Time-varying maximum transition run constraints

Maximum transition run (MTR(j)) constrained systems are used to improve detection performance in storage channels. Recently there has been a growing interest in time-varying MTR (TMTR) systems, after such codes were observed to provide high coding gain for EⁿPR4 channels for n = 2, 3. We investigate TMTR constraints parameterized by a vector, introduce the notion of tightness to classify such constraints and simplify their minimal graph presentations. We present new upper bounds on the capacity of TMTR constraints, and give an explicit linear ordering by capacity of all tight TMTR constraints up to period 4. We show that for MTR constrained systems with unconstrained positions, the set of sequences restricted to the constrained positions yields a natural TMTR constraint. Using TMTR constraints, we present a new upper bound on the tradeoff function for MTR systems that relates the density of unconstrained positions to the maximum code rates