Successive Approximation A/D Converter
There are many types of A/D converter designs appropriate for various applications. For audio digitization, the necessity for both speed and accuracy limits the choices to a few types. The successive approximation register (SAR) A/D converter (sometimes known as a residue converter) is a classical method for achieving good-quality audio digitization; a SAR converter is shown in Fgr. 10. This converter uses a D/A converter in a feedback loop, a comparator, and a control section. In essence, the converter compares an analog voltage input with its interim digital word converted to a second analog voltage, adjusting its interim conversion until the two agree within the given resolution. The device follows an algorithm that, bit by bit, sets the output digital word to match the analog input.
For example, consider an analog input of 6.92 V and an 8-bit SAR A/D converter. The operational steps of SAR conversion are shown in Fgr. 11. The most significant bit in the SAR is set to 1, with the other bits still at 0; thus the word 10000000 is applied to the internal D/A converter.
This word places the D/A converter's output at its half value This word places the D/A converter's output at its half value of 5 V. Because the input analog voltage is greater than the D/A converter's output, the comparator remains high. The first bit is stored at logical 1. The next most significant bit is set to 1 and the word 11000000 is applied to the D/A converter, with an interim output of 7.5 V. This voltage is too high, so the second bit is reset to 0 and stored. The third bit is set to 1, and the word 10100000 is applied to the D/A converter; this produces 6.25 V, so the third bit remains high. This process continues until the LSB is stored and the digital word 10110001, representing a converted 6.91 V, is output from the A/D converter.
This successive approximation method requires n D/A conversions for every one A/D conversion, where n is the number of bits in the output word. In spite of this recursion, SAR converters offer relatively high conversion speed.
However, the converter must be precisely designed. For example, a 16-bit A/D converter ranging over ±10 V with 1/2-LSB error requires a conversion accuracy of 3 mV. A 10-V step change in the D/A converter must settle to within 0.001% during a period of 1 µs. This period corresponds to an analog time constant of about 100 ns. The S/H circuit must be designed to minimize droop to ensure that the LSB, the last bit output to the SAR register, is accurate within this specification.
FGR. 10 A successive approximation register A/D converter showing an internal
D/A converter and comparator.
FGR. 11 The intermediate steps in an SAR conversion showing results of interim
D/A conversions.
Oversampling A/D Converter
As noted, analog lowpass filters suffer from limitations such as noise, distortion, group delay, and passband ripple; unless great care is taken, it’s difficult for downstream A/D converters to achieve resolution beyond 18 bits. In most applications, brick-wall analog anti-aliasing filters and SAR A/D converters have been replaced by oversampling A/D converters with digital filters. The implementation of a digital anti-aliasing filter is conceptually intriguing because the analog signal must be sampled and digitized prior to any digital filtering. This conundrum has been resolved by clever engineering; in particular, a digital decimation filter is employed and combined with the task of A/D conversion.
The fundamentals of oversampling A/D conversion are presented here.
In oversampling A/D conversion, the input signal is first passed through a mild analog anti-aliasing filter which provides sufficient attenuation, but only at a high half sampling frequency. To extend the Nyquist frequency, the filtered signal is sampled at a high frequency and then quantized. After quantization, a digital low-pass filter uses decimation to both reduce the sampling frequency to a nominal rate and prevent aliasing at the new, lower sampling frequency. Quantized data words are output at a lower frequency ( For example, 48 or 96 kHz). The decimation low-pass filter removes frequency components beyond the Nyquist frequency of the output sampling frequency to prevent aliasing when the output of the digital filter is resampled (undersampled) at the system's sampling frequency.
FGR. 12 A two-times oversampling A/D and D/A conversion system. Decimation
and interpolation digital filters increase and decrease the sampling frequency
while removing alias and image signal components.
Consider the oversampling A/D converter and D/A converter (both using two-times oversampling) shown in Fgr. 12. An analog anti-aliasing filter restricts the bandwidth to 1.5fs, where fs is the sampling frequency. The relatively wide transition band, from 0.5 to 1.5fs, is acceptable and promotes good phase response. For example, a 7th-order Butterworth filter could be used. The signal is sampled and held at 2fs, and then converted. The digital filter limits the signal to 0.5fs. With decimation, the sampling frequency of the signal is undersampled and hence reduced from 2fs to fs. This action is accomplished with a linear-phase finite impulse response (FIR) digital filter with uniform group delay characteristics. Upon playback, an oversampling filter doubles the sampling frequency, samples are converted to yield an analog waveform, and high-frequency images are removed with a low-order lowpass filter.
Many oversampling A/D converters use a very high initial sampling frequency (perhaps 64- or 128-times 44.1 kHz), and take advantage of that high rate by using sigma-delta conversion of the audio signal. Because the sampling frequency is high, word lengths of one or a few bits can provide high resolution. A sigma-delta modulator can be used to perform noise shaping to lower audio band quantization noise. A decimation filter is used to convert the sigma-delta coding to 16-bit (or higher) coding, and a lower sampling frequency. Consider an example in which one-bit coding takes place at an oversampling rate R of 72; that is, 72 × 44.1 kHz = 3.1752 MHz, as shown in Fgr. 13. The decimation filter provides a stopband from 20 kHz to the half-sampling frequency of 1.5876 MHz. One-bit A/D conversion greatly simplifies the digital filter design. An output sample is not required for every input bit; because the decimation factor is 72, an output sample is required for every 72 bits input to the decimation filter. A transversal filter can be used, with filter coefficients suited for the decimation factor. Following decimation, the result can be rounded to 16 bits, and output at a 44.1-kHz sampling frequency.
In addition to eliminating brick-wall analog filters, oversampling A/D converters offer other advantages over conventional A/D converters. Oversampling A/D converters can achieve increased resolution compared to SAR methods. For example, they extend the spectrum of the quantization error far outside the audio baseband. Thus the in-band noise can be made quite small. The same internal digital filter that prevents aliasing also removes out-of-band noise components. Increasingly, oversampling A/D converters are employed. This type of sigma-delta conversion is discussed in Section 18. Whichever A/D conversion method is used, the goal of digitizing the analog signal is accomplished, as data in two's complement or other form is output from the device.
FGR. 13 An oversampling A/D converter using one-bit coding at a high sampling
frequency, and a decimation filter.
For digitization systems in which real-time processing such as delay and reverberation is the aim, the signal is ready for processing through software or dedicated hardware. In the case of a digital recording system, further processing is required to prepare the data for the storage medium.
Record Processing
After the analog signal is converted to binary numbers, several operations must occur prior to storage or transmission. Although specific processing needs vary according to the type of output channel, systems generally multiplex the data, perform interleaving, add redundancy for error correction and provide channel coding. Although there is an uninteresting element of bookkeeping in this processing, any drudgery is critical to prepare the data for the output channel and ensure that playback ultimately will be satisfactorily accomplished.
Some digital audio programs are stored or transmitted with emphasis, a simple means of reducing noise in the signal. Pre-emphasis equalization boosts high frequencies prior to storage or transmission. At the output, corresponding de-emphasis equalization attenuates high frequencies. The net result is a reduction in the noise floor.
A common emphasis characteristic uses time constants of 50 and 15 µs, corresponding to frequency points at 3183 and 10,610 Hz, with a 6-dB/octave slope between these points, as shown in Fgr. 14. Use of pre-emphasis must be identified in the program material so that de-emphasis equalization can be applied at the output.
In analog recording, an error occurring during storage or transmission results in degraded playback. In digital recording, error detection and correction minimize the effect of such defects. Without error correction, the quality of digital audio recording would be greatly diminished.
Several steps are taken to combat the effects of errors. To prevent a single large defect from destroying large areas of consecutive data, interleaving is employed; this scatters data through the bitstream so the effect of an error is scattered when data is de-interleaved during playback.
During encoding, coded parity data is added; this is redundant data created from the original data to help detect and correct errors. A discussion of parity, check codes, redundancy, interleaving, and error correction is presented in Section 5.
FGR. 14 Pre-emphasis boosts high frequencies during recording, and de-emphasis
reduces them during playback to lower the noise floor.
Multiplexing is used to form a serial bitstream. Most digital audio recording and transmission is a serial process; that is, the data is processed as a single stream of information. However, the output of the A/D converter can be parallel data; for example, two 16-bit words may be output simultaneously. A data multiplexer converts this parallel data to serial data; the multiplexing circuit accepts parallel data words and outputs the data one bit at a time, serially, to form a continuous bitstream.
Raw data must be properly formatted to facilitate its recording or transmission. Several kinds of processing are applied to the coded data. The time-multiplexed data code is usually grouped into frames. To prevent ambiguity, each frame is given a synchronization code to delineate frames as they occur in the stream. A synchronization code is a fixed pattern of bits that is distinct from any other coded data bit pattern in much the same way that a comma is distinct from the characters in a sentence. In many cases, data files are preceded by a data header with information defining the file contents.
Addressing or timing data can be added to frames to identify data locations in the recording. This code is usually sequentially ordered and is distributed through the recording to distinguish between different sections. As noted, error correction data is also placed in the frame.
Identification codes might carry information pertinent to the playback processing. For example, specification of sampling frequency, use of pre-emphasis, table of contents, timing and track information, and copyright information can be entered into the data stream.
Channel Codes
Channel coding is an important example of a less visible, yet critical element in a digital audio system. Channel codes were aptly described by Thomas Stockham as the handwriting of digital audio. Channel code modulation occurs prior to storage or transmission. The digitized audio samples comprise 1s and 0s, but the binary code is usually not conveyed directly. Rather, a modulated channel code represents audio samples and other conveyed information.
It’s thus a modulation waveform that is interpreted upon playback to recover the original binary data and thus the audio waveform. Modulation facilitates data reading by further delineating the recorded logical states. Moreover, through modulation, a higher coding efficiency is achieved; although more bits might be conveyed, a greater data throughput can be achieved overall.
Storing binary code directly on a medium is inefficient.
Much greater densities with high code fidelity can be achieved through methods in which modulation code fidelity is low. The efficiency of a coding method is the number of data bits transmitted divided by the number of transitions needed to convey them. Efficiencies vary from about 50% to nearly 150%. In light of these requirements, PCM , for example, is not suitable for transmission or recording to a medium such as optical disc; thus, other channel modulation techniques must be devised. Although binary recording is concerned with storing the 0s and 1s of the data stream, the signal actually recorded might be quite different. Typically, it’s the transitions from one level to another, rather than the amplitude levels themselves, which represent the channel data. In that respect, the important events in a digitally encoded signal are the instants in time at which the state of the signal changes.
A channel code describes the way information is modulated into a channel signal, stored or transmitted, and demodulated. In particular, information bits are transformed into channel bits. The transfer functions of digital media create a number of specific difficulties that can be overcome through modulation techniques. A channel code should be self-clocking to permit synchronization at the receiver, minimize low-frequency content that could interfere with servo systems, permit high data rate transmission or high-density recording, exhibit a bounded energy spectrum, have immunity to channel noise, and reveal invalid signal conditions. Unfortunately, these requirements are largely mutually conflicting, thus only a few channel codes are suitable for digital audio applications.
The decoding clock in the receiver must be synchronized in frequency and phase with the clock (usually implicit in the channel bit patterns) in the transmitted signal.
In most cases, the frames in a binary bitstream are marked with a synchronization word. Without some kind of synchronization, it might be impossible to directly distinguish between the individual channel bits.
Even then, a series of binary 1s or 0s form a static signal upon playback. If no other timing or decoding information is available, the timing information implicitly encoded in the channel bit periods is lost. Therefore, such data must often be recorded in such a way that pulse timing is delineated. Codes that provide a high transition rate, which are suitable for regenerating timing information at the receiver, are called self-clocking codes.
Thus, one goal of channel modulation is to combine a serial data stream with a clock pulse to produce a single encoded waveform that is self-clocking. Generally, code efficiency must be diminished to achieve self-clocking because clocking increases the number of transitions, which increases the overall channel bit rate. The high- frequency signal produced by robust clocking content will decrease a medium's storage capacity, and can be degraded over long cable runs. A minimum distance between transitions (Tmin) determines the highest frequency in the code, and is often the highest frequency the medium can support. The ratio of Tmin to the length of a single bit period of input information data is called the density ratio (DR). From a bandwidth standpoint, a long Tmin is desirable in a code. Tmax determines the maximum distance between transitions sufficient to support clocking.
From a clocking standpoint, a shorter Tmax is desirable.
Time-axis variations such as jitter are characterized by phase variations in a signal, observable as a frequency modulation of a stable waveform. The constraints of channel coding and data regeneration fundamentally limit the maximum number of incremental periods between transitions, that is, the number of transitions that can be detected between Tmin and Tmax. An important consideration in modulation code design is tolerance in locating a transition in the code. This is called the window margin, phase margin, or jitter margin and notated as Tw. It describes the minimum difference between code wavelengths: the larger the clock window, the better the jitter immunity. The efficiency of a code can be measured by its density ratio that is the ratio of the number of information bits to the number of channel transitions. The product of DR and Tw is known as the figure of merit (FoM); by combining density ratio and jitter margin, an overall estimate of performance is obtained: the higher the numerical value of FoM, the better the performance.
An efficient coding format must restrict dc content in the coded waveform, which could disrupt timing synchronization; dc content measures the time that the waveform is at logical 1 versus the time at logical 0; a dc content of 0 is ideal. Generally, digital systems are not responsive to direct current, so any dc component of the transmitted signal may be lost. In addition, dc components result in a baseline offset that reduces the signal-to-noise ratio. The dc content is the fraction of time that the signal is high during a string of 1s or 0s minus the fraction of time it’s low. It results in a nonzero average amplitude value. For example, a nonreturn to zero (NRZ) signal (in which binary values are coded as high- or low-signal amplitudes) with all 0s or 1s would give a dc content of 100%.
FGR. 15 The digital sum value (DSV) monitors the dc content in a bitstream.
A. A coded waveform that is free of dc content over the measured interval.
B. A coded waveform that contains dc content.
The dc content can be monitored through the digital sum value (DSV). The DSV of a code can be thought of as the difference in accumulated charge if the code was passed through an ac coupling capacitor. In other words, it shows the dc bias that accumulates in a coded sequence. Fgr. 15 shows two different codes and their DSV; over the measured interval, the first code does not show dc content, the second does. The dc content might cause problems in transformer-coupled magnetic recording heads; magnetic heads sense domains inductively and hence are inefficient in reading low-frequency signals. The dc content can present clock synchronization problems, and lead to errors in the servo systems used for radial tracking and focusing in an optical system. These systems generally operate in the low-frequency region. Low-frequency components in the readout signal cause interference in the servo systems, making them unstable. A dc-free code improves both the bandwidth and signal-to-noise ratio of the servo system. In the Compact Disc format , for example, the frequency range from 20 kHz to 1.5 MHz is used for information transmission; the servo systems operate on signals in the 0- to 20-kHz range.
A single sampling pulse is easy to analyze because of its periodic nature in the time domain; Fourier analysis clearly shows its spectrum. However, a data stream differs in that the data pulses occur aperiodically, and in fact can be considered to be random. The power spectrum density, or power spectrum, shows the response of the data stream.
For example, Fgr. 16 shows the spectral response of three types of channel coding with random data sequences: nonreturn to zero (NRZ), modified frequency modulation (MFM), and biphase. A transmission waveform ideally should have minimal energy at low frequencies to avoid clocking and servo errors, and minimal energy at high frequencies to reduce bandwidth requirements. Biphase codes (there are many types, one being binary FM) yield a spectrum that has a broadband energy distribution. The MFM code exhibits a very narrow spectrum. The MFM and biphase codes are similar because they have no strong frequency components at low frequencies (lower than 0.2f where f = 1/T). If the value of f is 500 kHz , for example, and the servo signals don’t extend beyond 15 kHz, these codes would be suitable. The NRZ code has a strong dc content and could pose problems for a servo system.
FGR. 16 The power spectral density shows the response of a stream of random
data sequences. NRZ code has severe dc content; MFM code exhibits a very narrow
spectrum; biphase codes yield a broadband energy distribution.
To minimize decoding errors , formats can be developed in which data is conveyed with data patterns that are as individually unique as possible. For example, in the eight to-fourteen modulation (EFM) code devised for the Compact Disc format, 8-bit symbols are translated into 14 bit symbols, carefully selected for maximum difference between symbols. In this way, invalid data can be more easily recognized. Similarly, a data symbol could be created based on previous adjacent symbols and the receiver could recognize the symbol and its past history as a unique state. A state pattern diagram is used in which all transitions are defined, based on all possible adjacent symbols.
As noted, in many codes, the information is contained in the timing of transitions, not in the direction (low to high, or high to low) of the transitions. This is advantageous because the code is thus insensitive to polarity; the content won’t be affected if the signal is inverted. The EFM code enjoys this property.
FGR. 17 A comparison of simple and group-code waveforms for a common data
input.
Simple Codes
The channel code defines the logical 1 and 0 of the input information. We might assume a direct relationship between a high amplitude and logical 1, and a low amplitude and logical 0. However, many other relationships are possible; for example, in one version of frequency-shift keying (FSK), a logical 1 corresponds to a sine burst of 100 kHz and a logical 0 corresponds to a sine burst of 150 kHz. Methods that use only two values take full advantage of digital storage; relatively large variations in the medium don’t affect data recovery. Because digitally stored data is robust, high packing densities can be achieved. Various modulation codes have been devised to encode binary data according to the medium's properties. Of many, only a few are applicable to digital audio storage, on either magnetic or optical media. A number of channel codes are shown in Fgr. 17.
Perhaps the most basic code sends a pulse for each 1 and does not send a pulse for a 0; this is called return to zero (RZ) code because the signal level always returns to zero at the end of each bit period.
The nonreturn to zero (NRZ) code is also a basic form of modulation: 1s and 0s are represented directly as high and low levels. The direction of the transition at the beginning or end of a bit period indicates a 1 or 0. The minimum interval is T, but the maximum interval is infinite (when data does not change) thus NRZ suffers from one of the problems that encourages use of modulation: strings of 1s or 0s don’t produce transitions in the signal, thus a clock cannot be extracted from the signal. In addition, this creates dc content. The data density (number of bits per transition) for NRZ is 1.
The nonreturn to zero inverted (NRZI ) code is similar to the NRZ code, except that only 1s are denoted with amplitude transitions (low to high, or high to low); no transitions occur for 0s. For example, any flux change in a magnetic medium indicates a 1, with transitions occurring in the middle of a bit period. With this method, the signal is immune to polarity reversal. The minimum interval is T, and the maximum is infinite; a clock cannot be extracted. A stream of 1s generates a transition at every clock interval; thus, the signal's frequency is half that of the clock. A stream of 0s generates no transitions. Data density is 1.
In binary frequency modulation (FM), also known as biphase mark code, there are two transitions for a 1 and one transition for a 0; this is essentially the minimum frequency implementation of FSK. The code is self clocking. Biphase space code reverses the 1/0 rules. The minimum interval is 0.5T and the maximum is T. There is no dc content and the code is invertible. In the worst case, there are two transitions per bit, yielding a density ratio of 0.5, or an efficiency of 50%. FoM is 0.25. This code is used in the AES3 standard, described in Section 13.
In phase encoding (PE), also known as phase modulation (PM), biphase level modulation or Manchester code, a 1 is coded with a negative-going transition, and a 0 is coded with a positive-going transition. Consecutive 1s or 0s follow the same rule, thus requiring an extra transition.
These codes follow phase-shift keying techniques. The minimum interval is 0.5T and the maximum is T. This code does not have dc content, and is self-clocking. Density ratio is 0.5. The code is not invertible.
In modified frequency modulation (MFM) code, sometimes known as delay modulation or Miller code, a 1 is coded with either a positive- or negative-going transition in the center of a bit period , for each 1. There is no transition for 0s; rather, a transition is performed at the end of a bit period only if a string of 0s occurs. Each information bit is coded as two channel bits. There is a maximum of three 0s and a minimum of one 0 between successive 1s.
In other words, d = 1 and k = 3. The minimum interval is T and the maximum is 2T. The code is self-clocking, and can have dc content. Density ratio is 1 and FoM is 0.5.
Group Codes
Simple codes such as NRZ and NRZI code one information bit into one channel bit. Group codes use more sophisticated methods for great coding efficiency and overall performance. Group codes use code tables to convert groups of input words (each with m bits) into patterns of output words (each with n bits); the output patterns are specially selected for their desirable coding characteristics, and uniqueness that helps detect errors.
The code rate R for a group code is m/n. The value of the code rate equals the value of the jitter margin. In some group codes, the correspondence between the input information word and output codeword is not fixed; it might vary adaptively with the information sequence itself. These multiple modes of operation can improve code efficiency.
Group codes also can be considered as run-length limited (RLL) codes; the run length is the time between channel-bit transitions. This coding approach recognizes that transition spacings can be any multiple of the period, as shown in Fgr. 18. This breaks the distinction between data and clock transitions and instead specifies a minimum number d and maximum number k of 0s between two successive 1s. These Tmin and Tmax values define the code's run length and specifically determine the code's spectral limits; clearly, data density, dc content, and clocking are all influenced by these values. The value of the density ratio equals the value of Tmin, such that
DR = Tmin = (d + 1) (m)/n.
Similarly, jitter margin
Tw = m/n and FoM = (d + 1)(m2)/n2.
FGR. 18 Run-length limited (RLL) codes regulate the number of transitions
representing the channel code. In this way, transition spacings can be any
multiple of the channel period, increasing data density.
As always, density must be balanced against other factors, such as clocking. Generally, d is selected to be as large as possible for high density, and k is selected to be as large as possible while maintaining stable clocking.
Note that high k/d ratios can yield code sequences with high dc content; this is a shortcoming of RLL codes. The minimum and maximum lengths determine the minimum and maximum rates in the code waveform; by choosing specific lengths, the spectral response can be shaped.
RLL codes use a set of rules to convert information bits into a stream of channel bits by defining some relationship between them. A channel bit does not correspond to one information bit; the channel bits can be thought of as short timing windows, fractions of the clock period. Data density can be increased by increasing the number of possible transitions within a bit period. Channel bits are often converted into an output signal using NRZI modulation code; a transition defines a 1 in the channel bitstream. The channel bit rate is usually greater than the information bit rate, but if the run lengths between 1s can be distinguished, the overall information density can be increased. To ensure that consecutive codewords don’t violate the run length and to ensure dc-free coding, alternate codewords or merging bits may be placed between codewords; however, this decreases density. Generally, RLL codes are viable only in channels with low noise; For example, the required S/N ratio increases as minimum length d increases.
Fortunately, optical discs are suitable for RLL coding.
Technically, NRZ and NRZI are RLL codes because d = 0 and k = 8 MFM could be considered as a (1,3) RLL code.
In the group coded recording (GCR) code, data is parsed into four bits, coded into 5-bit words using a lookup table as shown in TBL. 1, and modulated as NRZI signals. This implementation is sometimes known as 4/5 MNRZI (modified NRZI ) code. There is a transition every three bits, because of the 4/5 conversion, the minimum interval is 0.8T, and the maximum interval is 2.4T. Adjacent 1s are permitted (d = 0) and the maximum number of 0s is 2 (k = 2). The code is self-clocking with great immunity to jitter, but exhibits dc content. The density ratio is 0.8.
TBL. 1 Conversion for the GCR (or 4/5 MNRZI ) code.
Groups of four information bits are coded as 5-bit patterns, and written in NRZI form.
TBL. 2 Conversion for 3PM (2,7) code. Three input bits are coded into a 6-bit
output word in which the minimum interval is maintained at 1.57 through pattern
inversion.
The three-position modulation ( 3PM) code is a (2,7) RLL adaptive code. Three input bits are converted into a 6 bit output word in which Tmin is 1.5T and Tmax is 6T, as shown in TBL. 2. There must be at least two channel 0s between 1s (d = 2). When 3PM words are merged, a 101 pattern might occur; this violates the Tmin rule. To prevent this, 101 is replaced by 010; the last channel bit in the coding table is reserved for this merging operation. The 3PM code is so called because of the three positions (d + 1) in the minimum distance. The code is self-clocking. For comparison, the duration between transitions for 3PM is 0.5T and for MFM is T. Thus, the packing density of 3PM is 50% higher than MFM. However, its maximum transition is 100% longer and its jitter margin 50% worse. 3PM exhibits dc content. Data density is 1.5.
In the 4/5 group code, groups of four input bits are mapped into five channel bits using a lookup table. The 16 channel codewords are selected (from the 32 possible) to yield a useful clocking signal while minimizing dc content.
Adjacent 1s are permitted (d = 0) and the maximum number of 0s is 3 (k = 3). Tmax = 16/5 = 3.2T. Density ratio is 0.8 and FoM is 0.64. The 4/5 code is used in the Fiber Distributed Data Interface (FDDI ) transmission protocol, and the Multichannel Audio Digital Interface (MADI ) protocol as described in Section 13.
As noted, RLL codes are efficient because the distance between transitions is changed in incremental steps. The effective minimum wavelength of the medium becomes the incremental run lengths. Part of this advantage is lost because it’s necessary to avoid all data patterns that would put transitions closer together than the physical limit.
Thus all data must be represented by defined patterns. The eight-to-fourteen modulation (EFM) code is an example of this kind of RLL pattern coding. The incremental length for EFM is one-third that of the minimum resolvable wavelength. Data density is not tripled, however, because 8 data bits must be expressed in a pattern requiring 14 incremental periods. To recover this data, a clock is run at the incremental period of 1T.
EFM code is used to store data on a Compact Disc; it’s an efficient and highly structured (2,10) RLL code. Blocks of 8 data bits are translated into blocks of 14-bit channel symbols using a lookup table that assigns an arbitrary and unique word. The 1s in the output code are separated by at least two 0s (d = 2), but no more than ten 0s (k = 10). That is, Tmin is 3 channel bits and Tmax is 11 channel bits. A logical 1 causes a transition in the medium; this is physically represented as a pit edge on the CD surface.
High recording density is achieved with EFM code. Three merging bits are used to concatenate 14-bit EFM words, so 17 incremental periods are required to store 8 data bits.
This decreases overall information density, but creates other advantages in the code. Tmin is 1.41T and Tmax is 5.18T. The theoretical recording efficiency is thus calculated by multiplying the threefold density improvement by a factor of 8/17, giving 24/17, or a density ratio of 1.41.
That is, 1.41 data bits can be recorded per shortest pit length. For practical reasons such as S/N ratio and timing jitter on clock regeneration, the ratio is closer to 1.25. In either case, there are more data bits recorded than are transitions on the medium. The merging bits completely eliminate dc content, but reduce efficiency by 6%. The conversion table was selected by a computer algorithm to optimize code performance. From a performance standpoint, EFM is very tolerant of imperfections, provides high density, and promotes stable clock recovery by a self clocking decoder. EFM is used in the CD format and is discussed in Section 7. The EFMPlus code used in the DVD format is discussed in Section 8. The 1-7PP code used in the Blu-ray format is discussed in Section 9.
Zero modulation (ZM) coding is an RLL code with d = 1 and k = 3; it uses a convolutional scheme, rather than group coding. One information bit is mapped into two data bits, coded with rules that depend on the preceding and succeeding data patterns, and written in NRZI code. As with many RLL codes that followed it, ZM uses data patterns that are optimal for its application (magnetic recording) and were selected by computer search.
Generally, the bitstream is considered as any number of 0s, two 0s separated by an odd number of 1s or no 1s, or two 0s separated by an even number of 1s. The first two types are coded as Miller code, and in the last, the 0s are coded as Miller code, but the 1s are coded as if they were 0s, but without alternate transitions. The density ratio is approximately 1. There is no dc content in ZM.
An eight-to-ten (8/10) modulation group code was selected for the DAT format in which 8-bit information words are converted to 10-bit channel words. The 8/10 code permits adjacent channel 1s, and there are no more than three channel 0s between 1s. The density ratio is 0.8, and FoM is 0.64. Bit synchronization and block synchronization are provided with a 3.2T + 3.2T synchronization signal, a prohibited 8/10 pattern. The ideal 8/10 codeword would have no net dc content, with equal durations at high and low amplitudes in its modulated waveform. However, there are an insufficient number of such 10-bit channel words to represent the 256 states needed to encode the 8-bit data input. Moreover, given the maximum run length limitation, only 153 channel codes satisfy both requirements. Thus 103 codewords must have dc content, or nonzero digital sum value (DSV). The DSV tallies the high-amplitude channel bit periods versus the low-amplitude channel bit periods as encoded with NRZI.
Two patterns are defined for each of the 103 nonzero DSV codewords, one with a +2 DSV and one with a -2 DSV; to achieve this, the first channel bit is inverted. Either of these codewords can be selected based on the cumulative DSV.
For example, if DSV ranges negatively, a +2 word is selected to tend toward a zero dc condition. Channel codewords are written to tape with NRZI modulation. The decoding process is relatively easy to implement because DSV need not be computed. Specifications for a number of simple and group codes are listed in TBL. 3.
TBL. 3 Specification for a number of simple and group codes.
Code Applications
Despite different requirements, there is similarity of design between codes used in magnetic or optical recording.
Practical differences between magnetic and optical recording codes are usually limited to differences designed to optimize the code for the specific application. Some codes such as 3PM were developed for magnetic recording, but later applied to optical recording. Still, most practical applications use different codes for either magnetic or optical recording.
Optical recording requires a code with high density. Run lengths can be long in optical media because clock regeneration is easily accomplished. The clock content in the data signal provides synchronization of the data, as well as motor control. Because this clock must be regenerated from the readout signal ( For example, by detecting pit edges) the signal must have a sufficient number of transitions to support regeneration, and the maximum distance between transitions ideally must be as small as possible. In an optical disc, dirt and scratches on the disc surface change the envelope of the readout signal, creating low-frequency noise. This decreases the average level of the readout signal. If the signal falls below the detection level, it can cause an error in readout. This low-frequency noise can be attenuated with a highpass filter, but only if the information data itself contains no low-frequency components. A code without dc content thus improves immunity to surface contamination by allowing insertion of a filter. Compared to simple codes, RLL codes generally yield a larger bit-error rate because of error propagation; a small physical error can affect proportionally more bits. Still, RLL codes offer good performance in these areas and are suitable for optical disc recording. Ultimately, a detailed analysis is needed to determine the suitability of a code for a given application.
In many receiving circuits, a phase-locked loop (PLL) circuit is used to re-clock the channel code , for example, from a storage medium. The channel code acts as the input reference, the loop compares the phase difference between the reference and its own output, and drives an internal voltage-controlled oscillator to the reference frequency, decoupling jitter from the signal. The comparison occurs at every channel transition, and interim oscillator periods count the channel periods, thus recovering the code. A synchronization code is often inserted in the channel code to lock the PLL. In an RLL code, a pattern violating the run length can be used for synchronization; For example, in the CD, two 11T patterns precede an EFM frame; the player can lock to the channel data, and won’t misinterpret the synchronization patterns as data.
Following channel coding, the data is ready for storage or transmission. For example, in a hard-disk recorder, the data is applied to a recording circuit that generates the current necessary for saturation recording. The flux reversals recorded on the disk thus represent the bit transitions of the modulated data. The recorded patterns might appear highly distorted; this does not affect the integrity of the data, and permits higher recording densities. In optical systems such as the Compact Disc, the modulation code results in pits. Each pit edge represents a binary 1 channel bit, and spaces between represent binary 0s. In any event, storage to media, transmission, or other real-time digital audio processing, marks the end of the digital recording chain.