EXIT Chart-based Design of LDPC Codes for Inter-Symbol Interference Channels

The subject of this paper is the design of lowdensity parity-check (LDPC) codes concatenated with a Gray mapped quaternary phase shift keying (QPSK) modulator for transmission over inter-symbol (ISI) channels. In particular, we will present several results considering important partial response channels (PRCs). Using an extrinsic information transfer (EXIT) chart-based analysis, we give insights into the behavior of an iterative detector/decoder for LDPC codes transmitted over ISI channels. In particular, we will discuss if there is a real need for LDPC codes specifically optimized for ISI channels. Using the proposed analysis method, we design LDPC codes tailored for ISI channels. We show that, if the channel impulse response is short, an ad hoc optimized LDPC code is very similar to that optimized for an additive white Gaussian noise (AWGN) channel, reducing significantly the need for code optimization. On the other hand, if the impulse response of the ISI channel is long, ad hoc optimized LDPC codes achieve sensible gain with respect to LDPC codes optimized for AWGN channel.