LDPC design for block differential modulation in optical communications

In coherent digital optical receivers, blind carrier phase recovery may incur errors, causing phase slips. A channel including blind phase estimation is modeled as an additive white Gaussian noise (AWGN) channel, affected by random phase slips that occur with a certain probability. For such a channel, block differential modulation (BDM) has been recently shown to achieve almost the same capacity as coherent AWGN channels. This paper proposes a concatenated coding scheme, with an inner code based on low-density parity-check (LDPC) codes, that embeds block differential demodulation, to make it robust to occasional phase slips. This additional feature comes at no practical cost and performs very close to a standard soft decoded LDPC code. The first design is a binary LDPC code, robust to phase rotations at multiples of π, to be used with BPSK. Then, the concept is extended to quaternary LDPC codes, robust to phase rotations at multiples of π/2, that can be used with 2-D digital constellations such as QPSK and 16-QAM.