IEEE Transactions on Information Theory

We show that for a wide range of channels and code ensembles with pairwise-independent codewords, with probability tending to 1 with the code length, expurgating an arbitrarily small fraction of codewords from a randomly selected code results in a code ...

The relay channel with unreliable helper is introduced and studied. The model is that of a classical relay channel where the input from the relay to the channel has an extra primitive link whose presence is not assured a priori. The extra link represents ...

This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on a divergence between the distributions of the source and reconstruction ...

We consider communication over a state-dependent discrete memoryless channel subject to a constraint that the output sequence must be nearly independent of the state sequence. We consider both cases where the transmitter knows (causally or noncausally) ...

Entropy comparison inequalities are obtained for the differential entropy <inline-formula> <tex-math notation="LaTeX">$h(X+Y)$ </tex-math></inline-formula> of the sum of two independent random vectors <inline-formula> <tex-math notation="LaTeX">$X,Y$ </...

In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests needed. We model ...

In this work, a novel data-driven methodology for designing neural polar decoders for channels with and without memory is proposed. The methodology is suitable for the case where the channel is given as a &#x201C;black-box&#x201D; and the designer has ...

We give a recursive construction for projective Reed-Muller codes in terms of affine Reed-Muller codes and projective Reed-Muller codes in fewer variables. From this construction, we obtain the dimension of the subfield subcodes of projective Reed-Muller ...

In response to the evolving landscape of data storage, researchers have increasingly explored non-traditional platforms, with DNA-based storage emerging as a cutting-edge solution. Our work is motivated by the potential of in-vivo DNA storage, known for ...

Schur product was originally proposed in coding theory for algebraic decoding algorithms and widely applied to solve some cryptographic problems in recent years. This shows the great importance of the Schur product in both coding theory and cryptography. ...

The self-orthogonality and divisibility are two important properties of linear codes. It is interesting to establish relationship between them. By the well-known Gleason-Pierce-Ward Theorem, all self-dual divisible codes have been totally classified. ...

This paper presents two repair schemes for low-rate Reed-Solomon (RS) codes over prime fields that can repair any node by downloading a constant number of bits from each surviving node. The total bandwidth resulting from these schemes is greater than that ...

The increasing demand for data storage has prompted the exploration of new techniques, with molecular data storage being a promising alternative. In this work, we develop coding schemes for a new storage paradigm that can be represented as a collection of ...

The (Schur) squares of linear codes are an interesting research topic in coding theory, and they have important applications in cryptography. Linear complementary dual codes (LCD codes) have been widely applied in data storage, communication systems, ...

In this paper, we construct infinitely many families of distance-optimal binary BCH codes with the minimum distance 6 and an infinite family of distance-optimal quaternary BCH codes with the minimum distance 4. We also construct several infinite families ...

Frameproof codes have been extensively studied for many years due to their application in copyright protection and their connection to extremal set theory. This paper investigates the upper bounds of the cardinalities of wide-sense t-frameproof codes. For ...

Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector-matrix multiplication on resistive crossbars. Prior work has concentrated on locating a single ...

Folded Reed-Solomon (FRS) and univariate multiplicity codes are prominent polynomial codes over finite fields renowned for achieving list decoding capacity. These codes have found many applications beyond the traditional scope of coding theory. In this ...

Let <inline-formula> <tex-math notation="LaTeX">$\textrm {S}(n,t,k)$ </tex-math></inline-formula> be the maximum size of a code containing only vectors of the kth shell of the integer lattice <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}^{n}$ </...

It is known that <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}_{p^{s}}$ </tex-math></inline-formula>-linear codes, which are the Gray map image of <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}_{p^{s}}$ </tex-math></inline-formula>-...

In this paper, we construct many infinite families of distance-optimal codes with new parameters, some of which are BCH codes and quasi-cyclic codes. In particular, we report the first infinite family of binary distance-optimal BCH codes with the minimum ...

Let F be a field with cardinality <inline-formula> <tex-math notation="LaTeX">$p^{\ell } $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$0\neq \lambda \in F$ </tex-math></inline-formula>, and <inline-formula> <tex-math ...

In this paper, we give a new upper bound on sizes of linear codes related to weight distributions of codes as follows. Let C be a linear <inline-formula> <tex-math notation="LaTeX">$[n,k,d]_{q}$ </tex-math></inline-formula> code, such that, between d and <...

Recently, Hyun et al. have utilized simplicial complexes to construct several infinite families of binary minimal and optimal linear codes. Building upon their work, we draw inspiration and extend their research by constructing codes over the ring <inline-...

Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic structure. In this ...

Optical orthogonal codes have applications in optical code-division multiple access communication systems. They can also be used to construct protocol sequences for multiuser collision channel without feedback, and constant weight codes for error ...

We give new characterizations of the largest minimum weights among LCD codes of large dimensions. Using the characterizations, we completely determine the largest minimum weights among binary LCD codes of length n and dimension <inline-formula> <tex-math ...

This paper focuses on the covariance-based activity detection problem in a multi-cell massive multiple-input multiple-output (MIMO) system. In this system, active devices transmit their signature sequences to multiple base stations (BSs), and the BSs ...

Measuring the distinguishability between quantum states is a basic problem in quantum information theory. In this paper, we develop optimal quantum algorithms that estimate both the trace distance and the (square root) fidelity between pure states to ...

We show that every three-dimensional subspace of qutrit-qudit complex or real systems has a distinguishable basis under one-way local projective measurements and classical communication (LPCC). This solves a long-standing open problem proposed in [J. ...