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In digital transmission it is sometimes desirable for the channel stream to have low power near zero frequency. Suppression of the low-frequency components is achieved by constraining the unbalance of the transmitted positive and negative pulses. Rate and spectral properties of unbalance constrained codes with binary symbols based on simple bi-mode coding schemes are calculated.

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All content in this area was uploaded by Kees Schouhamer Immink on Apr 15, 2019

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... In many applications (e.g. ac-coupled channels) it is an important requirement that the code spectrum should be poor around the zero frequency [2], [27], [28]. With the application of a low-pass loop filter we can satisfy this requirement. ...

... Earlier we have showed that the rate of a bit stuff encoder is given as 1 − P stuff , so according to (27), the coder's rate is ...

By generalizing the accumulated charge concept, we introduce a new class of constraints, the generalized charge constraint to control the spectral properties of a binary sequence. The new constraint limits the level at the output of a digital filter, diminishing those spectral components of the channel sequence being enhanced by the filter. A suitable coder structure, a feedback controlled bit stuff encoder is suggested to implement the new constraint. We demonstrate the spectral shaping property of the new coder structure and derive an approximate formula for the spectrum of the output binary signal. We also show that the coder performs a sigma-delta-like operation and the method is capable of implementing spectral and run-length constraints simultaneously. As a demonstration, we present a few particular spectral characteristics shaped by different examples of loop filters.
Full text available: http://regi.hte.hu/HXT4805DG225R7EC7896G9ED545133D0S/InfocomJ2012_I_komplett.pdf

... Two large important classes of channel constraints are run-length and spectral constraints. The run-length constraints [24], [30] bound the minimal or maximal lengths of certain types of channel subsequences, whereas the spectral constraints include dc-free [21] and higher order spectral-null constraints [22], [23], [31]. The spectral constraints also include codes that produce spectral zero at rational submultiples of symbol frequency [29] as well as constraints that give rise to spectral lines [16]. ...

... This number is , where is the number of states of the multimode finite automaton and is the trellis size. Instead, we use the RDS-N variance argument (Appendix B, [12], [21], and [22]). This enables us to judge the spectral performance of the code by using the size of its RDS-N range. ...

Constrained coding is used in recording systems to translate an
arbitrary sequence of input data to a channel sequence with special
properties required by the physics of the medium. Very often, more than
one constraint is imposed on a recorded sequence; typically, a
run-length constraint is combined with a spectral-null constraint. We
introduce a low-complexity encoder structure for composite constraints,
based on loose multimode codes. The first channel constraint is imposed
strictly, and the second constraint is imposed in a probabilistic
fashion. Relaxing the second constraint is beneficial because it enables
higher code rates and simplifies the encoder. To control the second
constraint a multimode encoder is used. We represent a set of multimode
coded sequences by a weighted trellis and propose using a limited
trellis search to select optimal output. Using this method, we modify
the EFM+ code used in digital versatile disk (DVD). We combine EFM+'s
run-length constraint with the first- and second-order spectral-null
constraints. The resulting EFM++ code gives more than 10-dB improvement
in suppression of low-frequency spectral content in the servo bandwidth
over the original EFM+ code with the same complexity

... For conventional dc-balanced codes we may numerically solve (38) using (35). Using a Taylor series approximation of (35), we obtain the useful approximation [20] f c ≈ a dc n , n 1, where ...

We investigate a new approach for designing spectral shaping block codes with a target spectrum, H_t(f), that has been specified at a plurality of frequencies. We analyze the probability density function of the spectral power density function of uncoded n-symbol bipolar code words. We present estimates of the redundancy and the spectrum of spectral shaping codes with specified target spectral densities H_t(f_i) at frequencies f_i. Constructions of low-redundancy codes with suppressed low-frequency content are presented that compare favorably with conventional dc-balanced codes currently used in data transmission and data storage devices with applications in consumer electronics.

... Let denote RDS Justesen [116] discovered a useful relation between the sum variance and the width of the spectral notch He found the following approximation of the cutoff frequency : (29) Extensive computations of samples of implemented channel codes, made by Justesen [116] and Immink [98] to validate the reciprocal relation (29) between and , have revealed that this relationship is fairly reliable. The sum variance of a maxentropic RDS-constrained sequence, denoted by , is given by [38] (30) Table XVII lists the sum variance for Fig. 26, which shows a plot of the sum variance versus the redundancy , affords more insight into the tradeoffs in the engineering of DC-balanced sequences. ...

Constrained codes are a key component in digital recording devices
that have become ubiquitous in computer data storage and electronic
entertainment applications. This paper surveys the theory and practice
of constrained coding, tracing the evolution of the subject from its
origins in Shannon's classic 1948 paper to present-day applications in
high-density digital recorders. Open problems and future research
directions are also addressed

The signal-to-noise ratio of pilot tracking tones embedded in binary coded formats has been assessed. It has been found that the signal-to-noise ratio can be improved when the redundancy of the code is increased. Since the signal-to-noise ratio of the pilot tracking tone limits the maximum attainable bandwidth of the servo system, a compromise has to be found between the redundancy of the code and the performance of the servo system. The signal-to-noise ratio of pilot tones based on the polarity switch technique, which is attractive as no lookup tables are required for encoding and decoding, is substantially smaller than that of codes based on the fixed disparity format.

The servo position information of magnetic tape or disk recorders
is often recorded as low-frequency components usually called pilot
tracking tones. Binary codes giving rise to a spectral null at an
arbitrary frequency are used to provide space for the allocation of
auxiliary pilot tones. Here, encoding methods are treated in which
binary data are mapped into constrained binary sequences for shaping the
spectrum. The rate and power spectral density function of memoryless
codes that exhibit spectral nulls are computed. The relationship between
the code redundancy and spectral notch width is quantified with a
parameter called the sum variance. It is found that twice the product of
the spectral notch width times the sum variance is approximately unity

A limit on the absolute value of the running digital sum of a
sequence is known as the charge constraint. Such a limit imposes a
spectral null at DC. The maximum-entropy distribution of a
charge-constrained sequence is presented. A closed-form expression for
the power spectral density of maximum-entropy charge-constrained
sequences is given and plotted

Spectrum shaping codes introduce redundancy and correlation into a
transmitted data stream in order to alter the transmitted spectrum
without affecting the pulse shape or peak-to-average power ratio. Most
are based on algebraic properties, or on a running digital sum. A new
and very general approach to spectral shaping, in which the Viterbi
algorithm is used at the transmitter to minimize the transmitted power
in specified bands, is introduced. The principal advantage is greatly
increased flexibility of width, depth, and placement of spectral
notches. The computational load at the transmitter is greater than that
of earlier algorithms, although the receiver is unaffected

Calderbank, Heegard, and Ozarow [1] have suggested a method of designing codes for channels with intersymbol interference, such as the magnetic recording channel. These codes are designed to exploit intersymbol interference. The standard method is to minimize intersymbol interference by constraining the input to the channel using run-length limited sequences. Calderbank, Heegard, and Ozarow considered an idealized model of an intersymbol interference channel that leads to the problem of designing codes for a partial response channel with transfer function (1 - D^{N}) /2 , where the channel inputs are constrained to be pm 1 . This problem is considered here. Channel inputs are generated using a nontrivial coset of a binary convolutional code. The coset is chosen to limit the zero-run length of the output of the channel and so maintain clock synchronization. The minimum squared Euclidean distance between outputs corresponding to distinct inputs is bounded below by the free distance of a second convolutional code which we call the magnitude code. An interesting feature of the analysis is that magnitude codes that are catastrophic may perform better than those that are noncatastrophic.

A new approach for encoding any string of information bits into a
sequence having bounded running digital sum is presented. The results
improve previously known values of the running digital sum for the same
rate. Also discussed are ways of incorporating an error-correcting
capability into these codes. Some general constructions are given and
tables are constructed for specific cases

The paper deals with the statistical analysis of the several kinds of signals encountered in digital transmission systems in which the data are coded by a line coder before being transmitted. In the preliminary sections, models of signals and systems are formulated. In particular, a general model is presented in which a line coder is split into three parts : a serial-to-parallel conversion, a finite-state sequential machine, and a parallel-to-serial conversion, where the fundamental coding function is described by a finite-state machine operating on blocks of source-symbols to produce blocks of code-symbols. On the basis of this model, the complete statistics of the coded sequence are evaluated in terms of the source probabilities. In the final part, consideration is given to spectral analysis, where both the continuous and the discrete part (spectral lines) of the spectral densities are calculated in closed form. The results obtained have a general validity and can be used for any line coding scheme, provided that the finite-state sequential machine modelling the coder has been specified. This is illustrated, throughout the paper, by four conveniently chosen examples of line coders.

General aspects of coding for optical fibre digital transmission systems are considered in this paper. Simplified mathematical models are developed which reveal the relationship between binary, multilevel and duobinary codes in terms of optical penalty. Various properties of binary block codes are discussed, in particular, how the properties relate to code efficiency.

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.

A survey is presented of the line codes most widely exploited of paired and coaxial cables. The reasons why these codes have been adopted in commercial systems are presented with reference to historical and practical factors. Specific systems are discussed to illustrate these considerations.

A practical method is described for encoding an unrestricted binary signal into a form suitable for transmission through a binary regenerated signal path while incurring only a small increase in modulation rate.

- M Davidson
- S F Haase
- J L Machamer
- L H Wallman

M. Davidson, S. F. Haase, J. L. Machamer and L. H. Wallman, IEEE Trans. Magn.
MAG-12, 584 (1976).