Final Remarks

Abstract

In this book, we have described a method for using low-density parity-check (LDPC) codes for constructing coded modulation schemes for generic communication channels. The basic idea is to use, at the transmitter side, an LDPC code concatenated with a modulator suitable for the particular channel. A good practical choice is to use a modulator whose behavior on the particular channel is well understood and whose practice of use is consolidated. At the receiver side, a soft demodulator, associated with the modulator and accounting for the communication channel statistical behavior, and a standard LDPC decoder iteratively exchange messages. We have shown how to design LDPC codes optimized for the particular transmission scheme. Depending on the specific choice of channel and modulation scheme, the optimized codes might entail remarkable performance gains with respect to standard LDPC codes, i.e., optimized for memoryless channels. It is interesting to note that LDPC codes optimized for a specific scenario are not, in general, good when applied to a different context. For example, a code optimized for the presence of a differential phase shift keying (PSK) modulator and a noncoherent channel has extremely poor performance if used jointly with a (non-differential) binary PSK (BPSK) modulator for transmission over an additive white Gaussian noise (AWGN) channel.