Guided Scrambling Research Articles

On the design of spectrum shaping codes for high-density data storage

This paper proposes systematic code design methods for constructing efficient spectrum shaping codes with the maximum runlength limited constraint k, which are widely used in data storage systems for digital consumer electronics products. Through shaping the spectrum of the input user data sequence, the codes can effectively circumvent the interaction between the data signal and servo signal in high-density data storage systems. In particular, we first propose novel methods to design high-rate k constrained codes in the non-return-to-zero (NRZ) format, which can not only facilitate timing recovery of the storage system, but also avoid error propagation during decoding and reduce the system complexity. We further propose to combine the Guided Scrambling (GS) technique with the k constrained code design methods to construct highly efficient spectrum shaping k constrained codes. Simulation results demonstrate that the designed codes can achieve significant spectrum shaping effect with only around 1% code rate loss and reasonable computational complexity.

Generation of balanced quadrature phase shift keyed sequences through guided scrambling

Balanced codes (also called DC-free codes) are widely used in binary communication systems to increase the likelihood of accurate symbol recovery with practical demodulators. Guided scrambling (GS) is recognised as a viable approach to efficiently generate DC-free binary sequences. In this study the authors extend the use of GS to generate balanced sequences of quadrature phase shift keyed (QPSK) symbols by using arithmetic from the ring of polynomials defined over the Galois field of four elements. In addition to ensuring adequate timing information and consistent decision thresholds to improve the performance of practical demodulators, balanced encoding of QPSK symbol sequences creates a null at DC in the spectrum of the equivalent complex baseband signal. This corresponds to a null at the centre frequency of the bandpass QPSK signal that enables the insertion of a pilot tone and avoidance of narrowband interference without filtering or distortion of the signal. The authors outline sufficient conditions for the generation of balanced GS QPSK sequences, and based upon these conditions the authors recommend scrambling polynomials and quotient selection criteria. The authors then present analytical and simulation results that confirm the generation of balanced sequences using this approach.

Worst Case Performance Assessment of DC-Free Guided Scrambling Coding by Integer Programming Model

For effective dc-free coding in the optical storage systems, guided scrambling (GS) multimode coding is popularly used. To reduce digital discrepancy of the coded sequence, functions of running digital sum (RDS) are used as criteria to choose the best candidate. Among these criteria, the minimum RDS (MRDS), minimum squared weight (MSW), and minimum threshold overrun (MTO) are suggested for effective dc-suppression. In this paper, we formulate integer programming models that are equivalent to MRDS, MSW, and MTO GS coding. Incorporating the MRDS integer programming model in maxmin setting, we develop an integer programming model that computes the worst case MRDS bound given scrambling polynomial and control bit size. In the simulation, we compare the worst case MRDS bound for different scrambling polynomials and control bit sizes. We find that careful selection of scrambling polynomial and control bit size are important factors to guarantee the worst case MRDS performance.

정수계획법 모형을 이용한 홀로그래픽 저장장치의 DC-억압 GS코딩의 성능평가

광저장장치의 DC-억압을 위한 멀티모드 코딩 기법 중 Guided Scrambling (GS) 코딩기법이 널리 사용된다. 홀로그래픽 저장장치를 위한 DC-억압 GS코딩에서는 후보코드 선택기준으로 심볼의 균등한 분포 및 심볼간 천이의 최대화 기준이 고려되었다. 본 연구에서는 후보코드행렬의 digital sum value (DSV)의 <TEX>$l_{\infty}$</TEX>-norm을 최소화하는 minimum DSV (MDSV) 기준 GS코딩을 정수계획법 모형으로 수식화하고, 제안된 모형을 사용하여 MDSV 기준과 최대천이강도 기준이 적용된 GS코딩의 성능을 제어비트수, 행렬크기 및 스크램블링 다항식들의 조합에 대하여 평가한다. For the DC-free encoding of source data, the Guided Scrambling (GS) technique is widely used as multi-mode coding in the optical data storage system. For DC-suppression GS coding in the holographic data storage system, the conservative array and balanced coding criteria are proposed. In this paper, equivalent integer programming models are developed to determine the optimal control bits for the minimum digital sum value (MDSV), conservative array, and balanced coding criteria. Using the proposed integer programming models, we compare the performance of GS encoding for the various combination of control bit/array sizes and scrambling polynomials.

홀로그래픽 저장장치에 대한 GS 인코딩의 정수계획법 모형 및 휴리스틱

In Guided Scrambling (GS) encoding for the holographic storage, after scrambling augmented source word into codeword, the best codeword satisfying modulation constraint is determined. Modulation constraints considered in this paper are strength which is the minimum number of transition between `0` and `1` in each row and column of codeword array and the symbol balancedness of codeword array. In this paper, we show that GS encoding procedure can be formulated as an integer programming model and develop a fast neighborhood search heuristic for fast computation of control bits. In the simulation, we compared the performance of heuristic algorithm with the integer programming model for various array and control bit size combinations.

A High-Bit-Rate (64/67) DC-Balance Line Code Scheme Based on Guided Scrambling

Guided scrambling is an example of multimode coding technique, which belongs to line code. This technique uses scrambling polynomials to form selection sets, by using proper selection criteria, the codeword with least contribution to DC (direct current) content will be chosen for transmitting. This paper designs this kind of GS (guided scrambling) line code which is suitable to be transmitted in long-distance UTP channel. According to the requirement of the real channel, this technique optimizes the design parameters, such as augmenting bits, scrambling polynomials, bit rate and selection criteria, to achieve the high bit rate of 64/67. The simulation experiment shows that this scheme is efficient in suppression of low frequency, and its PSD characteristics meet the requirement of transmission in long-distance UTP channel.

DC-free multimode code design using novel selection criteria for optical recording systems

DC-free run-length limited codes have been the cornerstone of all three generations of optical recording, CD, DVD and BD. Research into very efficient coding methods is paramount for the upcoming fourth generation. Guided Scrambling (GS) is an efficient coding method that has been reported in the literature. Under GS rules, a user word is translated into a plurality of possible candidate words, and among the candidate words the encoder selects the codeword with the least low-frequency spectral content. In our paper, we will present results of our attempts to improve the performance of GS-based codes. We will present new selection criteria and evaluate their performance and complexity. Specifically, we will evaluate the new selection criteria to the 2/3(1,7) parity preserving code used in Blu-Ray Disc.

Guided Scrambling Polynomials for Periodic Quotient Relationship Patterns

Guided scrambling (GS) is a constrained coding technique that can be used in digital communication systems to control the characteristics of the encoded sequence. In each encoding interval, a GS encoder constructs a quotient selection set with a number of codeword candidates and selects the best candidate to represent the source word. Relationships between candidates in the quotient selection set impact the quality of the transmitted sequence. In particular, in some applications it is desired that the quotient relationship patterns (QRPs) be periodic, and in other applications, periodic QRPs are to be avoided. QRPs are determined by the scrambling polynomial. In this correspondence, we derive the general form for scrambling polynomials that generate all periodic quotient relationship patterns.

DC-free trellis-based error-control codes

Trellis-based error-control (EC) codes, such as convolutional or turbo codes, are integrated with guided scrambling (GS) multimode coding to generate DC-free GS-convolutional/turbo codes. On the basis of the generators of the convolutional/turbo code, we employ puncturing or flipping to ensure that the EC-coded sequences are DC-free. At the receiver, convolutional/turbo decoding is performed before GS decoding to circumvent the performance degradation that can occur when GS decoding is performed prior to EC decoding. Performance of the new DC-free GS-convolutional/turbo codes is evaluated in terms of both spectral suppression and bit error rate (BER). It is shown that the new codes can provide superior BER performance and approximately the same suppression of low frequencies as the conventional concatenation of convolutional/turbo codes and DC-free GS codes.

Low-frequency performance of guided scrambling DC-free codes

We analyze the effect of coding parameters on low-frequency suppression in guided scrambling (GS) dc-free codes based on computer simulation. Simple expressions to accurately estimate the sum variance and low-frequency spectrum-weight of these codes are developed. Systematic design of GS dc-free codes is discussed.

Optimal Number of Control Bits in the Guided Scrambling Method for Holographic Data Storage

One of the major concerns regarding data detection in holographic data storage systems is overcoming interpage interference (IPI). In general, the IPI can be reduced by making the number of 1 (light) and 0 (dark) pixels the same in a recorded page and to have as many transitions as possible produced in each row and column. Such requirements can be satisfied by the guided scrambling (GS) method. In this paper, we investigate the optimum number of control bits to form a page.

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.

垂直磁気記録におけるＧｕｉｄｅｄ Ｓｃｒａｍｂｌｉｎｇ符号化ＰＲＭＬ方式の性能評価

The distortion due to low frequency cutoff degrades the performance of partial response maximum likelihood (PRML) system in a perpendicular magnetic recording. This paper presents an application of guided scrambling (GS) code to PRML system as an effective strategy for avoiding the distortion. The bit error rate performances of PR2ML systems for two types of GS codes, Galois field (GF) additive type and convolutional operation type, are obtained. The results indicate that GS coded PR2ML systems can achieve gains of about 6.3dB for GF additive type code and 4.4dB for convolutional operation type code over conventional Reed-Solomon coded PR2ML system at a normalized linear density of 1.5, a power ratio of jitter-like media noise to total noise of 80% and a low-cutoff frequency normalized by bit rate of 0.002.

Comparison of two guided scrambling schemes for optical disks

A guided scrambling (GS) coding technique is practically used to suppress the DC component within a channel bit stream. It is a candidate for a DC-free code in the next generation of the DVD standard. Typically the GS technique uses a convolutional operation or an addition operation in the Galois field (GF). This paper evaluates the performance of the convolutional GS and GF-addition GS on DC-component suppression, symbol error probability, and hardware complexity, and concludes that the GF-addition GS is more suitable for the next generation of the DVD standard than the convolutional GS with respect to the symbol error probability.

Runlength violation of weakly constrained code

Guided scrambling (GS) is used to control the runlength within codewords as well as to suppress dc components. A weakly constrained code designed by using a GS technique violates the imposed /spl kappa/-constraint with low probability, but achieves a code rate close to the channel capacity. In this study, the probability that codewords violate the k-constraint was measured by using convolutional GS and by using Galois-Field (GF)-addition GS. The occurrence probability of each runlength was also computed and then compared to a 24/25(0,8) block code having a high code rate and to the maxentropic runlength limited (RLL) sequence. The comparison shows that codes designed by these GS techniques attain extremely high code efficiency.

Frame synchronization in guided scrambling line codes

Guided scrambling (GS) ensures the existence of good line code properties in encoded bit sequences through appropriate augmentation of the source bit stream prior to self-synchronizing scrambling. At the receiver, a framing algorithm is required in order to identify the location of the augmenting bits in the unscrambled bit sequence. This paper proposes and analyzes a self-framing algorithm for achieving frame synchronization in GS line codes. This technique is based on the observation of a large number of transitions at codeword boundaries in the encoded sequence, and does not require any additional overhead. Analysis and simulation results confirm the viability of this technique.

Simple updating method for continuous encoding inguidedscrambling line codes

A simple method to perform continuous coding in a guided scrambling (GS) system is presented. This technique reduces the amount of circuitry required to perform the memory updating which is inherent to this operation. A successful implementation has been used in the design of a fully functional GS system.

映像情報ストレージ技術 ガロア体加算に基づいた直流成分抑圧方式とその性能評価

A DC component suppressing method, called Guided Scrambling (GS), has been proposed. GS constructs a selection set of channel bit streams by subjecting a source bit stream within a data block to several kinds of scrambling and to RLL (Run Length Limited) coding. The one which has the least DC component is then selected. Typically, this technique uses a convolutional operation or GF (Galois field) multiplication. The convolutional GS is good at suppressing the DC component, but has poor performance in the symbol error rate because a bit error propagates to an adjacent codeword before RS decoding. In the GF multiplicative GS, the error rate is lower, but performance in DC component suppression is worse, especially when a simple hardware configuration is used or when a source bit stream is not random. In this paper, we propose the GF additive GS method which generates a better channel bit stream with both these characteristics. We also analyze the spectrum and the average symbol error rate of this method with computer simulations, and show its advantages over other GSs.

Characteristics of guided scrambling encoders and their coded sequences

We derive several properties of guided scrambling (GS) encoders and the sequences they generate. We first highlight symmetrical aspects of the GS encoding mechanisms proposed to date, and then show that the existence of discrete components in the power spectrum of the pulse-amplitude-modulated encoded sequence can be predicted from the weight of the scrambling polynomial. We also show that with equiprobable source words, the block or continuous nature of the code has no effect on the statistics of the encoded sequence. We conclude by demonstrating how these properties simplify evaluation of the spectral characteristics of GS coded sequences.

Polynomials for guided scrambling line codes

Guided scrambling (GS) is a line coding technique developed specifically for high bit rate fiber optic transmission systems. This paper continues the development of GS coding by introducing more scrambling polynomials that can be used with this technique. First, a method is presented for constructing polynomials which can be used with balanced encoding. Then it is shown that these polynomials can be used as bases for large families of polynomials, an expansion whose usefulness is demonstrated with the presentation of power spectra for several code configurations. These results indicate that polynomials can be selected from these families to exercise control over average as well as worst-case statistics of the encoded bit stream, a property not available with any other single efficient, balanced line coding technique developed to date. Criteria for polynomial selection are given, and polynomials are recommended for several GS code configurations. >