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Performance of simple binary DC-constrained codes

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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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... 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 ...
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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. ...
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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 ...
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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.
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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
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  • 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).