Optimization of Variable Edge Degree Distributions to Compensate the Differential Penalty by LDPC Turbo Decoding

Differential modulation is often applied in fiber optical communications in order to compensate for cycle slips. However, differential modulation causes a performance degradation compared to coherent detection, called the differential penalty. We consider a low density parity check (LDPC) coded system and include the differential modulation in the optimization of the LDPC code with the intention of overcoming the differential penalty. In this paper special attention is paid on the optimization of the variable edge degree distribution of the LDPC code. In this case the optimization problem is non linear. Therefore we derive substitute linear optimization problems that allow to determine upper and lower bounds of the maximal achievable rate. The corresponding degree distributions are determined explicitly. We explain why this method works well in the differential case but fails in the coherent case. In the differential case these new bounds allow to conclude for which parameters the differential penalty can be overcome. We show in particular that this is possible for high rates.