Related papers: Multistage Compute-and-Forward with Multilevel Lat…
We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that…
The Compute-and-Forward protocol in quasi-static channels normally employs lattice codes based on the rational integers $\mathbb{Z}$, Gaussian integers $\mathbb{Z}\left[i\right]$ or Eisenstein integers $\mathbb{Z}\left[\omega\right]$, while…
We study the transmission over a cloud radio access network in which multiple base stations (BS) are connected to a central processor (CP) via finite-capacity backhaul links. We propose two lattice-based coding schemes. In the first scheme,…
In this paper, using compute-and-forward as an example, we provide an overview of constructions of lattices from codes that possess the right algebraic structures for harnessing interference. This includes Construction A, Construction D,…
This paper introduces a federated learning framework that enables over-the-air computation via digital communications, using a new joint source-channel coding scheme. Without relying on channel state information at devices, this scheme…
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.…
The problem of designing physical-layer network coding (PNC) schemes via nested lattices is considered. Building on the compute-and-forward (C&F) relaying strategy of Nazer and Gastpar, who demonstrated its asymptotic gain using…
We propose two coded schemes for the distributed computing problem of multiplying a matrix by a set of vectors. The first scheme is based on partitioning the matrix into submatrices and applying maximum distance separable (MDS) codes to…
Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we…
A new approach for designing bilayer and multi-layer LDPC codes is proposed and studied in the asymptotic regime. The ensembles are defined through individual uni-variate degree distributions, one for each layer. We present a construction…
Lattices possess elegant mathematical properties which have been previously used in the literature to show that structured codes can be efficient in a variety of communication scenarios, including coding for the additive white Gaussian…
Compute-forward is a coding technique that enables receiver(s) in a network to directly decode one or more linear combinations of the transmitted codewords. Initial efforts focused on Gaussian channels and derived achievable rate regions…
Low density parity check (LDPC) lattices are obtained from Construction D' and a family of nested binary LDPC codes. We consider an special case of these lattices with one binary LDPC code as underlying code. This special case of LDPC…
This work addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. In contrast to the standard approach in the literature which employs random…
This paper introduces a new scheme of LT codes, named multiple configurations. In multiple configurations LT codes (MC-LT codes), multiple sets of output symbols are simultaneously provided to receivers for recovering the source data. Each…
Construction C (also known as Forney's multi-level code formula) forms a Euclidean code for the additive white Gaussian noise (AWGN) channel from $L$ binary code components. If the component codes are linear, then the minimum distance is…
Recent work have shown that the quantization for matrix multiplication problem can be optimally solved by quantizing each column in each matrix using a nested lattice code, and then multiplying the de-quantized matrices. It was further…
In this paper we propose a new design criterion and a new class of unitary signal constellations for differential space-time modulation for multiple-antenna systems over Rayleigh flat-fading channels with unknown fading coefficients.…
A coding lattice $\Lambda_c$ and a shaping lattice $\Lambda_s$ forms a nested lattice code $\mathcal{C}$ if $\Lambda_s \subseteq \Lambda_c$. Under some conditions, $\mathcal{C}$ is a finite cyclic group formed by rectangular encoding. This…
We construct $\mathbb{Z}_p$-lattices and $\mathbb{F}_q[\![t]\!]$-lattices from cyclic $(f,\sigma)$-codes over finite chain rings, employing quotients of natural nonassociative orders and principal left ideals in carefully chosen…