Leech Constellations of Construction-A Lattices

@article{diPietro2017LeechCO,
  title={Leech Constellations of Construction-A Lattices},
  author={Nicola di Pietro and Joseph Jean Boutros},
  journal={IEEE Transactions on Communications},
  year={2017},
  volume={65},
  pages={4622-4631}
}
The problem of communicating over the additive white Gaussian noise (AWGN) channel with lattice codes is addressed in this paper. Theoretically, Voronoi constellations have proved to yield very powerful lattice codes when the fine/coding lattice is AWGN-good and the coarse/shaping lattice has an optimal shaping gain. However, achieving Shannon capacity with these premises and practically implementable encoding algorithms is in general not an easy task. In this paper, a new way to encode and… 

Figures from this paper

Geometric shaping: low-density coding of Gaussian-like constellations
TLDR
This paper proves that this discrete codebook is a real geometrically non-uniform Gaussian-like constellation that achieves channel capacity when the number of points goes to infinity and builds a special mapping to interface between non-binary low-density codes and the codebook, allowing the code alphabet size to be equal to the square root of the code book size.
Construction D’ Lattices for Power-Constrained Communications
TLDR
It is shown that rate 1/3 convolutional codes provide a more favorable performance-complexity trade-off than rate 1-1/2 convolutionals and Tail-biting convolutionAL codes have higher shaping gain than that of zero-tailed convolutionale codes.
Encoding and Decoding Construction D' Lattices for Power-Constrained Communications
TLDR
A design of quasi-cyclic low-density parity-check (QCLDPC) codes to form Construction D’ lattices that allows construction of nested lattice codes which are good for coding, good for shaping, and have low complexity encoding and decoding.
Design and Practical Decoding of Full-Diversity Construction A Lattices for Block-Fading Channels
TLDR
Some instances showing that algebraic Construction A lattices obtained from binary codes outperform the ones based on non-binary codes in block fading channels are provided.
On the Design of Multi-Dimensional Irregular Repeat-Accumulate Lattice Codes
TLDR
This paper designs lattice codes from Construction A lattices where the underlying linear codes are non-binary irregular repeat-accumulate (IRA) codes based on multi-dimensional lattice partitions with finite constellations and proves that their approach can ensure that the decoder’s messages exhibit permutation-invariance and symmetry properties.
On the design of multi-dimensional irregular repeat-accumulate lattice codes
TLDR
This work proposes a novel encoding structure to ensure that the decoder's messages exhibit permutation-invariance and symmetry properties, and shows that the densities of the messages in the iterative decoder can be well modeled by Gaussian distributions described by a single parameter.
Shaping for Construction D Lattices
TLDR
A new way to encode and index a construction-D Voronoi lattice code is presented which has linear complexity in the block length and is close to the expected gain of the E8, 0.65 dB.
Repeat-Accumulate Signal Codes
TLDR
To analyze the asymptotic behavior of a new class of state-constrained signal codes called repeat-accumulate signal codes (RASCs), Monte Carlo density evolution (MC-DE) is employed and the optimum filters can be efficiently found for the given parameters of the encoder.
Lattice Coding for Downlink Multiuser Transmission
  • Min Qiu
  • Computer Science, Business
    ArXiv
  • 2019
TLDR
This thesis attempts to address the lattice coding problem of the downlink communication between a base station and multiple users by providing a systematic design of practical coding and modulation schemes for downlink multiuser communication systems.
NEURAL LATTICE DECODERS
TLDR
It is shown that L1 regularization and a priori information about the lattice structure lead to a simplification of the model.
...
...

References

SHOWING 1-10 OF 70 REFERENCES
LDA Lattices Without Dithering Achieve Capacity on the Gaussian Channel
TLDR
A proof is provided that Voronoi constellations of LDA lattices achieve capacity of the AWGN channel under lattice encoding and decoding for every signal-to-noise ratio greater than 1.
Achieving AWGN Channel Capacity With Lattice Gaussian Coding
TLDR
The notion of good constellations, which carry almost the same mutual information as that of continuous Gaussian inputs, is introduced and addressed for the proposed lattice Gaussian coding scheme.
Shaping methods for low-density lattice codes
TLDR
This work proposes several efficient and practical shaping algorithms for LDLC, a recently-proposed lattice codes that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel.
Low-Density Parity-Check Lattices: Construction and Decoding Analysis
TLDR
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.
Shaping low-density lattice codes using Voronoi integers
TLDR
A lattice code construction that employs two separate lattices, a high dimension lattices for coding gain and a low-dimension lattice for shaping gain, is described, and can be implemented with lower complexity than previous LDLC approaches.
Lattice Coding for Signals and Networks: A Structured Coding Approach to Quantization, Modulation and Multiuser Information Theory
TLDR
It is shown how high dimensional lattice codes can close the gap to the optimal information theoretic solution, including the characterisation of error exponents, when generalising the framework to Gaussian networks.
Some “goodness” properties of LDA lattices
TLDR
It is proved that codes constructed using nested LDA lattices can achieve the capacity of the power constrained AWGN channel, the capacityof the dirty paper channel,The rates guaranteed by the computeand-forward protocol, and the best known rates for bidirectional relaying with perfect secrecy.
Low-Dimensional Shaping for High-Dimensional Lattice Codes
TLDR
Two low-complexity lattice code constructions that have competitive coding and shaping gains and mixed nested lattice codes, in which a high-dimensional coding lattice is nested inside a concatenation of low-dimensional shaping lattices, are proposed.
Low-Density Lattice Codes
TLDR
Low-density lattice codes (LDLC) are novel lattice code that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel and the paper discusses convergence results and implementation considerations.
Achieving 1/2 log (1+SNR) on the AWGN channel with lattice encoding and decoding
  • U. Erez, R. Zamir
  • Computer Science
    IEEE Transactions on Information Theory
  • 2004
TLDR
It is shown that such pairs exist for any desired nesting ratio, i.e., for any signal-to-noise ratio (SNR) and for the modulo-lattice additive noise channel lattice decoding is optimal, and the error exponent of the proposed scheme is lower bounded by the Poltyrev exponent.
...
...