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... Denote by ϑ 1 and ϑ 2 the lower and the upper bounds of this constrained range. The range of RDS bounded by ϑ 1 and ϑ 2 is said to be the digital sum variation (DSV), see [22], [23]. After the authors [23], DSV constrained RLL sequences are called DCRLL sequences. ...

Constant-weight and constant-charge binary sequences with constrained run
length of zeros are introduced. For these sequences, the weight and the charge
distribution are found. Then, recurrent and direct formulas for calculating the
number of these sequences are obtained. With considering these numbers of
constant-weight and constant-charge RLL sequences as coefficients of convergent
power series, generating functions are derived. The fact, that generating
function for enumerating constant-charge RLL sequences does not have a closed
form, is proved. Implementation of encoding and decoding procedures using
Cover's enumerative scheme is shown. On the base of obtained results, some
examples, such as enumeration of running-digital-sum (RDS) constrained RLL
sequences or peak-shifts control capability are also provided.

A new class of DC-free codes of odd length is presented. The new codes, related to polarity-switch (PS) codes, make use of a redefinition of the running digital sum. The spectral efficiency of the new codes is determined, and it is shown that they provide better power suppression in the low-frequency region than classical PS codes

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

This paper analyzes a block-coding scheme designed to suppress spectral energy near f = 0 for any binary message sequence. In this scheme, the polarity of each block is either maintained or reversed, depending on which decision drives the accumulated digit sum toward zero. The polarity of the block's last digit informs the decoder as to which decision was made.
Our objective is to derive the average power spectrum of the coded signal when the message is a random sequence of +1's and −1's and the block length (M) is odd. The derivation uses a mixture of theoretical analysis and computer simulation. The theoretical analysis leads to a spectrum description in terms of a set of correlation coefficients, {ρq}, q = 1, 2, etc., with the ρq's functions of M. The computer simulation uses FFT algorithms to estimate the power spectrum and autocorrelation function of the block-coded signal. From these results, {ρq} is estimated for various M. A mathematical approximation to ρg in terms of q and M is then found which permits a closed-form evaluation of the power spectrum. Comparisons between the final formula and simulation results indicate an accuracy of ±5 percent (±0.2 dB) or better.
The block-coding scheme treated here is of particular interest because of its practical simplicity and relative efficiency. The methods used to analyze it can be applied to other block-coding schemes as well, some of which are discussed here for purposes of comparison.

A systematic approach to the analysis and construction of channel codes for digital baseband transmission is presented. The structure of the codes is dominated by the set of requirements imposed by channel characteristics and system operation. These requirements may be translated into symbol sequence properties which, in turn, specify a set of permissible sequence states. State-dependent coding of both fixed and variable length is a direct result. Properties of such codes are discussed and two examples are presented.

Modulation constraints of practically any degree of complexity can be described by a state transition table with a finite number (Omega) of states. Examples include all (d,k;c) codes (where (Omega)

The role of line coding is to convert source data to a digital form resistant to noise in combination with such other impairments as a specific medium may suffer (notably intersymbol interference, digit timing jitter and carrier phase error), while being reasonably economical in the use of bandwidth. This paper discusses the nature and role of various constraints on code words and word sequences, including those commonly used on metallic lines, optical fibres, carrier channels and radio links ; and gives some examples from each of these applications. It should serve both as a general review of the subject and as an introduction to the companion papers on specific topics.

Techniques of symbolic dynamics are applied to prove the existence of codes suitable for certain input-restricted channels. This generalizes the earlier work of Adler, Coppersmith, and Hassner on the same problem.

This paper extends the result of earlier work on the application of arithmetic codes to the constrained channel problem. We specifically present a general length-based fixed rate implementation technique which performs the arithmetic coding recursions during each channel time unit. This technique is superior to an earlier unpublished code for general constrained channels. The approach permits the design of codes for sophisticated channel constraints.

Arithmetic codes have been studied in the context of compression coding, i.e., transformations to code strings which take up less storage space or require less transmission time over a communications link. Another application of coding theory is that of noiseless channel coding, where constraints on strings in the channel symbol alphabet prevent an obvious mapping of data strings to channel strings. An interesting duality exists between compression coding and channel coding. The source alphabet and code alphabet of a compression system correspond, respectively, to the channel alphabet and data alphabet of a constrained channel system. The decodability criterion of compression codes corresponds to the representability criterion of constrained channel codes, the generalized Kraft Inequality has a dual inequality due to the senior author.

The authors provide a self-contained exposition of modulation code
design methods based upon the state splitting algorithm. They review the
necessary background on finite state transition diagrams, constrained
systems, and Shannon (1948) capacity. The state splitting algorithm for
constructing finite state encoders is presented and summarized in a
step-by-step fashion. These encoders automatically have state-dependent
decoders. It is shown that for the class of finite-type constrained
systems, the encoders constructed can be made to have sliding-block
decoders. The authors consider practical techniques for reducing the
number of encoder states as well as the size of the sliding-block
decoder window. They discuss the class of almost-finite-type systems and
state the general results which yield noncatastrophic encoders. The
techniques are applied to the design of several codes of interest in
digital data recording

Constructions are presented of finite-state encoders for certain
(d,k) runlength-limited (RLL) constraints with direct current control.
In particular, an example is provided for a rate 8:16 encoder for the
(2,10)-RLL constraint that requires no look-ahead in decoding, thus,
performing favorably compared to the EFMPlus code used in the DVD
standard

A class of binary runlength codes, also known as (d,k) codes, is analyzed. These codes are developed by constructing a lossless source code that maps runlengths into unconstrained binary sequences. The source code is constructed for the maxentropic distribution on runlengths. The inverse of the source code, which outputs runlengths guided toward the ideal maxentropic distribution, is the (d,k) code. Four types of source codes are investigated for this purpose: Huffman, enumerative, variable-length-to-block, and Elias or arithmetic. The rates of the codes are each proven to converge to the capacity with increasing complexity. The codes are not state dependent and are variable rate except for the fixed-rate enumerative code. A combined source-(d,k) code is presented that is based on the arithmetic code.

A practical method for approaching the channel capacity of constrained channels

, "A practical method for approaching the channel capacity of constrained channels," IEEE Trans. Inform. Theory, vol. 43, pp. 1389-1399,
1997.