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Graceful Degradation of Magnetic Recording Channels
Abstract
Coding techniques are shown to provide an effective means of
controlling the effects of bandwidth and gain variation associated with
space losses. The combination of a specific channel code and a suitable
partial-response detection technique is proposed and studies for the
purpose of obtaining enhanced robustness. The technique presented for
encoding and decoding digital audio signals offers the advantage of a
graceful degradation of the performance when the signal is recorded on a
digital recorder with a wide range of bandwidths. This situation may
arise, for example, when contact between head and medium is
insufficient. The technique can also be used for digital video signals
or any other information that might carry significance information
A symposium on “Information Theory in the Benelux” was organized in Zoetermeer, in 1980. This symposium effectively signifies the informal naissance of the “Werkgemeenschap voor Information en Communicatietheorie” (WIC) – literally translated as ”Working Community for Information and Communication Theory”. Since 1980, the WIC Information Theory Symposium has become an annual event. The official start of the community originates from February 1984, and the subsequent formal community declaration was established in May 1986. Prof. Boxma (TU Delft), Prof. Groneveld (Univ. Twente), Prof. Schalkwijk (TU Eindhoven) and Prof. Van der Meulen (K.U. Leuven) are considered the founding fathers of the WIC community, secretarially supported by Dr. Best (Univ. Twente) in the board.
A new technique for encoding and decoding digital audio signals is presented. It offers the advantage of a graceful degradation of the audio performance when the signal is conveyed over channels with a wide range of bandwidths. The flexibility of the new techniques also provides a key to the future evolution of the quality of digital audio or video systems within the same digital format. The class of systems described may well be of particular value in applications involving the storage or broadcast of digital audio signals when the exact bandwidth of the communication system is unknown.
A magnetic recording channel can be regarded as a "partial-response" channel because of its inherent differentiation in the readback process. The conventional NRZI method of recording is shown to be equivalent to the "precoding" of this particular partial-response channel, the purpose of which is to limit the propagation of error in the channel output. Using this new viewpoint, one can readily adopt an error detection scheme (developed for general partial-response channels) that takes full advantage of the inherent redundancy in the three-level channel output. The detection scheme is optimum in the sense that it detects all detectable errors with minimum delay. The paper also describes a new high-density recording method, named the "Interleaved NRZI," which is obtained by molding an ordinary recording channel into a different type of partial-response channel, resulting in a potential increase in information density. Implementation of the corresponding optimum error detection scheme is also presented. Finally, performance of these error detection schemes is evaluated in terms of probabilities of detecting single and double errors within a certain finite delay.
The recent interest in the use of pulse code modulation (PCM) for the transmission of speech has made it desirable to determine the effects of digital line errors on certain codes. Improved performance for low-level talkers has been generally obtained by the use of instantaneous compressors and expandors (compandors) in order to avoid using a large number of digits in the PCM coder-decoder (codec). A comparison of the effects of digital errors for a logarithmically compandored system transmitting speech is made on the basis of mean square distortion power and the distribution of error magnitude. Results are obtained for the binary, Gray (reflected binary), and folded binary codes. The results indicate that the binary and Gray codes have a “click” as well as a “noise” component of distortion while the folded binary code produces only noise at low-talker levels. “Clicks” have been defined as errors which have amplitudes greater than half the full range amplitude; the remaining errors are considered “noise”. For the folded binary code, the most significant digit gives polarity information; the remaining digits represent the signal magnitude in binary code.
To study the performance of Partial Response (PR) systems used in digital VTR where high density recording is required, the conventional analysis on the error probability only for random noise is not sufficient, and it is important to analyze the performance taking into account the influence of increase in tape-to-head spacing. In this paper, first, the error probability is derived for PR(1, 0m-1, -1), PR(1, Om-1, 1), and PR(1) systems (m = 1, 2, …) in NRZ recording, taking into account the increase in tape-to-head spacing. Then the relationship between the increase in tape-to-head spacing and SNR at the reading point required to achieve the prescribed error probability is obtained. The results show that, PR(1, 0, -1) out of PR(1, 0m-l, -1) and PR(1, 1) out of PR(1, 0m-1, 1) exhibit excellent performance. Also, it was clarified that the PR(1, 1) system has good performance provided the increase in tape-to-head spacing is small and the PR(1, 0, -1) system is better for a large increase in spacing. Moreover, the relationship between timing jitter and required SNR is discussed.
For certain speech studies at the Bell Telephone Laboratories, it has been necessary to design some rather specialized magnetic recording equipment.
In connection with this work, it has been found experimentally and theoretically that introducing a spacing of d inches between the reproducing head and the recording medium decreases the reproduced voltage by 54.6 (d/λ) decibels when the recorded wavelength is λ inches. For short wavelengths this loss is many decibels even when the effective spacing is only a few ten-thousandths of an inch. On this basis it is argued that imperfect magnetic contact between reproducing head and recording medium may account for much of the high-frequency loss which is experimentally observed.
The application of Viterbi detection to Class IV partial response on a magnetic recording channel is discussed. The theoretical performance is analyzed in the presence of noise correlation and quantizing errors. A simplified algorithm is described which was implemented on a transverse-scan magnetic tape recorder operating at a linear density of 1800 bits/mm and a transfer rate of 120 Mbits/s. Following an initial 5 bit analog-to-digital conversion of the ternary waveform, the Viterbi detector is implemented entirely in high-speed digital emitter-coupled logic. An advantage of approximately 1.5 dB in effective signal-to-noise ratio is gained over a simple level detector, a result which agrees well with the theoretical development.
A new technique for encoding and decoding digital audio signals offers the advantage of a graceful degradation of the audio performance when the signal is conveyed over channels with a wide range of bandwidths. The flexibility of the new technique also provides a key to the future evolution of the quality of digital audio or video systems within the same digital format. The technique described may well be of particular value in applications involving the storage or broadcast of digital audio signals when the transmitter and receiver are ignorant of the exact bandwidth of the communication system.
An analysis is presented of the performance of partial response (PR) systems of types PR(1, 0, 0, . . . , 0, -1) and PR(1, 0, 0, . . . , 0, 1) for nonreturn-to-zero recording. The error probability is obtained as a function of the signal-to-noise ratio (SNR) at the reading point, the phase margin, the linear density, and the roll-off factor of a Nyquist equalizing waveform. Then as a numerical example a performance comparison of the PR systems is made by obtaining the relation between the phase margin and the SNR required to achieve the prescribed error probability.
This paper provides a tutorial introduction to recording codes for magnetic disk storage devices and a review of progress in code construction algorithms. Topics covered include: a brief description of typical magnetic recording channels; motivation for use of recording codes; methods of selecting codes to maximize data density and reliability; and techniques for code design and implementation.
In high-density magnetic recording, since the level of playback signal is low, its instrument noise margin may become seriously reduced, especially in view of the level fluctuation of the playback signal caused by tape-to-head spacing variations. Moreover, in high track density recording, the leakage from neighboring recorded tracks can importantly influence conclusions about overall system performance. Three detecting methods within the class of NRZ pulse recording formats have been compared: integrated detection of NRZ recording, amplitude detection of precoded NRZI recording, and partial response detection of precoded Interleaved NRZI recording. The comparisions are made with respect to the signal-to-noise ratio due to instrument noise in the playback process, the variation of separation allowed between the tape and head in the playback process, and the interference caused by leakage from adjacent recorded tracks. The results show the partial response detection method to promise the largest areal density among these three detection methods.