相关论文: On the decoding of lattices constructed via a sing…
A recent line of work on lattice codes for Gaussian wiretap channels introduced a new lattice invariant called secrecy gain as a code design criterion which captures the confusion that lattice coding produces at an eavesdropper. Following…
The non-binary low-density parity-check (NB-LDPC) codes can offer promising performance advantages but suffer from high decoding complexity. To tackle this challenge, in this paper, we consider NB-LDPC codes over finite fields as codes over…
In this paper, the concept of the {\it broken diagonal pair} in the chess-like square board is used to define some well-structured block designs whose incidence matrices can be considered as the parity-check matrices of some high rate cycle…
Encoding and indexing of lattice codes is generalized from self-similar lattice codes to a broader class of lattices. If coding lattice $\Lambda_{\textrm{c}}$ and shaping lattice $\Lambda_{\textrm{s}}$ satisfy $\Lambda_{\textrm{s}}…
In this paper, we present an improved union bound on the Linear Programming (LP) decoding performance of the binary linear codes transmitted over an additive white Gaussian noise channels. The bounding technique is based on the second-order…
We consider spatially coupled low-density parity-check codes with finite smoothing parameters. A finite smoothing parameter is important for designing practical codes that are decoded using low-complexity windowed decoders. By optimizing…
Computing the theta series of an arbitrary lattice, and more specifically a related quantity known as the flatness factor, has been recently shown to be important for lattice code design in various wireless communication setups. However,…
Lattice reduction-aided decoding features reduced decoding complexity and near-optimum performance in multi-input multi-output communications. In this paper, a quantitative analysis of lattice reduction-aided decoding is presented. To this…
We introduce fair-density parity-check (FDPC) codes targeting high-rate applications. In particular, we start with a base parity-check matrix $H_b$ of dimension $2 \sqrt{n} \times n$, where $n$ is the code block length, and the number of…
Low-density parity-check (LDPC) codes are specified by graphs, and are the error correction technique of choice in many communications and data storage contexts. Message passing decoders diffuse information carried by parity bits into the…
In this paper, the performance limits and the computational complexity of the lattice sequential decoder are analyzed for the unconstrained additive white Gaussian noise channel. The performance analysis available in the literature for such…
This study proposes an explicit construction method for quantum quasi-cyclic low-density parity-check (QC-LDPC) codes with a girth of 12. The proposed method designs parity-check matrices that maximize the girth while maintaining an…
Lattice decoders constructed with neural networks are presented. Firstly, we show how the fundamental parallelotope is used as a compact set for the approximation by a neural lattice decoder. Secondly, we introduce the notion of…
One approach to designing structured low-density parity-check (LDPC) codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity-check matrix contain all the variables involved in…
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…
A weak order on the set of maximal chains of the non-crossing partition lattice is introduced and studied. A $0$-Hecke algebra action is used to compute the radius of the graph on these chains in which two chains are adjacent if they differ…
The main objective of this thesis is a classification project for integral lattices. Using Kneser's neighbour method we have developed the computer program tn to classify complete genera of integral lattices. Main results are detailed…
This paper basically expresses the core fundamentals and brief overview of the research of R. G. GALLAGER [1] on Low-Density Parity-Check (LDPC) codes and various parameters related to LDPC codes like, encoding and decoding of LDPC codes,…
A new achievable rate region is given for the Gaussian cognitive many-to-one interference channel. The proposed novel coding scheme is based on the compute-and-forward approach with lattice codes. Using the idea of decoding sums of…
We study two-dimensional translation-invariant CSS stabilizer codes over prime-dimensional qudits on the square lattice under twisted boundary conditions, generalizing the Kitaev $\mathbb{Z}_p$ toric code by augmenting each stabilizer with…