Time-Varying Maximum Transition Run Constraints

Abstract

Abstract-Maximum transition run (MTR) 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 eliminate certain error events and thus provide high coding gain for E n PR4 channels for n = 2; 3.In this work, TMTR constraints parameterized by a vector, whose coordinates specify periodically the maximum runlengths of 1's ending at the positions, are investigated. A canonical way to classify such constraints and simplify their minimal graph presentations is introduced. It is shown that there is a particularly simple presentation for a special class of TMTR constraints and explicit descriptions of their characteristic equations are derived. New upper bounds on the capacity of TMTR constraints are established, and an explicit linear ordering by capacity of all tight TMTR constraints up to period 4 is given. For MTR constrained systems with unconstrained positions, it is shown that the set of sequences restricted to the constrained positions yields a natural TMTR constraint. Using TMTR constraints, a new upper bound on the tradeoff function for MTR systems that relates the density of unconstrained positions to the maximum code rates is determined.

Enumerative Encoding of TMTR Codes for Optical Recording Channel

“…Karabed and Siegel [12] proposed a class of modulation codes that take advantage of the well-defined spectral nulls presented in partial response channels. The time-varying maximum transition run (TMTR) code [2][3][4][5][6][7][8][9], which can be treated as a (0, k) modulation code, has recently been studied for partial response channels. The TMTR code matched to the partial response channel can delete some dominant error events and enhance the Euclidian distance of the partial response channel.…”

Grafos Reduzidos para Restrições Periódicas

“…Também são utilizados para incrementar a distância de códigos, o que fazem ao eliminar padrões de bits que ocorrem majoritariamente quando há eventos erro. Versões generalizadas dos códigos TMTR permitem a limitação de sequências máximas de uns em mais de duas "fases" da sequência [4].…”

On the Zeta Function of a Periodic-Finite-Type Shift

“…A new class of sofic shifts, called periodic-finite-type shifts (PFT's), was introduced by Moision and Siegel [9], who were interested in studying the properties of distance-enhancing codes, in which the appearance of certain words is forbidden in a periodic manner. The class of PFT's strictly includes the class of SFT's, and some other interesting classes of shifts, such as constrained systems with unconstrained positions [11], and shifts arising from the time-varying maximum transition run constraint [10].…”