Related papers: Low-Dimensional Shaping for High-Dimensional Latti…
Performance of concatenated multilevel coding with probabilistic shaping (PS) and Voronoi constellations (VCs) is analysed over AWGN channel. Numerical results show that VCs provide up to 1.3 dB SNR gains over PS-QAM with CCDM blocklength…
For a lattice/linear code, we define the Voronoi spherical cumulative density function (CDF) as the CDF of the $\ell_2$-norm/Hamming weight of a random vector uniformly distributed over the Voronoi cell. Using the first moment method…
The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary…
Low density lattice codes (LDLC) are a family of lattice codes that can be decoded efficiently using a message-passing algorithm. In the original LDLC decoder, the message exchanged between variable nodes and check nodes are continuous…
The simple cubic lattice defines a set of points at regular distances. The volume of the Voronoi cells around each point may serve as a weight for integration over the entire space. We add interstitial points to this grid according to the…
Linear nested codes, where two or more sub-codes are nested in a global code, have been proposed as candidates for reliable multi-terminal communication. In this paper, we consider nested array-based spatially coupled low-density…
In this paper we are concerned with finding the vertices of the Voronoi cell of a Euclidean lattice. Given a basis of a lattice, we prove that computing the number of vertices is a #P-hard problem. On the other hand we describe an algorithm…
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…
An energy-efficient approach is presented for shaping a bit-interleaved low-density parity-check (LDPC) coded amplitude phase-shift keying (APSK) system. A subset of the interleaved bits output by a binary LDPC encoder are passed through a…
In this paper a new class of lattices called turbo lattices is introduced and established. We use the lattice Construction D to produce turbo lattices. This method needs a set of nested linear codes as its underlying structure. We benefit…
A novel method guaranteeing nondecreasing girth is presented for constructing longer low-density parity-check (LDPC) codes from shorter ones. The parity-check matrix of a shorter base code is decomposed into N (N>=2) non-overlapping…
A novel construction of lattices is proposed. This construction can be thought of as Construction A with codes that can be represented as the Cartesian product of $L$ linear codes over $\mathbb{F}_{p_1},\ldots,\mathbb{F}_{p_L}$,…
In this paper, we present a general framework of designing geometrically shaped constellations for short-packet visible light communications with a peak- and an average-intensity constraints. By leveraging tools from large deviation theory,…
We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…
This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from difference covering arrays. While the original construction by Gallagher was by randomly allocating bits in a sparse parity-check matrix, over…
We define a novel search method and performance metric as a technique for optimizing the bit-to-symbol map of the $D_4$ and $E_8$ root lattices in reference to bit error rate. We hold other sources of lattice gain constant by fixing the…
The goal of learning to hash (L2H) is to derive data-dependent hash functions from a given data distribution in order to map data from the input space to a binary coding space. Despite the success of L2H, two observations have cast doubt on…
This work introduces coset Bombe codes, a novel class of multilevel coset codes that generalize polar codes to dense lattice structures. By leveraging multilevel coding with non-binary codes designed for the lattice modulations and making…
Nested codes have been employed in a large number of communication applications as a specific case of superposition codes, for example to implement binning schemes in the presence of noise, in joint network-channel coding, or in…
Lattice codes with optimal decoding coefficient are capacity-achieving when dimension $N \rightarrow \infty$. In communications systems, finite dimensional lattice codes are considered, where the optimal decoding coefficients may still fail…