-modal alignment is a crucial task in multimodal learning aimed at achieving semantic consistency between vision and language. This requires that image-text pairs exhibit similar semantics. Traditional algorithms pursue embedding…

This paper presents a novel scheme dubbed Collision Diversity (CoD) SCRAM, which is provisioned to meet the challenging requirements of the future 6G, portrayed in massive connectivity, reliability, and ultra-low latency. The conventional…

Grassmannian codes are known to be useful in error-correction for random network coding. Recently, they were used to prove that vector network codes outperform scalar linear network codes, on multicast networks, with respect to the alphabet…

Code clones are duplicate code fragments that share (nearly) similar syntax or semantics. Code clone detection plays an important role in software maintenance, code refactoring, and reuse. A substantial amount of research has been conducted…

By using the Gold map, we construct a partition of the hypercube into cosets of Hamming codes such that for every two cosets the corresponding Hamming codes are maximally nonparallel, that is, their intersection cardinality is as small as…

A hybrid automatic repeat request scheme with Chase combing (HARQ-CC) of polar codes is proposed. The existing analysis tools of the underlying rate-compatible punctured polar (RCPP) codes for additive white Gaussian noise (AWGN) channels…

Distributed source coding schemes are typically based on the use of channels codes as source codes. In this paper we propose a new paradigm, termed "distributed arithmetic coding", which exploits the fact that arithmetic codes are good…