Maximum transition run codes for data storage systems

Abstract

A b s t r a c t -A new code is presented which improves the minimum distanceproperties of sequence detectors operating at high linear densities. This code, which is called the maximum transition run code, eliminates data patterns producing three or more consecutive transitions while imposing the usual k-constraint necessary for timing recovery. The code possesses the simikr distance-gaining property of the (1,k) code, but can be implemented with considerably higher rates. Bit error rate simulations on fixed delay tree search with decision feedback and high order partial response maximum likelihood detectors confirm large coding gains over the conventional (0,k) code.

Modulation Code and Signal Characteristics for Signal Waveform Modulation Optical Disc

“…The MTR code is a class of code that imposes maximum run lengths on both the number of consecutive transitions j and the number of consecutive nontransitions k, characterized by MTRð j; kÞ. 7) This means that the consecutive number of ones and zeros in the encoded codeword series are respectively not more than j and k. The MTRð j; kÞ code is designed on the basis of the nonreturn to zero inverted (NRZI) scheme, where 1 represents a transition and 0 means no transition. The main characteristic of MTR is that it permits successive ones existing in the codewords.…”

“…Table I gives the encoding table, which transfers 7-bit binary user information into 8-bit channel codewords. In order to complete such a translation, 2 7 ¼ 128 codewords are picked from the 2 8 ¼ 256 data words to meet the limitation of MTRð j; kÞ. To simplify the level modulation the parameter j is set equal to 2.…”

An 8-State DC-Controllable Run-Length-Limited Code for the Optical-Storage Channel

“…8) A question is whether these maximum RMTR are reducible or not, because the Shannon capacities of RMTR-constrained codes have not been calculated, except in the case of d ¼ 0. 3) Table I shows the Shannon capacities of (1, k) and (2, k) RLL codes with RMTR constraint for k of 7 and 8. A sliding block code with a code rate below the Shannon capacity can be constructed using the Adler-Coppersmith-Hassner (ACH) algorithm.…”

“…Figure 1 is an 18-state finite-state transition diagram (FSTD) for (1, 7) RLL codes with a maximum RMTR of 5. The Shannon capacity is 0.6784, and the approximated eigenvector for a rate-2/3 code selected in this paper is [4,6,6,6,5,5,4,2,4,6,3,6,3,5,3,5,2,3] for the FSTD in Fig. 1.…”

“…The RMTR constraint in the case of d ¼ 0 is essentially the same as the maximum transition run (MTR) constraint of Moon and Brickner. 3) The MTR value equals r þ 1. The r of the 17PP code is 6.…”