Bounds for low-density parity-check codes over partial response channels

A bounding technique is used to evaluate the performance of high-rate low-density parity-check codes over partial response channels. Performance bounds for an ensemble of random codes, as well as for particular finite-geometry codes, are computed. Simulations are used to evaluate the bounds. The results show that the bounds appear to be valid for signal-to-noise ratios and code rates of interest in magnetic recording.