• Corpus ID: 52919335

Construction D$^\prime$ Lattices from Quasi-Cyclic Low-Density Parity-Check Codes

  title={Construction D\$^\prime\$ Lattices from Quasi-Cyclic Low-Density Parity-Check Codes},
  author={Siyu Chen and Brian M. Kurkoski and Eirik Rosnes},
  journal={arXiv: Information Theory},
Recently, Branco da Silva and Silva described an efficient encoding and decoding algorithm for Construction D$^\prime$ lattices. Using their algorithm, we propose a Construction D$^\prime$ lattice based on binary quasi-cyclic low-density parity-check (QC-LPDC) codes and single parity-check product codes. The underlying codes designed by the balanced-distances rule contribute in a balanced manner to the squared minimum distance of the constructed lattice, which results in a high lattice coding… 


Low-Density Parity-Check Lattices: Construction and Decoding Analysis
This paper introduces a method to construct high coding gain lattices with low decoding complexity based on LDPC codes and applies Construction D', due to Bos, Conway, and Sloane, to a set of parity checks defining a family of nestedLDPC codes to construct such lattices.
Practical Encoder and Decoder for Power Constrained QC LDPC-Lattice Codes
This work introduces quasi-cyclic LDPC (QC LDPC) lattices as a special case of LDPC lattices with one binary QC-LDPC code as their underlying code and provides a low-complexity decoding algorithm of QC LDPC-lattices based on the sum product algorithm.
Efficient encoding of low-density parity-check codes
It is shown how to exploit the sparseness of the parity-check matrix to obtain efficient encoders and it is shown that "optimized" codes actually admit linear time encoding.
Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices
  • M. Fossorier
  • Mathematics, Computer Science
    IEEE Trans. Inf. Theory
  • 2004
The results suggest that families of LDPC codes with such girth values are relatively easy to obtain and, consequently, additional parameters such as the minimum distance or the number of redundant check sums should be considered.
Channel Codes: Classical and Modern
Preface 1. Coding and capacity 2. Finite fields, vector spaces, finite geometries and graphs 3. Linear block codes 4. Convolutional codes 5. Low-density parity-check codes 6. Computer-based design of
Polar lattices: Where Arıkan meets Forney
The explicit construction of a new class of lattices based on polar codes, which are provably good for the additive white Gaussian noise (AWGN) channel, are proposed.
An Efficient Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices
An efficient algorithm to find all stopping sets, of size less than some threshold, of a fixed low-density parity-check (LDPC) matrix is introduced and simulation results of iterative decoding on the binary erasure channel show performance improvements for low-to-medium erasure probabilities when this redundant parity- check matrix is used for decoding.
Addendum to “An Efficient Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices”
The algorithm for determining the initial part of the stopping set weight spectrum is reviewed, which includes the codeword weight spectrum, and some improvements to the algorithm are provided to provide some improvements.
Multilevel codes: Theoretical concepts and practical design rules
This paper deals with 2/sup l/-ary transmission using multilevel coding (MLC) and multistage decoding (MSD) and shows that capacity can in fact be closely approached at high bandwidth efficiencies.
A > — Qn + o(n) in [21]. The latter two families of packings were obtained by applying Construction C of [15] to certain sequences of codes. Our first construction, Construction D (see 2.1),