Design of a rate 6/7 maximum transition run code

Abstract

Maximum transition run (MTR) codes provide significant minimum distance gains when used with sequence detectors operating at high linear densities. A method for reducing the RLL k constraint associated with MTR block codes is presented. A block decodable, rate 4/5 MTR code with k=4 illustrates the technique. This reduction of k is combined with sliding-block decoding to develop a 97.8% efficient rate 6/7 MTR code with k=8.

A PRML with modified branches of a dual MTR code for high-density PMR channels

“…The maximum lengths of successive data transitions of the rate 8/9 and 16/17 codes are 12 and 26 bits, respectively. In addition, we also compared the rate 6/7 (0, 8) MTR code that has the highest rate of the practical MTR codes with j=2 constraint [6].…”

“…The minimum distances of the rate 4/5, 5/6 and 6/7 MTR codes are greater than that of the rate 8/9 and 16/17 codes for high-density magnetic recording systems [5,6]. However, the code rates are reduced considerably in comparison with the rate 8/9 and 16/17 codes.…”

Signal space detectors for MTR-coded magnetic recording channels

“…The directions of these planes are also constrained to further simplify the detector Yi-1 = ak-l + ha,-, (3) …”

Performance and coding gains of MTR-RLL codes in partial response magnetic channels

“…Channel codes are used to eliminate troublesome patterns or to introduce certain desirable characteristics in the recorded sequences [5]. An important case of the former is suppression of minimum distance error events, which dominate the performance of sequence detectors.…”

“…The usual RLL k constraint is retained for timing recovery, leading to an encapsulation of the code parameters as MTR (j; k), where j is the maximum number of consecutive transitions. One design methodology for MTR block codes, shown in [5], is to maximize the code rate and then minimize the RLL k constraint. In doing so, however, it is possible to arrive at codes with reasonable rates but large values for k. To reduce k, a simple method for designing a two-state encoder for use with block decoding is proposed.…”