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In this chapter, we show how the use of differential coding and the presenceof phase slips in the transmission channel affect the total achievableinformation rates and capacity of a system. By means of the commonly used QPSKmodulation, we show that the use of differential coding does not decrease thetotal amount of reliably conveyable information over the channel. It is acommon misconception that the use of differential coding introduces anunavoidable differential loss. This perceived differential loss is rather aconsequence of simplified differential detection and decoding at the receiver.Afterwards, we show how capacity-approaching coding schemes based on LDPC andspatially coupled LDPC codes can be constructed by combining iterativedemodulation and decoding. For this, we first show how to modify thedifferential decoder to account for phase slips and then how to use thismodified differential decoder to construct good LDPC codes. This constructionmethod can serve as a blueprint to construct good and practical LDPC codes forother applications with iterative detection, such as higher order modulationformats with non-square constellations, multi-dimensional optimized modulationformats, turbo equalization to mitigate ISI (e.g., due to nonlinearities) andmany more. Finally, we introduce the class of spatially coupled (SC)-LDPCcodes, which are a generalization of LDPC codes with some outstandingproperties and which can be decoded with a very simple windowed decoder. Weshow that the universal behavior of spatially coupled codes makes them an idealcandidate for iterative differential demodulation/detection and decoding.

Advances in Detection and Error Correction for Coherent Optical Communications: Regular, Irregular, and Spatially Coupled LDPC Code Designs