Construction D' Lattices for Power-Constrained Communications

Designs and methods for nested lattice codes using Construction D' lattices for coding and convolutional code lattices for shaping are described. Two encoding methods and a decoding algorithm for Construction D' coding lattices that can be used with shaping lattices for power-constrained c...

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Vydané v:IEEE transactions on communications Ročník 70; číslo 4; s. 2200 - 2212
Hlavní autori: Zhou, Fan, Kurkoski, Brian M.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.04.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Algorithms
Binary system
Codes
Coding
Complexity
Construction
Construction D’ lattices
Convolutional codes
Decoding
Encoding
Error correcting codes
Gain
Lattices
Linear codes
nested lattice codes
Polynomials
QC-LDPC codes
shaping gain
ISSN:0090-6778, 1558-0857
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Shrnutí:Designs and methods for nested lattice codes using Construction D' lattices for coding and convolutional code lattices for shaping are described. Two encoding methods and a decoding algorithm for Construction D' coding lattices that can be used with shaping lattices for power-constrained channels are given. We construct nested lattice codes with good coding properties, high shaping gain, and low-complexity encoding and decoding. Convolutional code generator polynomials for Construction A lattices with the greatest shaping gain are given, as a result of an extensive search. It is shown that rate 1/3 convolutional codes provide a more favorable performance-complexity trade-off than rate 1/2 convolutional codes. Tail-biting convolutional codes have higher shaping gain than that of zero-tailed convolutional codes. A design for quasi-cyclic low-density parity-check (QC-LDPC) codes to form Construction D' lattices which have efficient encoding and indexing is presented. The resulting QC-LDPC Construction D' lattices are evaluated using four shaping lattices: the <inline-formula> <tex-math notation="LaTeX">E_{8} </tex-math></inline-formula> lattice, the <inline-formula> <tex-math notation="LaTeX">BW_{16} </tex-math></inline-formula> lattice, the Leech lattice and our best-found convolutional code lattice, showing a shaping gain of approximately 0.65 dB, 0.86 dB, 1.03 dB and 1.25 dB at dimension 2304.
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2022.3147235