Maximum transition run codes for generalized partial response channels

A new twins constraint for maximum transition run (MTR) codes is introduced to eliminate quasi-catastrophic error propagation in sequence detectors fo r generalized partial response channels with spectral nulls both at de and at the Nyquist frequency. Two variants of the twins constraint that depend on whether the generalized partial response detector trellis is unconstrain ed or j -constrained are studied. Deterministic finite-state transition dia grams that present the twins constraint are specified, and the capacity of the new class of MTR constraints is computed. The connection between (G, I) constraints and MTR(j)) constraints is clarified. Code design methodologie s that are based on look-ahead coding in combination with violation detecti on/substitution as well as on state splitting are used to obtain several sp ecific constructions of high-rate MTR codes.