相关论文: Construction C*: an inter-level coded version of C…

In this paper we propose constellations with suitable structure which allow one to construct codes with excellent diversity using geometrical symmetry and numerical methods. We also demonstrate how these structured constellations…

Multilevel lattice codes, such as those associated to Constructions $C$, $\overline{D}$, D and D', have relevant applications in communications. In this paper, we investigate some properties of lattices obtained via Constructions D and D'…

We present a general framework for studying the multilevel structure of lattice network coding (LNC), which serves as the theoretical fundamental for solving the ring-based LNC problem in practice, with greatly reduced decoding complexity.…

Spatially-coupled low-density lattice codes (LDLC) are constructed using protographs. Using Monte Carlo density evolution using single-Gaussian messages, we observe that the threshold of the spatially-coupled LDLC is within 0.22 dB of…

Lattice states are a class of quantum states that naturally generalize the fundamental set of Bell states. We apply recent results from quantum error correction and from one-way local operations and classical communication (LOCC) theory,…

Spatially-coupled (SC) LDPC codes have recently emerged as an excellent choice for error correction in modern data storage and communication systems due to their outstanding performance. It has long been known that irregular graph codes…

Lattices and partially ordered sets have played an increasingly important role in coding theory, providing combinatorial frameworks for studying structural and algebraic properties of error-correcting codes. Motivated by recent works…

Chaotic evolution of structures in Coupled map lattice driven by identical noise on each site is studied (a structure is a group of neighbouring lattice-sites for whom values of dynamical variable follow certain predefined pattern). Number…

The lattice of noncrossing partitions is well-known for its wide variety of combinatorial appearances and properties. For example, the lattice is rank-symmetric and enumerated by the Catalan numbers. In this article, we introduce a large…

This paper investigates the decoding of a remarkable set of lattices: We treat in a unified framework the Leech lattice in dimension 24, the Nebe lattice in dimension 72, and the Barnes-Wall lattices. A new interesting lattice is…

In this paper, we show that nested lattice codes achieve the capacity of arbitrary channels with or without non-casual state information at the transmitter. We also show that nested lattice codes are optimal for source coding with or…

The index coding problem involves a sender with K messages to be transmitted across a broadcast channel, and a set of receivers each of which demands a subset of the K messages while having prior knowledge of a different subset as side…

The scale and complexity of modern cloud infrastructure have made Infrastructure-as-Code (IaC) essential for managing deployments. While large Language models (LLMs) are increasingly being used to generate IaC configurations from natural…

In this paper, we present a method to construct the Leech lattice from other Niemeier lattices.

We propose a coding scheme that achieves the capacity of the compound MIMO channel with algebraic lattices. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned…

Low density lattice codes (LDLC) are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel. In LDLC a codeword x is generated directly at the n-dimensional…

In this paper, we characterize the congruences of an arbitrary i--lattice, investigate the structure of the lattice they form and how it relates to the structure of the lattice of lattice congruences, then, for an arbitrary non--zero…

A constant-dimension code (CDC) is a set of subspaces of constant dimension in a common vector space with upper bounded pairwise intersection. We improve and generalize two constructions for CDCs, the improved linkage construction and the…

This work presents an extension of the Construction $\pi_A$ lattices proposed in \cite{huang2017construction}, to Hurwitz quaternion integers. This construction is provided by using an isomorphism from a version of the Chinese remainder…

Spatially-coupled (SC) codes are a family of graph-based codes that have attracted significant attention thanks to their capacity approaching performance and low decoding latency. An SC code is constructed by partitioning an underlying…