On near-capacity coding systems for partial-response channels

We present a near-capacity coding system for higher-order partial-response channels, consisting of an outer set of interleaved low-density parity-check codes, an inner rate-1 shaping code, and a multistage decoder. The inner shaping code, which may be noninvertible, is designed to generate an output process similar to a binary Markov process that maximizes the mutual information for a given order. On the EPR4 channel, our system exhibits an iterative decoding threshold and a simulation BER of 10^-5 within 0.19 and 0.33 dB, respectively, of the information-theoretic limit for a third-order input process.