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Signal-to-noise ratio of pilot tracking tones embedded in binary coded signals
Abstract
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.
... Finally, the power spectrum of the process t, generated by the finite state machine with transition matrix B is proportional to S,(O) = i R(lkl)e-2"'ke, (1. 6) where k=-m R(k) = uTFBku, k =O,l;.+, (1.7) with F=diag(q,,q,;.., qw) and u=l/p[-m,-m+l;.., m -1, mlT (m = [ pb 1). ...
... In digital magnetic recorders part of the information storage capacity is exploited for recording servo position information. This information is often recorded as a low-frequency tone, ,usually called pilot tone, see [6]. The principle of operation is as follows. ...
The eigenstructure of bidiagonal Hessenberg-Toeplitz matrices is determined. These matrices occur as skeleton matrices of finite-state machines generating certain asymmetrically DC-constrained binary sequences that can be used for simulating pilot tracking tones in digital magnetic recording. The eigenstructure is used to calculate the Shannon upper bound to the entropy of the finite state machine as well as the power spectrum of the maxentropic process generated by it.
... 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]. Very often, more than one constraint is imposed on a recorded sequence. ...
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
Baseband modulation codes are widely applied in such diverse fields as digital line transmission [21, 28, 18, 116], digital optical transmission [111, 16], and digital magnetic and optical storage [ 105, 100, 106]. They act to translate the source data sequence d
n
into a sequence a
k
that is transmitted across the channel (Fig. 4.1; see also Chapter 3). The principal goal is to enable the receiver to produce reliable decisions \({\hat d_n}\) about d
n
. Code design should, therefore, account for the characteristics of both channel and receiver. (Because modulation coding is the only type of coding that we consider in this chapter, we shall usually say ‘coding’ where we mean ‘modulation coding’.)
Various equalization and detection techniques are considered for
the digital video cassette recorder (DVCR) application. Bit error rate
(BER) performances are evaluated based on computer simulation. The
equalization/detection schemes considered are class IV partial response
equalisation followed by Viterbi algorithm detection (PR4/VA), extended
class IV combined with VA detection (EPR4/VA), decision feedback
equalization (DFE) and fixed-delay tree search with decision feedback
(FDTS/DF). For all cases, the rate 24/25 modulation DC-controlled
channel code is used. The BER simulations are performed at different
channel SNR values and in the presence of off-track, head-tape space
variations and sampling phase error. The results show that the FDTS/DF
with a search depth of 3 has significant performance advantage and
improved robustness over other schemes under various channel conditions
Bit-error-rate (BER) performances of various DC free coding and
detection methods have been compared in digital tape recording
environments. Performance sensitivities to additive noise, head-tape
space variations and offtrack interference have been investigated at two
representative linear densities. The results indicate that the
performance ranking of different techniques depends strongly on the type
of interference assumed in the channel. In particular, the fixed delay
tree search with decision feedback (FDTS/DF) detector used in
conjunction with the rate 8/10 code performs comparably to or better
than the partial response maximum likelihood technique combined with the
rate 24/25 code in all cases considered, despite the significantly lower
code rate
The proper functioning of a digital video recorder is largely
governed by the selection of a suitable channel code in conjunction with
both the detection method and the tracking system. The channel code for
the digital video cassette recorder (DVCR) satisfies a variety of design
requirements. The paper provides an overview of those requirements. A
detailed description is given of the constriction of the new channel
code, called 24→25 code, that complies with the given constraints
and involves only a minor drawback in terms of the overhead needed. The
servo position information is recorded as low-frequency components,
pilot tracking tones, which are embedded in the recorded stream of
binary digits
An experimental digital video recording system based on small recording mechanics is described. High picture quality at moderate recording bit rates is obtained with component coded video and application of an advanced bit-rate reduction technique based on the discrete cosine transform (DCT). A single actuator allows for high tracking accuracy and multispeed playback. Reasonable picture quality has been obtained at 10 Mb/s. High picture quality, with hardly noticeable coding noise, was obtained at 19 Mb/s. For scenes with critical motion, the use of motion-adaptive processing is required.
Asymptotic results for the Perron-Frobenius eigenvalue of a
nonnegative Hessenberg-Toeplitz matrix as the dimension of the matrix
tends to ∞ are given. The results are used and interpreted in
terms of source entropies in the case where the Hessenberg-Toeplitz
matrix arises as the transition matrix of a finite-state machine
generating certain constrained sequences of ±1's
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.
The stochastic process appearing at the output of a digital encoder is investigated. Based upon the statistics of the code being employed, a systematic procedure is developed by means of which the average power spectral density of the process can be determined. The method is readily programmed on the digital computer, facilitating the calculation of the spectral densities for large numbers of codes. As an example of its use, the procedure is applied in the case of a specific multi-alphabet, multi-level code.
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.
The engineering design of a head-positioning system for an interchangeable-medium disk file is considered. Emphasis is placed upon three specific functions within the positioning system: (1) encoding and demodulation of information from the dedicated servo surface, (2) compensation and dynamics of the track-following control system, and (3) implementation of control electronics for a quasi-time-optimal, track-accessing control system. The examples used are taken from the IBM 3340 Disk Storage Facility.
Statistics of a synchronous binary message pulse train applied to a regenerative repeater are related to those of the original binary message, which is assumed ergodic. It is shown that the ensemble of possible message pulse trains is a nonstationary random process having a periodically varying mean and autocovariance. A spectral density is calculated which shows line-spectral components at harmonics of the pulse rate and a continuous density function, both with intensity proportional to the square of the absolute value of the Fourier transform of the standard pulse at the frequency considered. The continuous component has many properties similar to thermal noise but differs in that, under certain conditions described, it can exhibit regularly spaced axis crossings, can be exactly predicted over finite intervals and is capable of producing discrete components when nonlinear operations are performed on it, even though no line spectral terms are originally present. The analytical results are applied to the problem of deriving a timing wave from the message pulse train by shock-exciting a tuned circuit with impulses occurring at the axis crossings.
In digital transmission of binary (+1,-1) signals it is desirable that the stream of pulses which constitutes the signal have no dc, that is, that the power spectrum go to zero at zero frequency. It is desirable that, for a given efficiency or entropy, the spectrum rise slowly with increasing frequency. We have obtained the spectrum for selected blocks with equal numbers of plus ones and minus ones. For a given efficiency, this is better than the spectrum obtained by Rice, using the Monte Carlo method, for block encoding using polarity pulses. An algorithm given by Schalwijk should allow simple encoding into selected blocks.
The CTL tracking method is usually employed in VTRs etc.. in order to make the CTL tracking possible, the CTL signal synchronizing with reference signal is recorded on the tape and, during playback, the tracking servo works to maintain a constant phase between the drum revolution and the CTL signal. The CTL therefore, requires a stationary head to record or read the CTL signal, which opposes to simplify the mechanism. Furthermore, the manual tracking control is necessary, as the mechanical factors (for example, X-value, head mounting accuracy, and so on) introduce tracking error.
A technique for determining worst case run-length-limited (RLL) code patterns for data-to-servo coupling in magnetic buried servos is presented. The problem is reduced to a general dynamic programming problem, whose solution is described. The general problem can require large amounts of computation, so a method is also developed to determine approximate worst case patterns by solving a classical dynamic programming problem using the Viterbi algorithm. An error estimate for the approximate solution is also derived. Computational results are presented for the
A continuous servo system that shares the surface area of the medium with data on the same track, to improve the accuracy of servo-track following, uses only conventional media and a single head. A long-gap head records low-frequency servo signals deeply into the medium coating, and a short-gap head then erases the surface portion to stabilize the servo amplitude. Short-gap read-write heads then write and read high-frequency data signals without interference. Using frequency-separation filters and an ac-biased pulse-write method, an inductive head reads servos while simultaneously writing data. Servo-signal amplitude increases during data-write operations. Servo signals, which do not degrade after stabilization, provide information needed for track following and for various timing and control functions. Data reliability is unimpaired.
Current head-positioning servo methods require a spatial separation between the data and servo. This separation limits the accuracy with which a head-positioning servo system can follow a data track. The buried servo techniques described here allow servo information to be recorded in the same medium area as that used for data, a single head is used for both data and servo. These techniques provide high-bandwidth continuous head-position information with a potential for a high track-density servo system. The servo pattern consists of two single-frequency signals recorded deeply into the magnetic medium below the area used for data. The servo signals are detected by synchronous detection techniques and provide a continuous head-position error signal. The servo system uses this head-position error signal to follow a given data track and to seek new data tracks. Buried servo was implemented on a flexible disk drive. The track-following system had performance advantages when compared to a sector servo scheme implemented on a similar device.
In digital data transmission (respectively, storage systems), line codes (respectively, recording codes) are used to tailor the spectrum of the encoded sequences to satisfy constraints imposed by the channel transfer characteristics or other system requirements. For instance, pilot tone insertion requires codes with zero mean and zero spectral density at tone frequencies. Embedded tracking/focus servo signals produce similar needs. Codes are studied with spectral nulls at frequencies f=kf_{s}/n , where f , is the symbol frequency and k, n are relatively prime integers with k leq n; in other words, nulls at rational submultiples of the symbol frequency. A necessary and sufficient condition is given for a null at f in the form of a finite discrete Fourier transform (DFT) running sum condition. A corollary of the result is the algebraic characterization of spectral nulls which can be simultaneously realized. Specializing to binary sequences, we describe canonical Mealy-type state diagrams (directed graphs with edges labeled by binary symbols) for each set of realizable spectral nulls. Using the canonical diagrams, we obtain a frequency domain characterization of the spectral null systems obtained by the technique of time domain interleaving.
In pulse-amplitude modulation (PAM) digital transmission systems line encoding is used for shaping the spectrum of the encoded symbol sequence to suit the frequency characteristics of the transmission channel. In particular, it is often required that the encoded symbol sequence have a zero mean and spectral density vanishing at zero frequency. We show that the finite running digital sum condition is a necessary and sufficient condition for this to occur. The result holds in particular for alphabetic codes, which are the most widely used line codes.
Statistics of regenerative digital transmission Codes for zero spectral density at zero frequency
- W R Bennett
- G L Pierobon
W. R. Bennett, " Statistics of regenerative digital transmission, " Bell Syst. Tech. J., vol. 37, pp. 1501-1542, Nov. 1958. [ 101 G. L. Pierobon, " Codes for zero spectral density at zero frequency, " IEEE Trans. Inform. Theory, vol. IT-30, pp. 435-439, March 1984.
Alles uber Video (Philips Taschenbucher
- H Bahr
Method and apparatus for recording a digital information
- M H H Hoefelt
- E De Niet
- A M A Rijckaert