3 research outputs found
On the decoding of Barnes-Wall lattices
We present new efficient recursive decoders for the Barnes-Wall lattices
based on their squaring construction. The analysis of the new decoders reveals
a quasi-quadratic complexity in the lattice dimension and a quasi-linear
complexity in the list-size. The error rate is shown to be close to the
universal lower bound in dimensions 64 and 128.Comment: Presented at ISIT 202
Construction D' Lattices for Power-Constrained Communications
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 which are good for coding, good
for shaping, and have low-complexity encoding and decoding. An indexing method
for nested lattice codes is modified to avoid an integer overflow problem at
high dimension. Convolutional code generator polynomials for Construction A
lattices with the greatest shaping gain are given, the 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. For a given
dimension, tail-biting convolutional codes have higher shaping gain than that
of zero-tailed convolutional codes. A design for quasi-cyclic low-density
parity-check (LDPC) codes to form Construction D' lattices is presented, where
their parity-check matrices can be easily triangularized, thus enabling
efficient encoding and indexing. The resulting LDPC Construction D' lattices
are evaluated using four shaping lattices: the lattice, the
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
On the decoding of lattices constructed via a single parity check
This paper investigates the decoding of a remarkable set of lattices: We
treat in a unified framework the Leech lattice in dimension 24, the Nebe
lattice in dimension 72, and the Barnes-Wall lattices. A new interesting
lattice is constructed as a simple application of single parity-check principle
on the Leech lattice. The common aspect of these lattices is that they can be
obtained via a single parity check or via the k-ing construction. We exploit
these constructions to introduce a new efficient paradigm for decoding. This
leads to efficient list decoders and quasi-optimal decoders on the Gaussian
channel. Both theoretical and practical performance (point error probability
and complexity) of the new decoders are provided.Comment: Submitted to IEEE Transactions on Information Theor