  In this chapter, we show how the use of differential coding and the presence
of phase slips in the transmission channel affect the total achievable
information rates and capacity of a system. By means of the commonly used QPSK
modulation, we show that the use of differential coding does not decrease the
total amount of reliably conveyable information over the channel. It is a
common misconception that the use of differential coding introduces an
unavoidable differential loss. This perceived differential loss is rather a
consequence of simplified differential detection and decoding at the receiver.
Afterwards, we show how capacity-approaching coding schemes based on LDPC and
spatially coupled LDPC codes can be constructed by combining iterative
demodulation and decoding. For this, we first show how to modify the
differential decoder to account for phase slips and then how to use this
modified differential decoder to construct good LDPC codes. This construction
method can serve as a blueprint to construct good and practical LDPC codes for
other applications with iterative detection, such as higher order modulation
formats with non-square constellations, multi-dimensional optimized modulation
formats, turbo equalization to mitigate ISI (e.g., due to nonlinearities) and
many more. Finally, we introduce the class of spatially coupled (SC)-LDPC
codes, which are a generalization of LDPC codes with some outstanding
properties and which can be decoded with a very simple windowed decoder. We
show that the universal behavior of spatially coupled codes makes them an ideal
candidate for iterative differential demodulation/detection and decoding.
