Optimal finite alphabet sources over partial response channels

We present a serially concatenated coding scheme for partial response channels. The encoder consists of an outer irregular LDPC code and an inner matched spectrum trellis code. These codes are shown to offer considerable improvement over the i.i.d. capacity (> 1 dB) of the channel for low rates (approximately 0.1 bits per channel use). We also present a qualitative argument on the optimality of these codes for low rates. We also formulate a performance index for such codes to predict their performance for low rates. The results have been verified via simulations for the (1-D)/sqrt(2) and the (1-D+0.8D^2)/sqrt(2.64) channels. The structure of the encoding/decoding scheme is considerably simpler than the existing scheme to maximize the information rate of encoders over partial response channels.