Conditions on Degree Distributions to Compensate Differential Penalty by LDPC Turbo Decoding

Differential modulation causes a performance penalty compared to non-differential transmission, that can be diminished by a turbo loop between the differential demodulation and the forward error correction (FEC) decoder. To enhance this effect the low density parity check (LDPC) code has to be adjusted to this loop. Dependent on the used LDPC code the differential penalty can be completely or only partly overcome. In this paper we show under which conditions regarding code rate and complexity this penalty can be compensated completely. Therefore we use the extrinsic information transfer (EXIT) chart analysis and optimize the check edge degree distributions. We also show how we can construct LDPC codes that perform well in both the coherent and differential case. These codes are of interest, as in certain situation, like e.g. for a low quality channel estimation, due to fast changing channels, differential transmission is essential, while in other situations the channel estimation is sufficiently accurate to avoid differential transmission. Codes that perform well in both, the differential and coherent case allow to design only one code for both schemes. Finally we compare the optimized degree distributions in certain cases.