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| Paper IPM / M / 16462 |
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| Abstract: | |
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Block-fading channel (BF) is a useful model for
various wireless communication channels in both indoor and
outdoor environments. Frequency-hopping schemes and orthogonal
frequency division multiplexing (OFDM) can conveniently
be modelled as BF channels. Applying lattices in this type of
channel entails dividing a lattice point into multiple blocks such
that fading is constant within a block but changes, independently,
across blocks. The design of lattices for BF channels offers a
challenging problem, which differs greatly from its counterparts
like AWGN channels. Recently, the original binary Construction
A for lattices, due to Forney, has been generalized to a lattice
construction from totally real and complex multiplication (CM)
fields. This generalized algebraic Construction A of lattices
provides signal space diversity, intrinsically, which is the main
requirement for the signal sets designed for fading channels. In
this paper, we construct full-diversity algebraic lattices for BF
channels using Construction A over totally real number fields.
We propose two new decoding methods for these family of lattices
which have complexity that grows linearly in the dimension of the
lattice. The first decoder is proposed for full-diversity algebraic
LDPC lattices which are generalized Construction A lattices
with a binary LDPC code as underlying code. This decoding
method contains iterative and non-iterative phases. In order to
implement the iterative phase of our decoding algorithm, we
propose the definition of a parity-check matrix and Tanner
graph for full-diversity algebraic Construction A lattices. We
also prove that using an underlying LDPC code that achieves
the outage probability limit over one-block-fading channel, the
constructed algebraic LDPC lattices together with the proposed
decoding method admit diversity order n over an n-block-fading
channel. Then, we modify the proposed algorithm by removing
its iterative phase which enables full-diversity practical decoding
of all generalized Construction A lattices without any assumption
about their underlying code. In contrast with the known results
on AWGN channels in which non-binary Construction A lattices
always outperform the binary ones, we provide some instances
showing that algebraic Construction A lattices obtained from
binary codes outperform the ones based on non-binary codes
in block fading channels. Since available lattice construction
methods from totally real and complex multiplication (CM)
fields do not provide diversity in the binary case, we generalize
algebraic Construction A lattices over a wider family of number
fields namely monogenic number fields.
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