Maximum Run Length Research Articles

Stochastic model of digit transfer in computing

This paper describes a stochastic model of digit transfer. The main characteristics of the transfer process are the number of transfers, the number of groups of consecutive transfers, and the maximum number of consecutive transfers. Two binary numbers with a digit transfer form a triplet, and a sequence of these triplets generates a Markov chain. In our model, the above-mentioned characteristics can be described by functionals on trajectories of this chain: the number of events, the number of runs of these events, and the maximum run length. These characteristics can be efficiently used for estimating the computation speed.

High-Rate Maximum Runlength Constrained Coding Schemes Using Nibble Replacement

In this paper, we will present coding techniques for the character-constrained channel, where information is conveyed using <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -bit characters (nibbles), and where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</i> prescribed characters are disallowed. Using codes for the character-constrained channel, we present simple and systematic constructions of high-rate binary maximum runlength constrained codes. The new constructions have the virtue that large lookup tables for encoding and decoding are not required. We will compare the error propagation performance of codes based on the new construction with that of prior art codes.

Markers to construct DC free (d, k) constrained balanced block codes using Knuth's inversion

In this reported work, Knuth&apos;s balancing scheme, which was originally developed for unconstrained binary codewords is adapted. Presented is a simple method to balance the NRZ runlength constrained block codes corresponding to (d, k) constrained NRZI sequences. A short marker violating the maximum runlength or k constraint is used to indicate the balancing point for Knuth&apos;s inversion. The marker requires fewer overhead bits and less implementation complexity than indexing the balancing point&apos;s address by mapping it onto a (d, k) or runlength constrained prefix, such as when applying Knuth&apos;s original scheme more directly. The new code construction may be attractive for future magnetic and especially optical recording schemes. In fact the current optical storage media, such as the CD, DVD and Blue Ray Disc, all attempt to achieve some suppression of low frequency components of the constrained codes, by exploiting a limited degree of freedom within the set of candidate (d, k) words.

An expert system for control chart pattern recognition

This paper focuses on the design and development of an expert system for on-line detection of various control chart patterns so as to enable the quality control practitioners to initiate prompt corrective actions for an out-of-control manufacturing process. Using this expert system developed in Visual BASIC 6, all the nine most commonly observed control chart patterns, e.g., normal, stratification, systematic, increasing trend, decreasing trend, upward shift, downward shift, cyclic, and mixture can be recognized well, employing an optimal set of seven shape features. Based on an observation window of 32 data points, it can plot the control chart, compute the control limits, identify the control chart pattern, calculate the process capability index, determine the maximum run length, and identify the starting point of the maximum run length. After pattern recognition, it can also inform the users about various root assignable causes associated with a particular pattern along with the necessary pre-emptive actions. It opens up wide opportunities for quality improvement and real-time applications in diverse manufacturing processes. This developed expert system is built for a vertical drilling process and its recognition performance is tested using simulated process data.

Disentangling the effects of alternation rate and maximum run length on judgments of randomness

AbstractBinary sequences are characterized by various features. Two of these characteristics—alternation rate and run length—have repeatedly been shown to influence judgments of randomness. The two characteristics, however, have usually been investigated separately, without controlling for the other feature. Because the two features are correlated but not identical, it seems critical to analyze their unique impact, as well as their interaction, so as to understand more clearly what influences judgments of randomness. To this end, two experiments on the perception of binary sequences orthogonally manipulated alternation rate and maximum run length (i.e., length of the longest run within the sequence). Results show that alternation rate consistently exerts a unique effect on judgments of randomness, but that the effect of alternation rate is contingent on the length of the longest run within the sequence. The effect of maximum run length was found to be small and less consistent. Together, these findings extend prior randomness research by integrating literature from the realms of perception, categorization, and prediction, as well as by showing the unique and joint effects of alternation rate and maximum run length on judgments of randomness.

Turbo Equalization of Run Length Limited (1,9) and Low Density Parity Check Code for Super Resolution Nearfield Structure Read Only Memory Discs with 60 nm Minimum Mark Length

Due to severe intersymbol interference and low signal-to-noise ratio of super resolution nearfield structure (SuperRENS) random read-outs, turbo equalization techniques are applied to lower bit error rates. A d1k9r5 run length limited (RLL) modulation code having minimum runlength d = 1, maximum runlength k = 9 and repeated minimum transition run limitation of r = 5 has been developed with emphasis on low joint bit detection and demodulation (super-trellis) complexity for use within turbo equalization schemes. Bit error rate (BER) performance of d1k9r5 code over partial response-channels is similar to 17pp code while the super-trellis detector complexity of d1k9r5 code is reduced. Low-frequency suppression performance of d1k9r5 code is similar to that of 17pp code under the same DC control redundancy. BER results for measured data from a 60 nm SuperRENS read only memory disc employing an InSb mask layer, using d1k9r5 modulation and a high-rate quasi-cyclic low density parity check (LDPC) code, correspond well to simulation results. Continuously decreasing BERs down to 2 ×10-5 after five iterations show that a turbo equalization scheme incorporating d1k9r5 super-trellis detection can be successfully applied in SuperRENS storage systems together with an LDPC code.

A New 1.25-Gb/s Burst Mode Clock and Data Recovery Circuit Using Two Digital Phase Aligners and a Phase Interpolator

We propose a new Clock and Data Recovery (CDR) circuit for burst-mode applications. It can recover clock signals after two data transitions and endure long sequence of consecutive identical digits. Two Digital Phase Aligners (DPAs), triggered by rising or falling edges of input data, recover clock signals, which are then combined by a phase interpolator. This configuration reduces the RMS jitters of the recovered clock by 30% and doubles the maximum run length compared to a previously reported DPA CDR. A prototype chip is demonstrated with 0.18-μm CMOS technology. Measurement results show that the chip operates without any bit error for 1.25-Gb/s 231-1 PRBS with 200-ppm frequency offset and recovers clock and data after two clock cycles.

DC-Balanced Block Inversion Coding for High-Speed Links

A new 4B5B block inversion coding is proposed for dc-balanced transmission in high-speed optical parallel links. An 8-bit byte is partitioned into two 4-bit data and converted to two 5-bit blocks by an inversion encoding. The proposed coding greatly reduces circuit complexity with the minimum latency overhead of one clock for the encoder and none for the decoder. The maximum run length is 11.

Time-Varying Maximum Transition Run Constraints

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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> 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

Monotone runs of uniformly distributed integer random variables: A probabilistic analysis

Using a Markov chain approach and a polyomino-like description, we study some asymptotic properties of monotone increasing runs of uniformly distributed integer random variables. We analyze the limiting trajectories, which after suitable normalization, lead to a Brownian motion, the number of runs, which is asymptotically Gaussian, the run length distribution, the hitting time to a large length k run, which is asymptotically exponential, and the maximum run length which is related to the Gumbel extreme-value distribution function. A preliminary application to DNA analysis is also given.

Ascending runs of sequences of geometrically distributed random variables: a probabilistic analysis

Using a Markov chain approach and a polyomino-like description, we study some asymptotic properties of sequences of ascending runs of geometrically distributed random variables. We analyze the limiting trajectories, the number of runs and the run length distribution, the hitting time to a length k run and the maximum run length.

Runs of geometrically distributed random variables: a probabilistic analysis

Using a Markov chain approach and a polyomino-like description, we study some asymptotic properties of runs of geometrically distributed random variables. We analyze the limiting trajectories, the number of runs and the run length distribution, the hitting time to a length k run and the maximum run length.

Ascending runs of sequences of geometrically distributed random variables: a probabilistic analysis

Using a Markov chain approach and a polyomino-like description, we study some asymptotic properties of sequences of ascending runs of geometrically distributed random variables. We analyze the limiting trajectories, the number of runs and the run length distribution, the hitting time to a length k run and the maximum run length.

Rate 8/9 sliding block distance-enhancing code with stationary detector

A new distance-enhancing code for partial-response magnetic recording channels eliminates most frequent errors, while keeping the two-step code trellis time invariant. Recently, published trellis codes either have lower code rates or result in time-varying trellises with a period of nine, thus requiring a higher complexity of detectors and code synchronization. The new code introduces dependency between code words in order to achieve the same coding constraints as the 8/9 time-varying maximum transition runlength (TMTR) code, with the same code rate, but resulting in a trellis that has a period of 2. This code has been applied to the E/sup 2/PR4 and a 32-state generalized partial response (GPR) ISI target. The resulting two-step trellises have 14 and 28 states, respectively. Coding gain is demonstrated for both targets in additive white Gaussian noise.

Dual FDTS/DF: a unified approach to dual-detection and modification for MTR codes

Dual-detector decision-feedback schemes have recently gained considerable interest in magnetic recording. Schemes such as dual decision feedback equalization (DDFE), M2DFE, and dual FDTS/DF are dual-detector versions of DFE, multilevel DFE (MDFE), and fixed delay tree search with decision feedback fixed-delay tree search with decision feedback (FDTS/DF) detectors, respectively. At high recording densities, the dual-detector versions significantly improve bit-error-rate (BER) performance and reduce error propagation. In this paper, we first give a unified approach to the bit-error-rate analysis of dual-detector decision feedback schemes in an attempt to highlight their relationship, and then we show that the performance of dual FDTS/DF reduces to that of DDFE for /spl tau/=0 and reduces to that of M2DFE for /spl tau/=1 with d=1 code constraint. Further, we extend the dual FDTS/DF detection scheme to maximum transition run-length (MTR) coded channels. On the basis of both BER and error event analysis, we propose a modified dual FDTS/DF detection scheme for MTR-coded channels that improves BER performance. The new scheme modifies certain bits in the detection profess for preventing the dominant error event. Simulation results on 6/7 MTR-coded Lorentzian channel show that the modified detector gives around 1 dB SNR improvement over the advanced (trellis-coded extended partial response) TC-E/sup 2/PR detector.

Topological surgery encoding improvements based on adaptive bit allocation and DFSVQ

New methods to improve the encoding of the connectivity and geometry of the topological surgery scheme are proposed. In connectivity compression, after obtaining the vertex and triangle spanning trees by decomposing a three-dimensional object, bits are adaptively allocated to each run of two spanning trees on a threshold basis. The threshold is the length of a binary number of the maximum run length. If a run length exceeds the threshold, it is represented by a binary number of the run length. Otherwise, it is represented by a bit sequence. Therefore, compression efficiency is enhanced through an adaptive bit allocation to each run of two spanning trees. In geometry compression, since vertices represented by three-dimensional vectors are stored according to the order of the travelling along vertex spanning tree by depth-first searching, they have geometrical closeness. The geometry compression efficiency can be improved if the local characteristics of vectors are considered. Therefore, dynamic finite state vector quantization, which has subcodebooks depending on a local characteristic of vectors, is used to encode the geometry information. As it dynamically constructs a subcodebook by predicting an input vector's state, it produces less distortion and gives better visual quality than conventional methods.

Detecting Patterns by One-Sample Runs Test: Paradox, Explanation, and a New Omnibus Procedure

The standard nonparametric 1-sample runs test, which is based on the total number of runs, has recently been found to give anomalous results in the case of data consisting solely of runs of length 2. Furthermore, tests based on the total number of runs provide little information as to the length of the individual runs. An explanation for that anomaly is provided, and tests based on the length of runs are described. Such tests can be successfully applied to runs of length 2 but usually use asymptotic methods of assessing statistical significance. In addition, such tests generally impose arbitrary limits as to the maximum run length. A new procedure that allows the maximum run length to be empirically determined is described. In that procedure, one uses a Monte Carlo permutation test to ascertain statistical significance. The new Monte Carlo omnibus length-of-runs procedure is illustrated with examples from suicide research and from psycholinguistics.

The maximum run length in the generalized Bernoulli sequences

The maximum run length in the generalized Bernoulli sequences

Generalized algorithm for design of DC-free codes based on multilevel partition chain

A generalized algorithm for design of DC-free codes based on the multilevel partition chain is presented. The multilevel partition chain is formed from the code partition chain of Reed-Muller codes. Some parameters such as the maximum runlength and running digital sum (RDS) of DC-free codes are also obtained. The results show that the DC-free codes obtained by the presented design algorithm have good coding parameters.

Design and assessment of average of normals (AON) patient data algorithms to maximize run lengths for automatic process control

Achieving high quality and high productivity with automated testing processes will require process control systems that are optimized for the necessary error detection, minimum false rejection, and maximum run length. This study investigates whether run length could be monitored by average of normals (AON) algorithms that truncate the patient test distribution and estimate the average of a suitable number of patient results. The design of AON algorithms for individual analytes is facilitated by computer-simulated power curves that consider the ratio of the population biological variation (Spop) to the test method variation (Smeas), represent a range of Spop/Smeas ratios from 2 to 15, and include numbers of patient test results from 10 to 600. The potential applications of AON algorithms are assessed for 38 tests whose quality requirements represent the total error criteria from the Ontario Medical Association Laboratory Proficiency Testing Program, Spop/Smeas ratios from 0 to 32, critical systematic shifts from 0.02 to 10.85 Smeas, and test workloads representative of a regional reference laboratory. Approximately half of these tests provide high potential for applying AON algorithms to monitor run length.