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Block-decodable runlength-limited codes via look-ahead technique

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Abstract

The terms (d,k)- constrained sequence and runlength-limited (RLL) sequence are usually used as synonyms, and traditionally the design of encoders that generate RLL sequences is almost always conducted by designing encoders that generate (d,k)-constrained sequences followed by a precoder. It is generally believed that this design procedure does not entail a losss of performance in terms of coder complexity and error propagation. In this paper, however, we will show that it is surprisingly profitable in terms of error propagation to design RLL encoders directly, i.e. without the intermediate step of a (d,k)-constrained sequence.
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BLOCK.DECODAßII RIJNLENGTIJ.LIMITED CODES
\1,\ LOOK.AIIEAD TECHNIQUE
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... The corresponding decoder limits error propagation to the same extent as a block decoder: only one block. In this paper, we do not consider a more general notion of block decodability that can sometimes be achieved at the cost of replacing finite-state encoders with look-ahead encoders [7], [6]. ...
... However, if we restrict to constraints that satisfy either the Franaszek condition or the straight-line condition, then we have the following result on block-decodable encoder. Note that this is in contrast to Immink's result [7], [8] in which he shows that the code rate may be improved by designing the code in NRZ domain. This is because he considers a more general type of encoder which involves a nondeterministic input tag assignment and a positive-delay encoding). ...
Article
A constrained system is presented by a finite-state labeled graph. For such systems, we focus on block-type-decodable encoders, comprising three classes known as block, block-decodable, and deterministic encoders. Franaszek (1968) gives a sufficient condition which guarantees the equality of the optimal rates of block-decodable and deterministic encoders for the same block length. We introduce another sufficient condition, called the straight-line condition, which yields the same result. Run-length limited RLL(d,k) and maximum transition run MTR(j,k) constraints are shown to satisfy both conditions. In general, block-type-decodable encoders are constructed by choosing a subset of states of the graph to be used as encoder states. Such a subset is known as a set of principal states. For each type of encoder and each block length, a natural problem is to find a set of principal states which maximizes the code rate. We show how to compute the asymptotically optimal sets of principal states for deterministic encoders and how they are related to the case of large but finite block lengths. We give optimal sets of principal states for MTR(j,k)-block-type-decodable encoders for all codeword lengths. Finally we compare the code rate of nonreturn to zero inverted (NRZI) encoders to that of corresponding nonreturn to zero (NRZ) and signed NRZI encoders.
... A technique called state-combination [35] uses an approximate eigenvector with all components equal to zero, one, or two to construct block-decodable codes that can be encoded by employing one-symbol look-ahead, a special case of bounded-delay encodable codes. State-combination is especially suited to the construction of (d, k) RLL codes. ...
... On the other hand, if this number is relatively large, then such methods are less suitable because of the increasing number of choices for the state-splitting steps. In that case, use a method based on merging bits, or a method for (almost) block-decodable codes such as [35] or [33], or any other more heuristic method that does the job. ...
Chapter
Modulation codes such as runlength-limited codes have been widely employed in magnetic and optical data storage systems. We review the main techniques involved in the design and use of these codes: the maximal code rate or capacity, graphical presentations of constraints, encoders and decoders, and code construction methods such as the ACH state-splitting algorithm. We conclude this survey by discussing some recent developments and research trends.
... One-dimensional (1D) run-length limited (RLL) code was previously proposed for magnetic and optical recording systems [4][5][6] to specify the minimum and maximum run-length of bit 1's that may occur in a recorded data sequence. In practice, the RLL code is normally defined by two parameters that are d and k, where the parameter d is used for controlling the highest transition frequency that means it can avoid the ISI effect, while the parameter k is used to ensure that the transition of the 978-1-7281-6486-1/20/$31.00 ©2020 IEEE recorded bit data has properly appeared, which can help the synchronization process to precisely recover the sampled data sequence [7]. ...
Conference Paper
The severity of inter-symbol interference (ISI) and inter-track interference (ITI) effects caused by the reduction of the spacing between bit islands in the along- and across-track directions to acquire ultra-high areal densities (ADs) is the main problem in bit-patterned magnetic recording (BPMR) systems. We call these two effects as two-dimensional (2D) interference, which can degrade the overall system performance. Practically, a one-dimensional (1D) modulation code, e.g., run-length limited (RLL) code, is essentially utilized to prevent the severe ISI effect. The use of 2D detectors is also one of the important ways to cope with the severe ITI; however, its complexity is quite high. To avoid the severe ITI effect and complex 2D detectors; therefore, we propose to apply the 1D RLL code as the 2D modulation code. Then, the 2D modulation encoding constraint is employed to reduce the number of states and branches in the trellis of the proposed modified 2D Viterbi detector. Simulation results reveal that the proposed detector not only delivers a lower complexity but also provides superior bit error rate gain, especially at ultra-high ADs and/or large location fluctuation.
... Since the asymptotic information rate C d can only be approached from the left side, any RLL code can be measured by the proximity of its rate to the asymptotic information rate. Table 3.2 shows C d as a function of d. [20][21][22][23][24][25] is called the look-ahead encoding technique. A block-code is said to be look-ahead if the encoding is done as a function of not only the present and past inputs, but also of a finite number of inputs yet to come. ...
Article
In the treatment of channel coding as a separate operation independent of the modulation, the coded set of sequences generally has a smaller channel symbol duration than the uncoded set of sequences for the same information rate. Accordingly, the power spectrum density (PSD) of the channel signals changes essentially. On the other hand, if the modulation is designed in conjunction with the channel coding, error correction can be achieved without leading to any essential changes in the PSD. In this thesis, two combined coding and modulation schemes are studied. Narrowband powerline communication (PLC) is considered as a practical application. The thesis can be divided into two parts. In the first part, combined coding and modulation scheme based on the single carrier modulation is proposed. An run-length limited (RLL) encoder is introduced between the channel encoder and the constant envelope modulator to control the minimum channel symbol duration (the minimum duration in which the channel symbol stays constant) of a set of block waveforms defined in a constant time. As a single carrier modulation, noncoherent FSK and PSK are considered. Accordingly, it is shown that high coding gains can be achieved at the same information rate without leading to an essential change in the PSD. The maximum-likelihood (ML) receiver structures are derived and investigated for the additive white Gaussian noise (AWGN) and the impulsive noise channel models. In the second part of the thesis, OFDM modulation is considered. If the discrete Fourier transform (DFT) of the transmitted OFDM symbol contains a small number of zeros or known data, there is a similarity between the inverse DFT (IDFT) and RS encoder. In practice, not all subcarriers are used to carry information. Some subcarriers are set to zero or known data (pilot symbols) for different purposes, that include channel estimation, synchronization or cancelation of the DC value. An iterative impulsive noise suppression algorithm is proposed, which exploits the impulsive noise structure in the time and frequency domain and uses the existing redundancy to decode the errors. The simulation results show that the influence of impulsive noise can be essentially reduced. Bei der klassischen Kanalcodierung wird die Datenrate durch Einfügen von Redundanzen bewusst erhöht, um dadurch eine Absicherung gegen auftretende Fehler zu erreichen. Die Erhöhung der Datenrate erfordert eine wesentliche Änderung im Power-Spektrum. Aber bei vielen Anwendungen ist eine möglichst effiziente Nutzung des Power-Spektrums gefordert. In dieser Arbeit werden Codierung und Modulation gemeinsam betrachtet, so dass die Verbesserung der Übertragungsqualität keine wesentliche Änderung in dem Power-Spektrum erfordert. Das Power-Spektrum wird durch Power-Spektrum-Dichte analysiert. Als praktische Anwendung der Arbeit wird die Schmalband-Powerline-Kommunikation (Narrowband Power Line Communication) betrachtet. Powerline ist der Begriff für die Übertragung von Daten über Stromkabel. Im Gegensatz zu konventionellen Kommunikationskanälen kann die Störung auf Stromnetze nicht als additives weißes Gaußsches Rauschen (AWGN) modelliert werden. Das ist darauf zurückzuführen, dass neben Hintergrundrauschen auch Schmalbandstörungen und insbesondere Impulsstörungen vorkommen. Beim Auftreten eines Impulses sind Bit- oder Burstfehler bei einer Datenübertragung sehr wahrscheinlich. Im ersten Teil werden Einzelträgerverfahren betrachtet. Ein sogenannter RLL- (Run-length Limited) Code wird verwendet, um die Anzahl aufeinanderfolgender Symbole mit gleichem Wert nach unten zu begrenzen. Dementsprechend wird gezeigt, dass im gemeinsamen blockweisen RLL Encoder/Modulator der minimale euklidische Abstand erhöht werden kann, ohne wesentliche Änderung in der Power-Spektrum-Dichte. Im Empfänger erfolgen Demodulation und Decodierung nicht getrennt, sondern in einem Schritt, wobei alle Vorteile der Maximum-Likelihood-Decodierung mit Verwendung von Soft-Decision erhalten bleiben. Ein wesentlich größerer Codierungsgewinn ergibt sich bei der Verkettung mit einem RS- (Reed-Solomon) Code. Zunächst werden die Auswirkungen von Impulsstörungen auf RLL-codierte Einzelträgerverfahren erläutert. Die Modellierung von Impulsstörungen als nicht-Gauß'sche Verteilungen wurde in der Literatur durch verschiedene Ansätze vorgestellt. In der Arbeit wird das Klasse-A Modell von Middleton angewendet. Im zweiten Teil der Arbeit wird OFDM- (Orthogonal Frequency Division Multiplexing) Verfahren betrachtet. Insbesondere durch die Impulsstörungen werden in der Datenübertragung erhebliche Störeffekte hervorgerufen. In OFDM werden die Modulation bzw. Demodulation mit Hilfe einer IDFT bzw. DFT (Inverse Discrete Fourier Transform, Discrete Fourier Transform) ausgeführt. Die bisherigen Überlegungen zur Kompensation von Impulsstörungen behandeln nur das OFDM-Verfahren mit einer großen Anzahl von Unterträgern (>256). In diesem Fall wird die Energie des Störimpulses durch die DFT auf viele Unterträger verteilt. Wenn die Anzahl der Unterträger kleiner als 256 ist, ist die Verteilung der Störung nicht uniform. Wenn die DFT der gesendeten OFDM-Symbol eine kleine Anzahl von Nullen oder bekannten Daten enthält, gibt es eine Ähnlichkeit zwischen der IDFT und RS-Encoder. Die OFDM-Signale beinhalten häufig Pilotinformationen und zu Null gesetzte Träger in der Signalstruktur. Es werden Verfahren zur Kompensation von Impulsstörungen durch Pilotinformationen und zu Null gesetzte Träger untersucht bzw. entwickelt, die eine Steigerung der Robustheit der Datenübertragung ermöglichen. Als Zielkriterium wird dabei die Senkung der Bitfehlerrate bei einer impulsgestörten Übertragung herangezogen. Für die Modellierung von Impulsstörungen wird das vereinfachte "Klasse-A"\, Modell von Middleton verwendet.
Article
Full-text available
We introduce and investigate the class of bounded-delay-encodable block-decodable (BDB) codes. Several characterizations for this class of codes are given, and some construction methods, especially for one-symbol look-ahead BDB codes, are described. In another direction, we use our results to show the existence of a decision procedure for some basic coding problems. Zndex Terms-RLL code, BDB code, block-decodable code, principal state-set, look-ahead coding.
Conference Paper
This paper addresses low frequency range power-line communications (PLC), where the transmitters are output voltage and bandwidth limited. We propose an efficient transmission method of combining Reed Solomon (RS) coding with run length limited (RLL) codes. Our proposed transmission model consists of three main parts: RS encoder followed by a one or two bit(s) look-ahead RLL encoder and 2-FSK modulator. The resulting transmission has a constant envelope signal modulation, no bandwidth expansion and more concentrated spectra in the carrier frequencies. This is an important result, directly applicable to the CENELEC band. In addition, a soft decoder based on minimum distance criteria for the RLL codes is introduced to yield an additional coding gain. We present the spectral analysis of RLL coding. Finally, the performance of the detectors is analyzed theoretically as well as through simulations.
Conference Paper
The terms (d,k)-constrained sequence and runlength-limited (RLL) sequence are usually used as synonyms, and traditionally the design of encoders that generate RLL sequences is almost always conducted by designing encoders that generate (d,k)-constrained sequences followed by a precoder. It is generally believed that this design procedure does not entail a loss of performance in terms of coder complexity and error propagation. In this paper, however, we will show that it is surprisingly profitable in terms of error propagation to design RLL encoders directly, i.e. without the intermediate step of a (d,k)-constrained sequence.
Article
In most recording channels, modulation codes are employed to transform user data to sequences that satisfy some desirable constraint. Run-length-limited (RLL(d,k)) and maximum transition run (MTR(j,k)) systems are examples of constraints that improve timing and detection performance. A modulation encoder typically takes the form of a finite-state machine. Alternatively, a look-ahead encoder can be used instead of a finite-state encoder to reduce complexity. Its encoding process involves a delay called look-ahead. If the input labeling of a look-ahead encoder allows block decodability, the encoder is called a bounded-delay-encodable block-decodable (BDB) encoder. These classes of encoders can be viewed as generalizations of the well-known deterministic and block-decodable encoders. Other related classes are finite-anticipation and sliding-block decodable encoders. In this paper, we clarify the relationship among these encoders. We also discuss the characterization of look-ahead and BDB encoders using the concept of path-classes. To minimize encoder complexity, look-ahead is desired to be small. We show that for nonreturn to zero inverted (NRZI) versions of RLL|,(0,k),RLL(1,k), and RLL(d,infin), a BDB encoder does not yield a higher rate than an optimal block-decodable encoder. However, for RLL(d,k) such that dges4 and d+2lesk<infin, we present a BDB encoder with look-ahead one that has a higher rate than any block-decodable encoder. For MTR, we prove that no BDB encoder is asymptotically better than an optimal BDB encoder with look-ahead one
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An input-constrained channel, or simply a constraint, is a set S of words that is generated by a finite labeled directed graph. An encoder for S maps, in a lossless manner, sequences of unconstrained input blocks into sequences of channel blocks, the latter sequences being words of S. In most applications, the encoders are finite-state machines and, thus, presented by state diagrams. In the special case where the state diagram of the encoder is (output) deterministic, only the current encoder state and the current channel block are needed for the decoding of the current input block. In this work, the problem of designing coding schemes that can serve two constraints simultaneously is considered. Specifically, given two constraints S<sub>1</sub> and S <sub>2</sub> such that S<sub>1</sub>⊆S<sub>2</sub> and two described rates, conditions are provided for the existence of respective deterministic finite-state encoders &epsi;<sub>1</sub> and &epsi;<sub>2 </sub>, at the given rates, such that (the state diagram of) &epsi;<sub>1</sub> is a subgraph of &epsi;<sub>2</sub> Such encoders are referred to as nested encoders. The provided conditions are also constructive in that they imply an algorithm for finding such encoders when they exist. The nesting structure allows to decode &epsi;<sub>1 </sub> while using the decoder of &epsi;<sub>2</sub>. Developments in optical recording suggest a potential application that can take a significant advantage of nested encoders
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