Based on lattice Gaussian distributions and ideal
lattices, we present a unified framework of lattice coding to
achieve the channel capacity and secrecy capacity of wireless
channels in the presence of Gaussian noise. The standard additive
white Gaussian-noise (AWGN) channel, block fading channel, and
multi-input multi-output (MIMO) fading channel are considered,
which form a hierarchy of increasingly challenging problems in
coding theory. To achieve channel capacity, we apply Gaussian
shaping to a suitably defined good lattice for channel coding.
To achieve secrecy capacity, we use a secrecy-good lattice nested
with a coding lattice.