Run-length Limited Research Articles

Performance of run-length limited (4, 18) code for optical storage systems

In this paper, the authors investigate the performance of recently presented run-length limited (4, 18) code for high density optical storage systems. The construction of the code is described simply. The code has code rate R = 1/3 and density ratio (DR) = 1.67. The bit error rate (BER) performance for decision feedback equalizer (DFE) and partial response maximum likelihood (PRML) detector are simulated, considering signal-to-noise ratio (SNR) and optical channel jitter. The result shows that the performance of the code is acceptable. The encoder and decoder of the code are implemented by complex programmable logic device (CPLD) chip and the hardware resources required for encoder and decoder are␣low.

신호패턴 종속잡음 채널을 위한 신호검출

고밀도의 저장기록장치 채널의 주요 신호검출 오류의 원인은 천이 지터잡음이다. 이러한 채널환경에서 최적의 신호검출기 구현을 위해서는 고도의 복잡도가 요구되는데 이는 지터잡음이 신호와 상관관계가 있고 잡음간에도 상관관계가 존재하기 때문이다. 본 논문에서는 계산량과 하드웨어 복잡도 관점에서 효율적인 두 가지 종류의 신호검출기에 대해서 설명한다. 이는 전통적인 비터비 복호기의 가지값을 변화시킨 형태이며 같은 이진데이터 값의 반복을 제한하는 부호와 함께 결합하여 일반적인 PR 채널에 적용된다 기존의 비터비 알고리즘의 복잡도와 비교하면 비터비 트렐리스에서 각각의 가지값을 계산할 때 추가적으로 하나의 곱셈기 혹은 덧셈기의 증가가 요구된다. Transition jitter noise is one of major sources of detection errors in high density recording channels. Implementation complexity of the optimal detector for such channels is high due to the data dependency and correlated nature of the jitter noise. In this paper, two types of hardware efficient sub-optimal detectors are derived by modifying branch metric of Viterbi algorithm and applied to partial response (PR) channels combined with run length limited modulation coding. The additional complexity over the conventional Viterbi algorithm to incorporate the modified branch metric is either a multiplication or an addition for each branch metric in the Viterbi trellis.

A Study of Interactive Processing Between PRML Detection and Erasure Error Correction in Perpendicular Recording

In this paper, the interactive processing between a partial-response maximum-likelihood (PRML) channel and a decoder for the Reed-Solomon (RS) code is studied in perpendicular magnetic recording channel. Whereas in conventional systems a run-length-limited (RLL) encoder/decoder is insides the RS encoder/decoder, in this paper, we permute their positions so that the PRML channel and RS decoder can interact. Accordingly, the RS decoder can acquire reliability information from a PRML channel without interruption by the RLL decoder. It is demonstrated by computer simulation that the proposed system provides an SNR improvement of 0.8-1.1 dB compared with a conventional system at a linear density normalized by user bit interval, K, of 1.5.

Run-Length-Limited (4, 13) Code for High Density Optical Storage Systems

In this paper, we propose a new (4, 13) run-length-limited (RLL) code for high-density optical storage systems. The code rate of this code is 1/3, and the resulting density ratio is 1.67, which is larger than that of EFMPlus code used for digital versatile disc (DVD) systems. The bit error rate (BER) performance of the code is analyzed considering noise and channel jitter. The (4, 13) RLL code has very low complexity of hardware since the mapping rule is simple. The encoding and decoding circuits of the code are implemented using a complex programmable logic device (CPLD) chip.

Erasure Detection Algorithms for Magnetic Recording Channels

The effects of precoding on the detection of erasures based on violations of run-length-limited (RLL) constraints for low-density parity-check (LDPC) coded magnetic recording channels are investigated and an improved erasure detection algorithm is proposed. Its performance on an ME/sup 2/PR4 channel is evaluated using computer simulations.

A New Run-length-limited (2,7) Parity Preserving Code Limiting the Repeated Minimum Transition Run for Optical Storage Systems

In this paper, a new run-length-limited (RLL) (2,7) parity preserving (PP) repeated minimum transition run (RMTR) 4 code is proposed. The proposed code shows better performance in terms of density ratio, RMTR, DC component suppression, flexible adaptation for a partial response maximum likelihood (PRML) [1] system and bit error rate (BER) as compared with (2,10) code [2] (currently applied in storage systems) or (1,7) PP code [3] (highly recommended for next-generation optical recording systems). On the basis of the results of experiments on optical storage systems, the superiority of the proposed code is established.

Modified Partial Response Maximum Likelihood Detection Using the Relative Probability of the 17PP Code for Optical Storage Systems

In this paper, we propose a modified calculation method of the branch metric in partial response maximum likelihood (PRML) detection for high-density optical storage systems. The scheme is related to the relative probability of the run-length limited code. Hence, we also present the relative probabilities of the 17PP coded sequences for 2nd-, 3rd- and 4th-orders of PR targets. The modified PRML detection using the relative probability of the 17PP coded sequence has better bit error rate (BER) performance than conventional PRML detection.

Improved Bit-Stuffing Bounds on Two-Dimensional Constraints

We derive lower bounds on the capacity of certain two-dimensional (2-D) constraints by considering bounds on the entropy of measures induced by bit-stuffing encoders. A more detailed analysis of a previously proposed bit-stuffing encoder for (d,/spl infin/)-runlength-limited (RLL) constraints on the square lattice yields improved lower bounds on the capacity for all d /spl ges/ 2. This encoding approach is extended to (d,/spl infin/)-RLL constraints on the hexagonal lattice, and a similar analysis yields lower bounds on the capacity for d /spl ges/ 2. For the hexagonal (1,/spl infin/)-RLL constraint, the exact coding ratio of the bit-stuffing encoder is calculated and is shown to be within 0.5% of the (known) capacity. Finally, a lower bound is presented on the coding ratio of a bit-stuffing encoder for the constraint on the square lattice where each bit is equal to at least one of its four closest neighbors, thereby providing a lower bound on the capacity of this constraint.

Symbol Error Probability for Guided Scrambling Over a Recording Channel

We derive expressions for the symbol error probabilities for a recording code concatenated with a Reed-Solomon (RS) code. The recording code is structured by a guided scrambling (GS) code for the direct current (DC) suppression in conjunction with a runlength-limited (RLL) code. As for the GS codes, convolutional GS and Galois field (GF) addition GS schemes are examined. As for the RLL codes, two types of RLL codes are investigated. One is a traditional RLL code where a bit length m of an RS symbol is an integer multiple of a bit length p of an RLL source symbol. The other is a new type of high-rate RLL code where p>m. We compute the RS symbol error rates when these RLL codes are combined with the two GS schemes.

Independent Sets in Regular Hypergraphs and Multidimensional Runlength-Limited Constraints

Let G be a t-uniform s-regular linear hypergraph with r vertices. It is shown that the number of independent sets $\IS(\hgraph)$ in $\hgraph$ satisfies \[ \log_2 \IS(\hgraph) \le \frac{r}{t} \left( 1 + O \biggl( \frac{\log^2(ts)}{s} \biggr) \right) . \] This leads to an improvement of a previous bound by Alon obtained for t = 2 (i.e., for regular ordinary graphs). It is also shown that for the Hamming graph $\Hamming(n,q)$ (with vertices consisting of all n-tuples over an alphabet of size q and edges connecting pairs of vertices with Hamming distance $1$), \[ \frac{\log_2 \IS(\Hamming(n,q))}{q^n} = \frac{1}{q} + O \biggl(\frac{\log^2 (q n)}{q n} \biggr). \] The latter result is then applied to show that the Shannon capacity of the n-dimensional $(d,\infty)$-runlength-limited (RLL) constraint converges to 1/(d+1) as n goes to infinity.

Edge-position modulation for high-speed wireless infrared communications

Driven by the Infrared Data Association (IrDA), wireless infrared communication has become a very popular and widely used method for short-range data transmission between mobile devices such as laptops, PDAs and mobile phones. The quality and speed of infrared communications are mainly limited by the bandwidth of the infrared transceivers. Therefore, it is important to use a modulation technique with a high bandwidth efficiency, while simultaneously maintaining a low bit-error rate and high power efficiency. Consequently, the IrDA has continuously improved the modulation techniques of its standards by introducing return to zero (inverted), RZ(I), for the serial infrared (SIR) mode, 4-pulse position modulation (4-PPM) for the fast infrared (FIR) mode and HHH(1,13) for the latest very fast infrared (VFIR) mode (serial infrared physical layer specification, version 1.4, May 2001). This article presents a new modulation scheme called edge position modulation (EPM) with run-length-limited (RLL) coding, which offers an increased bandwidth efficiency over the previous methods and an attractive power efficiency. Since the novel modulation technique can be optimised to the characteristics of the wireless infrared channel, it also maintains low bit-error rates.

Wireless infrared communication system based on edge position modulation

Driven by the Infrared Data Association (IrDA) wireless infrared communication has become a very popular and widely used method for short range data transmission between mobile devices like laptops, PDAs and mobile phones. Quality and speed of infrared communications are mainly limited by the bandwidth of the infrared transceivers. Therefore it is important to use a modulation technique with a high bandwidth efficiency, while simultaneously maintaining a low bit error rate and high power efficiency. Consequently, IrDA has continuously improved the modulation techniques of its standards (IrDA, 2001) by introducing Return to Zero inverted (RZI), 4 Pulse Position Modulation (4-PPM) and HHH(1, 13), whereby the latest is basically a 2/3-rate Run-Length-Limited (RLL) code (Hirt, Hassner, Heise, 2001). Recently the authors have published a novel modulation scheme called Edge Position Modulation (EPM) with Run-Length-Limited (RLL) coding (Luftner et al., 2003). This article will continue this work by presenting a completely new RLL(5, 12) code that is optimized for EPM.

Wireless infrared communications with edge position modulation for mobile devices

Driven by the Infrared Data Association, wireless infrared communication has become a very popular and widely used method for short-range data transmission between mobile devices like laptops, PDAs, and mobile phones. Especially in ad hoc connection applications, IrDA excels over radio-based solutions like Bluetooth or cable-based solutions like USB, due to the point-and-shoot characteristic of infrared communication. The quality and speed of infrared communications are mainly limited by the bandwidth of infrared transceivers. Therefore, it is important to use a modulation technique with high bandwidth efficiency, while simultaneously maintaining a low bit error rate and high power efficiency. Consequently, the IrDA has continuously improved the modulation techniques of its standards by introducing return to zero inverted (RZI) for the serial infrared (SIR) mode, 4-PPM for the fast infrared mode, and HHH(1,13) for the latest very fast infrared mode. This article presents a new modulation scheme called edge position modulation (EPM) with RLL coding, which offers increased bandwidth efficiency over the previous methods and attractive power efficiency. Since the novel modulation technique can be optimized to the characteristics of the wireless infrared channel, it also maintains low bit error rates.

Efficient dc-free RLL codes for optical recording

We report on new dc-free runlength-limited codes (DCRLL) intended for the next generation of DVD. The efficiency of the newly developed DCRLL schemes is extremely close to the theoretical maximum, and as a result, significant density gains can be obtained with respect to prior art coding schemes. With a newly developed DCRLL (d=2) code we can achieve a 9% higher overall rate than that of DVD's EFMPlus.

Run-length limited (4, 18) code for high density optical storage systems

A run-length limited (RLL) code for high density optical storage system is presented. The density ratio of the code is 1.67, which is larger than that of EFMPlus code used for DVD systems. The fix-length (4, 18) RLL code with code rate m/n=1/3 is attractive for storage systems.

Parallel constrained coding with application to two-dimensional constraints

A (one-dimensional) constraint is defined as the set of all finite words that axe generated by a given labeled finite directed graph G. Examples of constraints include the (d, k)-runlength-limited (RLL) constraints and the symmetric runlength (SRLL) constraints. In the latter, the runlengths of 0's, as well as the runlengths of 1's, are between d and k, except that the first and last runlengths may be shorter than d. A commonly-used coding model for constraints is that of a finite-state encoder at a fixed rate p:q. In this work, we explore the possibility of obtaining simple coding schemes by encoding several input streams simultaneously, i.e., in parallel. The coding model is still a finite-state encoder at a fixed rate p:q. Yet, an input p-block is mapped into q output symbols, each belonging now to a different track; the sequence generated along each track belongs to a given constraint S. Decoding is carried out by reading q tracks at a time and reconstructing the respective input p-block. If the resulting encoder is block decodable, then such a reconstruction requires only the knowledge of the current symbol in each track.

Performance comparison of (1,7) RLL coded PRML systems and 16/17 (0,6/6) coded PRML systems in perpendicular magnetic recording using double‐layered media

AbstractThe performance of a partial response maximum likelihood (PRML) system in perpendicular magnetic recording that uses double‐layered media perpendicular to the MR head is evaluated. The codes of (1,7) RLL and 16/17 (0,6/6), which are commonly used in modern hard disk equipment, are used as the recording codes. The relationship between the normalized linear density and the desired SNR at the reading point for a bit error rate of 10−4 is determined from a computer simulation, assuming equalization by a transversal filter, and a comparative study is performed. It is shown that a (1,7) RLL coded PRML system has better performance when the recording density is comparatively low. For high recording density, a 16/17 (0,6/6) coded PRML system has shown better performance. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 85(5): 43–49, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.1106

Turbo Decoding with Run Length Limited Code for Optical Storage

A new turbo decoding method with a run length limited (RLL) code for optical storage is proposed. The system entails a trellis code that joins the RLL code, the non-return-to-zero inverse (NRZI) conversion, and the partial response (PR) channel as the inner code. The inner a posteriori probability (APP) decoder is able to utilize the extrinsic information fed back from the output of the outer decoder. A turbo-coded (1, 7)RLL-constrained PR2 channel was simulated. The full, partial, and serial turbo decoding systems with the inner APP decoder achieved coding gains of 4.7 dB, 4.3 dB, and 3.3 dB, respectively, over the uncoded (1, 7)RLL-constrained PR2 channel at a bit error rate (BER) of 10-5. The full and partial turbos were also improved by 1.2 dB and 0.8 dB, respectively, over the partial turbo with the RLL soft-input soft-output (SISO) decoder at a BER of 10-5.

Construction of Efficient Dc-Free Runlength-Limited Codes for Optical Recording

We will report on new dc-free runlength-limited codes (DCRLL) intended for the next generation of digital versatile disc (DVD). The efficiency of the newly developed DCRLL schemes is extremely close to the theoretical maximum, and as a result, significant density gains can be obtained with respect to prior art coding schemes. Preferred embodiments of the codes (footprints) and respective hardware realization will be considered.

Turbo-coded optical recording channels with DVD minimum mark size

Recent work on turbo codes applied to partial response (PR) optical recording channels has focused on unconstrained channels. In this paper, we consider the application of turbo codes to a (1,7) constrained, PR-equalized optical recording channel with digital versatile disc (DVD) parameters. The addition of a (1,7) run-length-limited (RLL) constraint requires the use of a soft RLL decoder to communicate with the turbo code. Although soft RLL decoders were previously developed for use with iterative decoding, application to a practical optical channel has not been addressed until now. Here, results on both correlated noise and media noise optical recording channel models are given for two PR targets, 1+D and 1+D+D/sup 2/+D/sup 3/. We achieved coding gains of 4 to 6.3 dB over a baseline RLL-coded system. We also evaluated system performance at smaller mark sizes, and found that density gains of 17% and 22% are achievable for the two targets, respectively.