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The authors describe a new technique for constructing fixed-length (d, k) runlength-limited block codes. The new codes are very close to block-decodable codes, as decoding of the retrieved sequence can be accomplished by observing (part of) the received codeword plus a very small part of the previous codeword. The basic idea of the new construction is to uniquely represent each source word by a (d, k) sequence with specific predefined properties, and to construct a bridge of β, 1&les;β<d, merging bits between every pair of adjacent words. The new constructions have the virtue that only one look-up table is required for encoding and decoding

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... , x q ) and y = (y 1 , . . . , y q ) without the constraint violation we employ a trick from [1]. Note that x q is always 0. The 2-constraint can then be violated if and only if x q−1 = y 1 = 1. ...
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A coding scheme for reliable informa- tion transmission via a runlength-limited channel is often implemented as a concate- nation of an inner modulation code with an outer error-correcting code. The outer decoder has to deal with errors introduced not only by the channel but also by the inner decoder itself. We present a new almost block-decodable rate 1/2 (2,1)- constrained code that avoids error ampli- fication and has very simple encoding and decoding procedures. We then estimate the redundancy of the error-correcting code re- quired to achieve reliable transmission over the channel with random bit shifts and flips.
... , x n ) and y = (y 1 , . . . , y n ) without a constraint violation, a trick from [25] may be employed. Note that x n is always 0. The two constraints can then be violated if and only if x n−1 = y 1 = 1. ...
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This paper considers the application of constrained coding to 40-Gb/s dispersion-managed single-channel optical communication systems limited by intrachannel four-wave mixing (IFWM). It is shown that when transmitted sequences obey the so-called (2, infin) constraint, runlength-limited codes can be designed to not only suppress ghost pulse formation but also improve the data rate by as much as 50% without increasing the transmission bandwidth. Since IFWM is a highly pattern-dependent effect, coding schemes with certain characteristics are preferable. Two different codes with simple encoding and decoding algorithms are constructed, and their performance is analyzed and compared to that of a realistic benchmark system. One of the codes turns out to be consistently better than the other due to its superior statistical properties. The qualitative conclusions are confirmed by numerical simulations. An extension of the method to multichannel links is also considered, and similar gain in data rate is demonstrated
... , x n ) and y = (y 1 , . . . , y n ) without a constraint violation, we employ a trick from [8]. Note that x n is always 0. The 2-constraint can then be violated if and only if x n−1 = y 1 = 1. ...
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Constrained coding as a method to increase the data rate in dispersion-managed soliton (DMS) communication systems is proposed. This approach is well known and widely used in the context of magnetic and optical recording systems. This paper shows that it is also applicable to DMS systems due to certain similarities between the underlying physical channels. Since timing jitter is an important error-generating mechanism for solitons, a coding scheme specifically designed to combat pulse shifts is also presented, and its properties in the framework of a particular information-theoretic channel model are analyzed. A connection between the model used and the real physical channel is then established. Next, the coded system is compared with the original one from the channel capacity point of view with the help of numerical examples. Finally, the fact that the application of constrained coding may alleviate soliton pulse-to-pulse interaction is exploited. This, in turn, opens the door to the usage of higher-than-usual map strengths and ultimately leads to a significant increase of up to 50% in the bit rate.
Book
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Preface to the Second Edition About five years after the publication of the first edition, it was felt that an update of this text would be inescapable as so many relevant publications, including patents and survey papers, have been published. The author's principal aim in writing the second edition is to add the newly published coding methods, and discuss them in the context of the prior art. As a result about 150 new references, including many patents and patent applications, most of them younger than five years old, have been added to the former list of references. Fortunately, the US Patent Office now follows the European Patent Office in publishing a patent application after eighteen months of its first application, and this policy clearly adds to the rapid access to this important part of the technical literature. I am grateful to many readers who have helped me to correct (clerical) errors in the first edition and also to those who brought new and exciting material to my attention. I have tried to correct every error that I found or was brought to my attention by attentive readers, and seriously tried to avoid introducing new errors in the Second Edition. China is becoming a major player in the art of constructing, designing, and basic research of electronic storage systems. A Chinese translation of the first edition has been published early 2004. The author is indebted to prof. Xu, Tsinghua University, Beijing, for taking the initiative for this Chinese version, and also to Mr. Zhijun Lei, Tsinghua University, for undertaking the arduous task of translating this book from English to Chinese. Clearly, this translation makes it possible that a billion more people will now have access to it. Kees A. Schouhamer Immink Rotterdam, November 2004
Book
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Since the early 1980s we have witnessed the digital audio and video revolution: the Compact Disc (CD) has become a commodity audio system. CD-ROM and DVD-ROM have become the de facto standard for the storage of large computer programs and files. Growing fast in popularity are the digital audio and video recording systems called DVD and BluRay Disc. The above mass storage products, which form the backbone of modern electronic entertainment industry, would have been impossible without the usage of advanced coding systems. Pulse Code Modulation (PCM) is a process in which an analogue, audio or video, signal is encoded into a digital bit stream. The analogue signal is sampled, quantized and finally encoded into a bit stream. The origins of digital audio can be traced as far back as 1937, when Alec H. Reeves, a British scientist, invented pulse code modulation \cite{Ree}. The advantages of digital audio and video recording have been known and appreciated for a long time. The principal advantage that digital implementation confers over analog systems is that in a well-engineered digital recording system the sole significant degradation takes place at the initial digitization, and the quality lasts until the point of ultimate failure. In an analog system, quality is diminished at each stage of signal processing and the number of recording generations is limited. The quality of analog recordings, like the proverbial 'old soldier', just fades away. The advent of ever-cheaper and faster digital circuitry has made feasible the creation of high-end digital video and audio recorders, an impracticable possibility using previous generations of conventional analog hardware. The general subject of coding for digital recorders is very broad, with its roots deep set in history. In digital recording (and transmission) systems, channel encoding is employed to improve the efficiency and reliability of the channel. Channel coding is commonly accomplished in two successive steps: (a) error-correction code followed by (b) recording (or modulation) code. Error-correction control is realized by adding extra symbols to the conveyed message. These extra symbols make it possible for the receiver to correct errors that may occur in the received message. In the second coding step, the input data are translated into a sequence with special properties that comply with the given "physical nature" of the recorder. Of course, it is very difficult to define precisely the area of recording codes and it is even more difficult to be in any sense comprehensive. The special attributes that the recorded sequences should have to render it compatible with the physical characteristics of the available transmission channel are called channel constraints. For instance, in optical recording a '1' is recorded as pit and a '0' is recorded as land. For physical reasons, the pits or lands should neither be too long or too short. Thus, one records only those messages that satisfy a run-length-limited constraint. This requires the construction of a code which translates arbitrary source data into sequences that obey the given constraints. Many commercial recorder products, such as Compact Disc and DVD, use an RLL code. The main part of this book is concerned with the theoretical and practical aspects of coding techniques intended to improve the reliability and efficiency of mass recording systems as a whole. The successful operation of any recording code is crucially dependent upon specific properties of the various subsystems of the recorder. There are no techniques, other than experimental ones, available to assess the suitability of a specific coding technique. It is therefore not possible to provide a cookbook approach for the selection of the 'best' recording code. In this book, theory has been blended with practice to show how theoretical principles are applied to design encoders and decoders. The practitioner's view will predominate: we shall not be content with proving that a particular code exists and ignore the practical detail that the decoder complexity is only a billion times more complex than the largest existing computer. The ultimate goal of all work, application, is never once lost from sight. Much effort has been gone into the presentation of advanced topics such as in-depth treatments of code design techniques, hardware consequences, and applications. The list of references (including many US Patents) has been made as complete as possible and suggestions for 'further reading' have been included for those who wish to pursue specific topics in more detail. The decision to update Coding Techniques for Digital Recorders, published by Prentice-Hall (UK) in 1991, was made in Singapore during my stay in the winter of 1998. The principal reason for this decision was that during the last ten years or so, we have witnessed a success story of coding for constrained channels. The topic of this book, once the province of industrial research, has become an active research field in academia as well. During the IEEE International Symposia on Information Theory (ISIT and the IEEE International Conference on Communications (ICC), for example, there are now usually three sessions entirely devoted to aspects of constrained coding. As a result, very exciting new material, in the form of (conference) articles and theses, has become available, and an update became a necessity. The author is indebted to the Institute for Experimental Mathematics, University of Duisburg-Essen, Germany, the Data Storage Institute (DSI) and National University of Singapore (NUS), both in Singapore, and Princeton University, US, for the opportunity offered to write this book. Among the many people who helped me with this project, I like to thank Dr. Ludo Tolhuizen, Philips Research Eindhoven, for reading and providing useful comments and additions to the manuscript. Preface to the Second Edition About five years after the publication of the first edition, it was felt that an update of this text would be inescapable as so many relevant publications, including patents and survey papers, have been published. The author's principal aim in writing the second edition is to add the newly published coding methods, and discuss them in the context of the prior art. As a result about 150 new references, including many patents and patent applications, most of them younger than five years old, have been added to the former list of references. Fortunately, the US Patent Office now follows the European Patent Office in publishing a patent application after eighteen months of its first application, and this policy clearly adds to the rapid access to this important part of the technical literature. I am grateful to many readers who have helped me to correct (clerical) errors in the first edition and also to those who brought new and exciting material to my attention. I have tried to correct every error that I found or was brought to my attention by attentive readers, and seriously tried to avoid introducing new errors in the Second Edition. China is becoming a major player in the art of constructing, designing, and basic research of electronic storage systems. A Chinese translation of the first edition has been published early 2004. The author is indebted to prof. Xu, Tsinghua University, Beijing, for taking the initiative for this Chinese version, and also to Mr. Zhijun Lei, Tsinghua University, for undertaking the arduous task of translating this book from English to Chinese. Clearly, this translation makes it possible that a billion more people will now have access to it. Kees A. Schouhamer Immink, Rotterdam, November 2004
Article
Full-text available
Many modulation systems used in magnetic and optical recording are based on binary run-length-limited codes. We generalize the concept of dk -limited sequences of length n introduced by Tang and Bald by imposing constraints on the maximum number of consecutive zeros at the beginning and the end of the sequences. It is shown that the encoding and decoding procedures are similar to those of Tang and Bald. The additional constraints allow a more efficient merging of the sequences. We demonstrate two constructions of run-length-limited codes with merging rules of increasing complexity and efficiency and compare them to Tang and Bahl's method.
Article
Full-text available
In magnetic or optical storage devices, it is often required to map the data into runlength-limited sequences. To ensure that cascading such sequences does not violate the runlength constraints, a number of merging bits are inserted between two successive sequences. A theory is developed in which the minimum number of merging bits is determined, and the efficiency of a runlength-limited fixed-length coding scheme is considered
Article
A special case with binary sequences was presented at the IEEE 1969 International Symposium on Information Theory in a paper titled “Run-Length-Limited Codes.
Article
The paper describes a technique for constructing fixed-length block codes for (d, k)-constrained channels. The codes described are of the simplest variety-codes for which the encoder restricted to any particular channel state is a one-to-one mapping and which is not permitted to “look ahead” to future messages. Such codes can be decoded with no memory and no anticipation and are thus an example of what Schouhamer Immink (1992) has referred to as block-decodable. For a given blocklength n and given values of (d, k), the procedure constructs a code with the highest possible rate among all such block codes, and it does so without the iterative search that is typically used (i.e., Franaszek's recursive elimination algorithm). The technique used is similar to Beenker and Immink's (1983) “Construction 2” in that every message is associated with a (d, k, l, r) sequence of length n-d; however the values used in the present approach are l=k-d and r=k-1, as opposed to Beenker and Schouhamer Immink's values of l=r=k-d. Thus the present approach demonstrates that “Construction 2” is optimal for d=1 but is suboptimal for d>1. Furthermore, the structure of the present codes permits enumerative coding techniques to simplify encoding and decoding