DC-free Codes Research Articles

On Efficient Concatenation of LDPC Codes With Constrained Codes

In this article, an efficient concatenation of error correction codes with constrained codes is proposed. Generally, constrained codes are designed to match specified channels, whereas error correction coding schemes are designed to correct the channel errors. Both play important roles to ensure the integrity of data in data storage systems. In this study, we first investigate the design of k-constrained codes combined with a low-density parity-check (LDPC) code, and then we extend the idea to the design of dc-free k-constrained LDPC codes. Simulation results show that the proposed designs achieve an improved bit error rate (BER) performance, compared to prior art schemes. In particular, the proposed design for the dc-free k-constrained codes not only fully eliminates the effect of error propagation in a reverse configuration but also achieves significant dc suppression.

Simple evaluation of squared weight

Squared weight is an excellent metric on which to base codeword selection in DC-free multimode coding. It has, however, been considered too complex to implement in practice. In this Letter, the authors present a simple approach to evaluate this metric that enables it to be implemented in high-speed digital logic.

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.

Evaluation of the capacity of constrained codes with multiple constrained signalling dimensions

Constrained sequence codes are widely used to meet constraints imposed by digital communication systems. This study presents methods to evaluate the capacity of constrained codes that have multiple independently or dependently constrained signalling dimensions. The authors outline a straightforward analysis technique when the signalling dimensions are independent, and demonstrate how the capacity can be evaluated, estimated or upper bounded when the signalling dimensions are dependent. Their motivation for this work is capacity analysis of DC-free codes with complex-valued symbols, and they present results for these types of codes throughout the study.

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.

DC-억압 변조를 위한 GS 코딩의 최악 성능 평가 MaxMin 모형

광기록 정보저장장치에서 인코딩된 시퀀스의 DC-억압을 위해 Guided Scrambling 기법이 널리 사용된다. 후보 코드시퀀스 중 최적의 DC-억압 코드를 선택하기 위해 digital sum value (DSV)의 함수로 정의된 기준을 사용한다. 이 중 minimum DSV (MDSV), minimum squared weight (MSW), minimum threshold overrun (MTO) 등이 널리 사용된다. 본 연구에서는 MDSV, MSW, MTO 기준을 채택하는 GS 코딩 알고리즘과 동등한 정수계획법 모형을 제안한다. 개발된 MDSV 정수계획법 모형을 MaxMin 형태의 모형으로 확장하여 스크램블링 다항식과 제어 비트에 따른 MDSV GS 코딩의 최악 성능을 평가할 수 있는 모형을 개발하였다. 모의실험에서는 다수의 스크램블링 다항식 및 제어비트 조합에 대하여 MDSV 최악 성능을 계산하였다. For effective DC-free coding in the optical storage systems, the Guided Scrambling algorithm is widely used. To reduce digital discrepancy of the coded sequence, functions of digital sum value (DSV) are used as criteria to choose the best candidate. Among these criteria, the minimum digital sum value (MDSV), minium squared weight (MSW), and minimum threshold overrun (MTO) are popular methods for effective DC-suppression. In this paper, we formulate integer programming models that are equivalent to MDSV, MSW, and MTO GS coding. Incorporating the MDSV integer programming model in MaxMin setting, we develop an integer programming model that computes the worst case MDSV bound given scrambling polynomial and control bit size. In the simulation, we compared the worst case MDSV bound for different scrambling polynomial and control bit sizes. We find that careful selection of scrambling polynomial and control bit size are important factor to guarantee the worst case MDSV performance.

Variable-Length Constrained Sequence Codes

We outline the construction of simple, high rate constrained sequence codes with variable-length source words and variable-length codewords based on the search of partial extension of a minimal set of codeword lengths. We present optimal word length mappings for a subset of constrained sequence codes, and provide examples of (d, k) and DC-free codes with few codewords and average code rates greater than 99% of capacity.

DC‐free codes with complex‐valued signalling constellations

The use of spectral shaping constrained codes is commonplace in baseband digital communication systems. In this study, the authors consider the use of constrained codes in bandpass systems through the design of DC-free codes for the complex baseband representations of commonly used signalling constellations including quaternary phase shift keying, eight-phase shift keying and sixteen quadrature amplitude modulation. The authors construct DC-free codes for these signalling alphabets and present their spectral performance. They show that, similar to DC-free codes for baseband systems, the variance of the running digital sum remains a good indicator of spectral performance and that Justesen's relationship between the sum variance and cut-off frequency holds.

A new DC-free multimode code design with error correction capability for optical storage systems

DC-free run-length limited codes have been the cornerstone of all three generations of optical recording, CD, DVD and BD. Research into efficient coding methods is paramount for the upcoming fourth generation. A Multimode coding technique is an efficient coding method that has been reported in the literatures. Under multimode coding 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 a new coding technique for constructing error correcting high-rate DC-free multimode code using a low-density parity-check (LDPC) code for future high-density optical recording. The scheme achieves reliable DC-suppression and obtains considerable bit error rate (BER) performance gain through the iterative decoding (or turbo equalization) with the concatenated detector.

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.

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.

DC-Free Coding of Run-Length-Limited Codes for Multi-Level Optical Recording Systems

Optical storage systems require the channel data sequence having DC-free characteristic. DC-free coding schemes for binary sequence are difficult to apply directly for high-rate multi-level optical recording systems. Thus, we present an effective coding scheme that DC-content is sufficiently controlled by inserting redundancy bits less than 1.25% for multi-level optical recording systems. This method is very simple and can be used for all multi-level run-length-limited codes.

DC-Free Error-Control Block Codes

DC-free codes and error-control (EC) codes are widely used in digital transmission and storage systems. To improve system performance in terms of code rate, bit-error rate (BER), and low-frequency suppression, and to provide a flexible tradeoff between these parameters, this paper introduces a new class of codes with both dc-control and EC capability. The new codes integrate dc-free encoding and EC encoding, and are decoded by first applying standard EC decoding techniques prior to dc-free decoding, thereby avoiding the drawbacks that arise when dc-free decoding precedes EC decoding. The dc-free code property is introduced into standard EC codes through multimode coding techniques, at the cost of minor loss in BER performance on the additive white Gaussian noise channel, and some increase in implementation complexity, particularly at the encoder. This paper demonstrates that a wide variety of EC block codes can be integrated into this dc-free coding structure, including binary cyclic codes, binary primitive BCH codes, Reed-Solomon codes, Reed-Muller codes, and some capacity-approaching EC block codes, such as low-density parity-check codes and product codes with iterative decoding. Performance of the new dc-free EC block codes is presented.

An integrated error control and DC-free code based on multimode coding

Optical disk storage systems use both error control (EC) codes and dc-free constrained sequence (CS) codes in order to increase the reliability of the data read from the disk. We present a method of integrating these coding techniques in order to overcome drawbacks with the conventional manner in which these coding procedures are concatenated. Our technique is based on the principle of multimode coding. Each source word (SW) is represented by a set of complementary EC codewords (CWs), and from this set the encoder selects the EC CW that best meets the CS goals of the system. The decoding structure avoids the problem of error propagation during CS decoding by performing error correction before removing the effects of the CS code. Power spectra of encoded sequences generated by a hardware implementation have a null at 0 Hz, confirming that these coded sequences are dc-free. BER simulations demonstrate the superior performance of this combined EC and CS code on a dc-constrained noisy channel.

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.

Modified minimum squared weight selection criterion for DC-free multimode codes

The minimum squared weight (MSW) criterion has been shown to yield excellent performance for DC-free multimode codes in terms of coding efficiency. However, it is demonstrated that the MSW criterion is not sufficient to guarantee the generation of DC-free sequences. To overcome this drawback, a modified MSW criterion is proposed that integrates the MSW criterion with a word-end running digital sum constraint that ensures DC balance.

Advanced DC-free track code pattern using diphase code for perpendicular recording

We describe an advanced dc-free track code pattern that uses diphase code for a perpendicular recording. Track code error rates are compared between diphase code, dummy-bit code, and conventional dibit code. The diphase code improves writing ability during servo track writing and maintains equivalent medium noise. Therefore, the diphase code exhibits a superior track code error rate within a wide range of radius on experimental hard disk drives.

A Performance Metric for Codes With a High-Order Spectral Null at Zero Frequency

Sum-variance is a well-known metric for assessing the performance of dc-free codes (first-order spectral-null codes), however, as we show in this paper, it is unsuitable for comparing the magnitude of spectral components of high-order spectral-null (HOSN) codes at low frequencies. In this paper, we introduce a new performance metric for evaluating the spectrum compression of arbitrarily HOSN codes around zero frequency; we call this metric the low-frequency spectrum weight (LFSW). We show that the asymptotic low-frequency spectral components of Kth-order spectral-null codes (K/spl ges/1) are exclusively determined by the order K and the LFSW, and that the LFSW equals the zero-frequency value in the spectrum of the corresponding sequence of Kth-order running digital sum values. We derive this result for symbol-by-symbol encoding, and then extend it to block HOSN codes. We then derive a closed-form expression for the LFSW of HOSN codes constructed through state-independent encoding. Closed-form expressions for LFSW of first-order zero-disparity codes and for the asymptotic LSFW of maxentropic dc-free sequences are also given.

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.

DC-free binary convolutional coding

A novel DC-free binary convolutional coding scheme is presented. The proposed scheme achieves the DC-free coding and error-correcting capability simultaneously. The scheme has a simple cascaded structure of the running digital sum (RDS) control encoder and the conventional convolutional encoder. A given sequence becomes DC-free if and only if the absolute RDS value of the sequence is bounded by a constant for any time instant. The RDS control encoder generates a sequence which gives the convolutional-coded sequence with a bounded RDS value. The structure allows us to exploit efficient soft-decision decoding which attains additional coding gains compared with hard-decision decoding over an additive white Gaussian noise (AWGN) channel. Bounds on the RDS value are explicitly established for the proposed scheme. By using the bounds, we have performed computer searches for finding good RDS control encoders. The proposed scheme provides wide varieties of reasonable tradeoffs between the coding gain, the RDS constraint, and decoding complexity. For example, a 64-state DC-free coding scheme with the overall rate 6/16 and the minimum free distance 10 has been obtained. This scheme satisfies a bounded RDS constraint (from -18 to +18) and it yields a considerably high asymptotic coding gain (over an AWGN channel) of 5.7 dB.