Power- and bandwidth-efficient differentially encoded transmission over slo
wly time-varying fading channels with noncoherent reception and without cha
nnel state information is considered. For high bandwidth efficiencies, comb
ined phase and amplitude modulation is used. For increased power efficiency
, channel coding and multiple-symbol differential detection are applied, i.
e., interleaving and detection are based on blocks of N > 2 consecutive sym
bols. The presented concepts are directly applicable to transmission over f
lat fading channels. However, concentrating on the situation of frequency-s
elective channels, we consider their application to multicarrier transmissi
on using orthogonal frequency-division multiplexing (OFDM). When coding acr
oss subcarriers, OFDM transforms the actual frequency-selective channel int
o a slowly time-varying frequency-nonselective fading channel. This paper p
resents a design for multilevel coding schemes to approach theoretical limi
ts for power- and bandwidth-efficient noncoherent transmission over the equ
ivalent fading channel. It is shown that bit-interleaved coded modulation,
which relies on Gray labeling, is competitive only in the case of conventio
nal differential detection with N = 2. The theoretic considerations are wel
l approved by simulation results, where turbo codes are applied as componen
t codes.